墙体非稳态传热计算方法适应性及地下结构传热特性分析与研究
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摘要
在建筑负荷、系统模拟和能耗分析时,为了获得准确的室内负荷和能牦,传导传递函数(CTF)系数的准确性是至关重要的。然而,当CTF方法计算CTF系数时,很有可能产生不准确甚至错误的结果。鉴于此,本文通过改变单层、三层和六层板壁中材料层的厚度、导热系数、密度以及比热的大小,详细分析了当前应用非常广泛的CTF系数计算方法——状态空间法、直接求根法和频域回归法的适应性和可靠性,并分析了它们产生误差的根源,以便人们在计算和使用CTF系数时,提高精度和避免误差。计算结果表明：当板壁为轻型和中型时,状态空间法和直接求根法保持了良好的精度和稳定性,其相对误差的绝对值都小于5%；当板壁越来越重型时,状态空间法和直接求根法的计算精度开始大幅度波动,其最大相对误差达到了：17.34%和16.83%(单层),38.7%和-17.49%(三层),81.61%和-72.50%(六层)。不管是单层还是多层板壁,也不管板壁特性参数怎么变化,频域回归法相对误差的绝对值都不超过0.6%。总之,频域回归法的计算精度和适应性是三种方法中最好的,而直接求根法的计算精度和适应性稍好于状态空间法。
随着建筑地上围护结构的隔热保温日益加强,由地下结构传热引起的建筑能耗就变成建筑总能耗中越来越重要的部分。因此,充分、透彻分析和研究地下结构与大地之间的热传递过程,并进一步研究其能耗状况及其计算方法,就成为一件刻不容缓的事情。以往的计算方法大多都采用了传统的数值方法,例如有限差分法、有限元法和有限体积法等,它们都是以单元或网格为基础的,编程实现和实际应用比较复杂和困难。为了克服传统数值方法的这些不足,本文引进一种摆脱了单元或网格的束缚,编程容易实现,而且前、后处理过程非常简单的数值方法——无单元伽辽金方法,来处理复杂的地下结构二维传热问题,并在其求解导热偏微分方程的基础上,分析和研究地下结构的传热特性和能耗状况,从而为工程和设计人员提供依据和参考。本文的具体研究工作及主要结论如下：
1.第3章引入了无单元伽辽金方法。首先介绍了形函数的构造方法——移动最小二乘法的基本原理；其次,介绍了权函数的选取原则,影响域的确定原则,第一类边界条件的处理方法,并且引进了形函数及其导数的快速算法；然后,从变分原理出发,得到了拉格朗日乘子法和罚函数法系统离散方程组：最后,介绍了程序实现步骤以及计算伽辽金弱形式积分的高斯-勒让德方法,在高级编程语言MATLAB工作平台上自主开发了无单元伽辽金方法程序。
2.第4章分析了权函数及其影响域的放大系数对无单元伽辽金方法计算精度和收敛率的影响。计算结果表明：无单元伽辽金方法具有非常高的计算精度和收敛率,四次样条权函数最适合处理导热问题。当罚参数取值合适时,罚函数法与拉格朗日乘子法具有相当的计算精度。罚函数法非稳态分析的CPU时间比拉格朗日乘子法少。当放大系数增大时,不管是哪一种权函数,无单元伽辽金方法CPU时间均有大幅度增加。
3.地下结构传热模型包括了墙壁、地板、屋顶、地基、基脚、砾砂层以及大地土壤层等,考虑了地下水位线和隔热保温对地下结构室内能耗的影响。
4.提出了基于基准节点间距的分区均匀布置节点方法产生无单元伽辽金方法的离散节点。
5.对地下水位线、远场边界、土壤导热系数、室外风速以及屋顶离地表面距离分别进行了灵敏度研究,分析了它们对稳态传热地下结构室内能耗的影响,分析了隔热保温层的厚度、长度以及布置位置对稳态传热地下结构室内能耗的影响。
6.提出了预先计算三个周期的初始条件确定方法,采用3个周期后准稳定分布温度场作为初始条件,计算结果表明这种方法是正确的、合理的。
7.地下结构非稳态传热的室内能耗对土壤导热系数的变化非常灵敏,因此,确定土壤导热系数需特别谨慎。
8.隔热保温使得地下结构非稳态传热的地板、墙壁和屋顶热流的振幅和均值的绝对值大幅度减小,时间延迟大幅度增加。
9.北京地区室外温度的年周期变化最为明显,其次是日周期变化；大地土壤层对室外温度波的衰减剧烈,特别是对周期较短振幅较小的温度波,地下结构越深,衰减程度越大。
Conduction transfer function (CTF) is widely used to calculate conduction heal transfer in building cooling/heating loads and energy calculations. The limitation of a methodology possibly results in imprecise or false CTF coefficients. There are three popular methods, state-space (SS) method, direct root-finding (DRF) method and frequency-domain regression (FDR) method to calculate CTF coefficients. The second chapter of this dissertation investigated the applicability of three methods as Fourier number and thermal structure factor were varied and in detail explained the sources that introduce error in the CTF solutions. The results show that the calculation error of SS and DRF methods becomes increasing as the reciprocal of the product of Fourier number and thermal structure factor becomes increasing. The maximal error reaches17.34%and16.83%(single-layered slab),38.7%and-17.49%(three-layered slab),81.61%and-72.50%(six-layered slab). However, the absolution value of the calculation error of FDR method always remains within0.6%no matter how Fourier number and thermal structure factor are varied. Thus, FDR method is more robust and reliable than SS and DRF methods. And it is more practical to calculate CTF coefficients and may be a better choice to calculate the cooling/heating loads for building structures for the architect/designer.
As above-ground components of the building thermal fabric become more energy efficient, the heat transfer between the building and the ground becomes relatively more important and can no longer be neglected. Thus, it is necessary to design and analyze adequately the ground-coupled heat transfer problems. Most of the former calculation methods are based on conventional numerical solutions such as finite difference, finite element or finite volume technique. These methods are based on the mesh or element. Therefore, it is very complex and difficult to apply and program. To overcome the problems, in this dissertation, the element-free Galerkin method (EFGM) was introduced in chapter3. In the EFGM, the construction of the approximation requires only nodal data—no element structure is needed. The numerical integration of the Galerkin weak form needs only simple integration cells—no element connectivity is needed. The EFGM requires no postprocessing for the output of field variables which are derivatives of the primary-dependent variables since these quantities are already very smooth.
In this dissertation, the EFGM was utilized to cope with the complex two-dimensional ground-coupled heat transfer problems. The energy status and heat transfer characteristics of underground structures were analyzed and investigated in detail. They can be used as a reference for the engineer and designer. The work and main conclusions of this dissertation are as follows:
1. In chpter3. firstly, the fundamental principles of the moving least square approximation, which was employed for the construction of the shape function in the EFGM. were introduced and derived in detail mathematically. Secondly, the selection principles of both weight function and domain of influence were discussed. The penalty function and Lagrange multiplier techniques were used to enforce the essential boundary conditions due to their simplicity. A fast algorithmic of the shape function and the derivative was introduced. Thirdly, the discretization of the governing equations by EFGM using both penalty function and Lagrange multiplier techniques was derived from the variational principle. Finally, Gauss-Legendre integration method was used to compute the integration of the Galerkin weak form. The process of the EFGM program was interpreted. Based on the MATLAB work desktop, the EFGM program for the ground-coupled heat transfer problems was developed.
2. The effects of weight functions and the scaling parameter on the accuracy and convergence rate of the EFGM were discussed in detail by comparison with the analytical solutions of several thermal examples. The results show that the EFGM has very high accuracy and convergence rate. The quartic spline weight function is the most appropriate for heat conduction problems. When an appropriate penalty parameter values, the penalty function method has almost given the same accuracy as the Lagrange multiplier method. In the unsteady analysis, the CPU time of the penalty function method is less than the Lagrange multiplier method. When the scaling parameter increases, no matter what kind of weight function, the CPU time has increased substantially.
3. The heat transfer model of underground structures involves the wall, floor, roof, foundation, footing, gravel sand and the soil layer. The influence of the water table line and thermal insulations on energy consumption of underground structures is taken into consideration.
4. Based on the definition of basic distance of nodes, zone uniform distributing node method is put forward for generating discrete nodes in the EFGM.
5. In the steady-state analysis, the sensitivity analyses of the water table, far field boundary, soil thermal conductivity, outdoor surface wind speed and distance of the roof from the ground surface were carried out. The relationship between energy consumption of underground structures and correlative parameters was investigated in detail. Furthermore, the relationship between energy consumption of underground structures and insulation thickness, length and layout of the location was investigated in detail.
6. In order to obtain initial conditions in the unsteady analysis, three cycles pre-calculation method was proposed. The third cycle quasi-steady distribution of temperature field was taken as initial conditions. The results show that this method is correct and reasonable.
7. In the unsteady analysis, parameter sensitivity investigations show that indoor energy consumption of underground structures is very sensitive to the soil thermal conductivity. Therefore, the soil thermal conductivity must be determined cautiously.
8. In the unsteady analysis, due to insulation, the absolute value of the amplitude and mean of the floor, wall and roof heat flux significantly decreased, and the time delay substantially longer.
9. The amplitude of1year period harmonic is highest and the second is1day period in Beijing. Sinusoidal temperatures are all attenuated by the soil layer, especially for the shorter period and smaller amplitude waves. The deeper underground structure locates, the bigger the level of the attenuation is.
随着建筑地上围护结构的隔热保温日益加强,由地下结构传热引起的建筑能耗就变成建筑总能耗中越来越重要的部分。因此,充分、透彻分析和研究地下结构与大地之间的热传递过程,并进一步研究其能耗状况及其计算方法,就成为一件刻不容缓的事情。以往的计算方法大多都采用了传统的数值方法,例如有限差分法、有限元法和有限体积法等,它们都是以单元或网格为基础的,编程实现和实际应用比较复杂和困难。为了克服传统数值方法的这些不足,本文引进一种摆脱了单元或网格的束缚,编程容易实现,而且前、后处理过程非常简单的数值方法——无单元伽辽金方法,来处理复杂的地下结构二维传热问题,并在其求解导热偏微分方程的基础上,分析和研究地下结构的传热特性和能耗状况,从而为工程和设计人员提供依据和参考。本文的具体研究工作及主要结论如下：
1.第3章引入了无单元伽辽金方法。首先介绍了形函数的构造方法——移动最小二乘法的基本原理；其次,介绍了权函数的选取原则,影响域的确定原则,第一类边界条件的处理方法,并且引进了形函数及其导数的快速算法；然后,从变分原理出发,得到了拉格朗日乘子法和罚函数法系统离散方程组：最后,介绍了程序实现步骤以及计算伽辽金弱形式积分的高斯-勒让德方法,在高级编程语言MATLAB工作平台上自主开发了无单元伽辽金方法程序。
2.第4章分析了权函数及其影响域的放大系数对无单元伽辽金方法计算精度和收敛率的影响。计算结果表明：无单元伽辽金方法具有非常高的计算精度和收敛率,四次样条权函数最适合处理导热问题。当罚参数取值合适时,罚函数法与拉格朗日乘子法具有相当的计算精度。罚函数法非稳态分析的CPU时间比拉格朗日乘子法少。当放大系数增大时,不管是哪一种权函数,无单元伽辽金方法CPU时间均有大幅度增加。
3.地下结构传热模型包括了墙壁、地板、屋顶、地基、基脚、砾砂层以及大地土壤层等,考虑了地下水位线和隔热保温对地下结构室内能耗的影响。
4.提出了基于基准节点间距的分区均匀布置节点方法产生无单元伽辽金方法的离散节点。
5.对地下水位线、远场边界、土壤导热系数、室外风速以及屋顶离地表面距离分别进行了灵敏度研究,分析了它们对稳态传热地下结构室内能耗的影响,分析了隔热保温层的厚度、长度以及布置位置对稳态传热地下结构室内能耗的影响。
6.提出了预先计算三个周期的初始条件确定方法,采用3个周期后准稳定分布温度场作为初始条件,计算结果表明这种方法是正确的、合理的。
7.地下结构非稳态传热的室内能耗对土壤导热系数的变化非常灵敏,因此,确定土壤导热系数需特别谨慎。
8.隔热保温使得地下结构非稳态传热的地板、墙壁和屋顶热流的振幅和均值的绝对值大幅度减小,时间延迟大幅度增加。
9.北京地区室外温度的年周期变化最为明显,其次是日周期变化；大地土壤层对室外温度波的衰减剧烈,特别是对周期较短振幅较小的温度波,地下结构越深,衰减程度越大。
Conduction transfer function (CTF) is widely used to calculate conduction heal transfer in building cooling/heating loads and energy calculations. The limitation of a methodology possibly results in imprecise or false CTF coefficients. There are three popular methods, state-space (SS) method, direct root-finding (DRF) method and frequency-domain regression (FDR) method to calculate CTF coefficients. The second chapter of this dissertation investigated the applicability of three methods as Fourier number and thermal structure factor were varied and in detail explained the sources that introduce error in the CTF solutions. The results show that the calculation error of SS and DRF methods becomes increasing as the reciprocal of the product of Fourier number and thermal structure factor becomes increasing. The maximal error reaches17.34%and16.83%(single-layered slab),38.7%and-17.49%(three-layered slab),81.61%and-72.50%(six-layered slab). However, the absolution value of the calculation error of FDR method always remains within0.6%no matter how Fourier number and thermal structure factor are varied. Thus, FDR method is more robust and reliable than SS and DRF methods. And it is more practical to calculate CTF coefficients and may be a better choice to calculate the cooling/heating loads for building structures for the architect/designer.
As above-ground components of the building thermal fabric become more energy efficient, the heat transfer between the building and the ground becomes relatively more important and can no longer be neglected. Thus, it is necessary to design and analyze adequately the ground-coupled heat transfer problems. Most of the former calculation methods are based on conventional numerical solutions such as finite difference, finite element or finite volume technique. These methods are based on the mesh or element. Therefore, it is very complex and difficult to apply and program. To overcome the problems, in this dissertation, the element-free Galerkin method (EFGM) was introduced in chapter3. In the EFGM, the construction of the approximation requires only nodal data—no element structure is needed. The numerical integration of the Galerkin weak form needs only simple integration cells—no element connectivity is needed. The EFGM requires no postprocessing for the output of field variables which are derivatives of the primary-dependent variables since these quantities are already very smooth.
In this dissertation, the EFGM was utilized to cope with the complex two-dimensional ground-coupled heat transfer problems. The energy status and heat transfer characteristics of underground structures were analyzed and investigated in detail. They can be used as a reference for the engineer and designer. The work and main conclusions of this dissertation are as follows:
1. In chpter3. firstly, the fundamental principles of the moving least square approximation, which was employed for the construction of the shape function in the EFGM. were introduced and derived in detail mathematically. Secondly, the selection principles of both weight function and domain of influence were discussed. The penalty function and Lagrange multiplier techniques were used to enforce the essential boundary conditions due to their simplicity. A fast algorithmic of the shape function and the derivative was introduced. Thirdly, the discretization of the governing equations by EFGM using both penalty function and Lagrange multiplier techniques was derived from the variational principle. Finally, Gauss-Legendre integration method was used to compute the integration of the Galerkin weak form. The process of the EFGM program was interpreted. Based on the MATLAB work desktop, the EFGM program for the ground-coupled heat transfer problems was developed.
2. The effects of weight functions and the scaling parameter on the accuracy and convergence rate of the EFGM were discussed in detail by comparison with the analytical solutions of several thermal examples. The results show that the EFGM has very high accuracy and convergence rate. The quartic spline weight function is the most appropriate for heat conduction problems. When an appropriate penalty parameter values, the penalty function method has almost given the same accuracy as the Lagrange multiplier method. In the unsteady analysis, the CPU time of the penalty function method is less than the Lagrange multiplier method. When the scaling parameter increases, no matter what kind of weight function, the CPU time has increased substantially.
3. The heat transfer model of underground structures involves the wall, floor, roof, foundation, footing, gravel sand and the soil layer. The influence of the water table line and thermal insulations on energy consumption of underground structures is taken into consideration.
4. Based on the definition of basic distance of nodes, zone uniform distributing node method is put forward for generating discrete nodes in the EFGM.
5. In the steady-state analysis, the sensitivity analyses of the water table, far field boundary, soil thermal conductivity, outdoor surface wind speed and distance of the roof from the ground surface were carried out. The relationship between energy consumption of underground structures and correlative parameters was investigated in detail. Furthermore, the relationship between energy consumption of underground structures and insulation thickness, length and layout of the location was investigated in detail.
6. In order to obtain initial conditions in the unsteady analysis, three cycles pre-calculation method was proposed. The third cycle quasi-steady distribution of temperature field was taken as initial conditions. The results show that this method is correct and reasonable.
7. In the unsteady analysis, parameter sensitivity investigations show that indoor energy consumption of underground structures is very sensitive to the soil thermal conductivity. Therefore, the soil thermal conductivity must be determined cautiously.
8. In the unsteady analysis, due to insulation, the absolute value of the amplitude and mean of the floor, wall and roof heat flux significantly decreased, and the time delay substantially longer.
9. The amplitude of1year period harmonic is highest and the second is1day period in Beijing. Sinusoidal temperatures are all attenuated by the soil layer, especially for the shorter period and smaller amplitude waves. The deeper underground structure locates, the bigger the level of the attenuation is.
引文
[1]刘伟.建筑节能新标准新要求与节能达标规划设计、施工新技术实用手册.第一版.北京：中国建筑科技出版社,2007,1-100
[2]陈友明.王盛卫.建筑围护结构非稳定传热分析新方法.第一版.北京：科学出版社,2004,69-317
[3]Claridge D E. Design methods for earth-contact heat transfer. In:Advances in solar energy (ed. Boer K). Boulder, Colorado:American Solar Energy Society, 1987.305-350
[4]Shipp P H. Basement, Crawlspace and Slab-on-Grade Thermal Performance. In: Proceeding of the ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of Buildings Ⅱ. Las Vegas, Nevada:1982,160-179
[5]Claesson J, Hagentoft C. Heat loss to the ground from a building—Ⅰ. General theory. Building and Environment,1991,26(2):195-208
[6]Bahnfleth W P, Pedersen C O. A Three-Dimensional Numerical Study of Slab-on-Grade Heat Transfer. ASHRAE Transactions,1990,96(2):61-72
[7]Rees S J, Spitler J D, Davies M G, et al. Qualitative comparison of North American and U.K. cooling load calculation methods. HVAC and R Research, 2000.6(1):75-99
[8]Romine T B. Cooling load calculation. Art or science. ASHRAE Journal,1992, 34(1):14-24
[9]彦启森,赵庆珠.建筑热过程.第一版.北京：中国建筑工业出版社,1986,1-180
[10]James J. Cooling Load Analysis of A Bank. ASHVE Transactions,1937,43(1): 327-344
[11]Kratz A P, Konzo S. Study of Summer Cooling in the Research Residence at the University of Illinois. ASHVE Transactions,1933,39(1):95-118
[12]Houghten F C, Blackshaw J C, Pugh E M, et al. Heat Transmission as Influenced by Heat Capacity and Solar Radiation. ASHVE Transactions,1932, 38(1):232-284
[13]Gilkey H T, Bahnfleth D R, Roose R W. Cooling a Small Residence House with a Two-Horse Power Mechanical Condensing Unit. ASHVE Transactions,1953, 59(1):283-304
[14]Mackey C O, Wright L T. Periodic Heat Flow-Homogeneous Walls or Roofs. ASHVE Transactions,1944,50(1):293-312
[15]Mackey C O, Wright L T. Periodic Heat Flow-Composite Walls or Roofs. ASHVE Transactions,1946,52(1):283-296
[16]Stewart J P. Solar Heat Gains Through Walls and Roofs for Cooling Load Calculations. ASHVE Transactions,1948,54(1):361-388
[17]ASHRAE. Handbook of Fundamentals.1967, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[18]Carrier Air Conditioning Company. Handbook of Air-Conditioning System Design.1st ed. New York:McGraw-Hill,1965,1-40
[19]Brisken W R, Reque S G. Heat Load Calculations by Thermal Response. ASHVE Transactions,1956,62(1):391-424
[20]Mitalas G P, Stephenson D G. Room Thermal Response Factors. ASHRAE Transactions,1967,73(1):Ⅲ.2.1-Ⅲ.2.10
[21]Stephenson D G, Mitalas G P. Calculation of heat conduction transfer functions for multi-layer slabs. ASHRAE Transactions,1971,77(2):117-126
[22]ASHRAE. Handbook of Fundamentals.1972, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[23]Rudoy W, Duran F. Development of an Improved Cooling Load Calculation Method. ASHRAE Transactions,1975,81(2):19-69
[24]Sowell E F. Load Calculations for 200,640 Zones. ASHRAE Transactions,1988, 94(2):716-736
[25]Spitler J D, Mcquiston F C, Lindsey K L. The CLTD/SCL/CLF Cooling Load Calculation Method. ASHRAE Transactions,1993,99(1):183-192
[26]Pedersen C O, Fisher D E, Liesen R J. Development of a Heat Balance Procedure for Calculating Cooling Loads. ASHRAE Transactions,1997,103(2): 459-468
[27]Spitler J D, Fisher D E, Pedersen C O. The Radiant Time Series Cooling Load Calculation Procedure. ASHRAE Transactions,1997,103(2):503-515
[28]Spitler J D, Fisher D E. Development of Periodic Response Factors for Use with the Radiant Time Series Method. ASHRAE Transactions,1999,105(2): 491-509
[29]ASHRAE. Handbook of Fundamentals.2001, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[30]ASHRAE. Handbook of Fundamentals.2005, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[31]ASHRAE. Handbook of Fundamentals.2009, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[32]Chantrasrisalai C. Fisher D E, Iu I, et al. Experimental Validation of Design Cooling Load Procedures:the Heat Balance Method. ASHRAE Transactions, 2003.109(2):160-173
[33]Iu I S, Chantrasrisalai C, Eldridge D S. et al. Experimental Validation of Design Cooling Load Procedures:the Radiant Time Series Method. ASHRAE Transactions.2003.109(2):139-150
[34]Burch D M, Seem J E, Walton G N, et al. Dynamic Evaluation of Thermal Bridges in a Typical Office Building. ASHRAE Transactions,1992,98(1): 291-301
[35]Hittle D C. A Comparison of Building Energy Use Calculation with Actual and Synthesized Weather Data. ASHRAE Transactions.1979,85(2):167-189
[36]CIBSE. CIBSE GUIDE A3:Thermal properties of building structures.1st ed. London:The Chartered Institution of Building Services Engineers,1986,1-101
[37]Hittle D C, Pedersen C O. Calculating Building Heating Loads Using the Frequency Response of Multi-layered slabs. ASHRAE Transactions,1981, 87(2):545-568
[38]丁国良,张春路.空调动态负荷计算的新型谐波法.上海交通大学学报,1996,30(8)：100-103
[39]Davies M G. Current Methods to Handle Wall Conduction and Room Internal Heat Transfer. ASHRAE Transactions,1999,105(2):142-150
[40]Stephenson D G, Mitalas G P. Cooling Load Calculations by Thermal Response Factor Method. ASHRAE Transactions,1967,73(1):Ⅲ.1.1-Ⅲ.1.7
[41]Mitalas G P. Calculation of Transient Heat Flow through Walls and Roofs. ASHRAE Transactions,1968,74(2):182-188
[42]Kusuda T. Thermal Response Factors for Multi-Layer Structures of Various Heat Conduction Systems. ASHRAE Transactions,1969,75(1):246-271
[43]Spitler J D, Fisher D E. On the Relationship Between the Radiant Time Series and Transfer Function Methods for Design Cooling Load Calculations. HVAC&R Research,1999,5(2):123-136
[44]Mitalas G P, Arseneault J G. Fortran IV program to calculate z-transfer functions for the calculation of transient heat transfer through walls and roofs. In:Use of Computers for Environmental Engineering Related to Buildings. Gaithersburg, MD:NBS Building Science Series,1971
[45]ASHRAE. Handbook of Fundamentals.1977, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[46]ASHRAE. Handbook of Fundamentals.1981, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[47]ASHRAE. Handbook of Fundamentals.1985, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[48]Peavy B A. A Note on Response Factors and Conduction Transfer Functions. ASHRAE Transactions,1978,84(1):688-690
[49]Hittle D C. Calculating Building Heating And Cooling Loads Using the Frequency Response of Multilayered Slabs:[University of Illinois PH.D. Thesis]. Urbana Champaign:University of Illinois,1981,221
[50]Stephenson D G. Ouyang K. Frequency domain analysis of the accuracy of Z-transfer function for walls. In:CIB 5th International Symposium. Bath, England:1986
[51]Harris S M, McQuiston F C. A Study to Categorize Walls and Roofs on the Basis of Thermal Response. ASHRAE Transactions,1988,94(2):688-714
[52]ASHRAE. Handbook of Fundamentals.1989, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[53]ASHRAE. Handbook of Fundamentals.1993, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[54]ASHRAE. Handbook of Fundamentals.1997, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[55]Ouyang K, Haghighat F. A procedure for calculating thermal response factors of multi-layer walls—State space method. Building and Environment,1991,26(2): 173-177
[56]李灏,张春路,丁国良.计算墙体反应系数的模型降价方法.上海交通大学学报,1998,32(7)：14-17
[57]丁国良,张春路,王险峰等.状态空间法计算墙体Z传递函数.暖通空调,1997,27(02)：15-17
[58]Davies M G. Solutions to Fourier's equation and unsteady heat flow through structures. Building and Environment,1995,30(3):309-321
[59]Davies M G.A Time-Domain Estimation of Wall Conduction Transfer Function Coefficients. ASHRAE Transactions,1996,102(1):328-343
[60]Davies M G. Wall transient heat flow using time-domain analysis. Building and Environment,1997,32(5):427-446
[61]陈友明,王盛卫.计算多层墙体响应系数的频域回归方法.湖南大学学报：自然科学版,2000,27(5)：71-77
[62]左政,陈友明.用频域回归方法计算圆柱形墙体的瞬时热流.湖南大学学报：自然科学版,2001(S1)：1-8
[63]Wang S, Chen Y. A novel and simple building load calculation model for building and system dynamic simulation. Applied Thermal Engineering.2001. 21(6):683-702
[64]Chen Y, Wang S. Frequency-domain regression method for estimating CTF models of building multilayer constructions. Applied Mathematical Modelling. 2001,25(7):579-592
[65]Macey H H. Heat loss through a solid floor. Journal of Institution of Fuel.1949. 22:369-371
[66]Latta J K, Boileau G G. Heat losses from house basements. Canadian Builders, 1969,19(10):39-42
[67]Delsante A E, Stokes A N, Walsh P J. Application of Fourier transforms to periodic heat flow into the ground under a building. International Journal of Heat and Mass Transfer,1983,26(1):121-132
[68]Delsante A E. Theoretical calculations of the steady-state heat losses through a slab-on-ground floor. Building and Environment,1988,23(1):11-17
[69]Hagentoft C. Steady-state heat loss for an edge-insulated slab:Part Ⅰ. Building and Environment,2002,37(1):19-25
[70]Hagentoft C. Periodic heat loss for an edge insulated slab:Part Ⅱ:A mixed boundary value problem. Building and Environment,2002,37(1):27-34
[71]Hagentoft C, Claesson J. Heat loss to the ground from a building—Ⅱ. Slab on the ground. Building and Environment,1991,26(4):395-403
[72]Hagentoft C. Heat losses and temperature in the ground under a building with and without ground water flow—Ⅱ. Finite ground water flow rate. Building and Environment,1996,31(1):13-19
[73]Hagentoft C. Heat losses and temperature in the ground under a building with and without ground water flow—Ⅰ. Infinite ground water flow rate. Building and Environment,1996,31 (1):3-11
[74]曹宝山.触地围护结构传热问题的分析研究.天津城建学院学报,1994(4)：7-24
[75]谈莹莹,闫晓娜.地下区域动态传热研究.科技创新导报,2008(32)：201-205
[76]谈莹莹.建筑墙体简化传热模型及触地结构传热计算方法研究：[湖南大学 硕士学位论文].长沙：湖南大学,2006
[77]Kusuda T, Bean J W. Simplified Methods for Determining Seasonal Heat Loss from Uninsulated Slab-on-Grade Floors. ASHRAE Transactions.1984,90(1B): 611-631
[78]Shen L S, Ramsey J W. An investigation of transient. two-dimensional coupled heat and moisture flow in the soil surrounding a basement wall. International Journal of Heat and Mass Transfer.1988.31(7):1517-1527
[79]Shen L S, Ramsey J W. A Simplified Thermal Analysis of Earth-Sheltered Buildings Using a Fourier-Series Boundary Method. ASHRAE Transactions. 1983,89(1B):438-448
[80]Krarti M, Claridge D E, Kreider J F. ITPE technique applications to time-varying two-dimensional ground-coupling problems. International Journal of Heat and Mass Transfer,1988,31(9):1899-1911
[81]Krarti M, Claridge D E, Kreider J F. The ITPE technique applied to steady-state ground-coupling problems. International Journal of Heat and Mass Transfer, 1988,31(9):1885-1898
[82]Krarti M, Choi S. Optimum insulation for rectangular basements. Energy and Buildings,1995,22(2):125-131
[83]Choi S, Krarti M. Thermally optimal insulation distribution for underground structures. Energy and Buildings,2000,32(3):251-265
[84]Chuangchid P, Krarti M. Foundation heat loss from heated concrete slab-on-grade floors. Building and Environment,2001,36(5):637-655
[85]程宝义,袁艳平,茅靳丰等.建筑材料热特性对地下工程围护结构热行为的影响.暖通空调,2004,34(12)：15-18
[86]Kusuda T, Achenbach P R. Numerical Analyses of the Thermal Environment of Occupied Underground Spaces with Finite Cover Using a Digital computer. ASHRAE Transactions,1963,69:439-451
[87]Davies G R. Thermal analysis of earth covered buildings. In:Proceedings of 4th National Passive Solar Conference. Kansas City:1979,744-748
[88]Ambrose C W. Modelling losses from slab floors. Building and Environment, 1981,16(4):251-258
[89]Xie X N, Jiang Y, Xia J J. A new approach to compute heat transfer of ground-coupled envelope in building thermal simulation software. Energy and Buildings,2008,40(4):476-485
[90]谢晓娜.建筑模拟软件中楼地动态传热问题的处理.见：2005年全国暖通空 调专业委员会空调模拟分析学组学术交流会.北京：2005
[91]谢晓娜,江亿DeST的热物理模型中地下部分传热研究.见：全国暖通空调制冷2004年学术年会.兰州：2004
[92]谢晓娜.建筑能耗模拟用楼地和热桥传热计算方法研究：[清华大学学位论文].北京：清华大学,2006
[93]谢晓娜,宋芳婷,张晓亮等.建筑环境设计模拟分析软件DeST第11讲与地面相邻区域动态传热问题的处理.暖通空调,2005,35(6)：55-63
[94]燕达.谢晓娜,宋芳婷等.建筑环境设计模拟分析软件DeST第一讲建筑模拟技术与DeST发展简介.暖通空调,2004,34(7)：48-56
[95]Szydlowski R F, Kuehn T H. Analysis of Transient Heat Loss in Earth-sheltered structures. Underground Space,1981,5(4):237-246
[96]Saxhof B, Poulsen K E. Foundations for Energy Conservation Houses:A Thermal Analysis based on Examples from Five Low-energy Houses at Hjorteker. Low-Energy House Project, Report No 130,1982.
[97]Rock B A. Sensitivity Study of Slab-on-Grade Transient Heat Transfer Model Parameters. ASHRAE Transactions,2004,110(1):177-184
[98]Wang F S. Mathematical modelling and computer simulation of insulation systems in below grade applications. In:Proceedings of the ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of Buildings Ⅰ. Orlando, Florida:ASHRAE,1979,456-471
[99]Mitalas G P. Calculation of Below-Grade Residential Heat Loss:Low-rise residential building. ASHRAE Transactions,1987,93(1):743-783
[100]Mitalas G P. Calculation of Basement Heat Loss. ASHRAE Transactions,1983, 89(1B):420-437
[101]Bligh T P, Willard T E. Modeling the thermal performance of earth-contact buildings, including the effect of phase change due to soil freezing. Computers & Structures,1985,21(1-2):291-318
[102]Deru M P. Ground-coupled heat and moisture transfer from buildings: [Colorado State University Ph.D. Thesis]. Fort Collins, Colorado, US:Colorado State University,2001
[103]Deru M, Judkoff R, Neymark J. Whole Building Energy Simulation with a Three-Dimensional Ground-Coupled Heat Transfer Model. ASHRAE Transactions,2003,109(1):557-565
[104]Mihalakakou G, Santamouris M, Asimakopoulos D, et al. On the ground temperature below buildings. Solar Energy,1995,55(5):355-362
[105]Adjali M H, Davies M, Littler J. Three-dimensional earth-contact heat flows:A comparison of simulated and measured data for a buried structure. Renewable Energy,1998,15(1-4):356-359
[106]Zoras S, Davies M, Wrobel L C. Earth-contact heat transfer:improvement and application of a novel simulation technique. Energy and Buildings,2002,34(4): 333-344
[107]Zoras S, Davies M, Adjali M H. A novel tool for the prediction of earth-contact heat transfer:a multi-room simulation. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2001,215(4):415-422
[108]Zoras S. A Novel Tool for the Prediction of Building Earth-contact Heat Transfer:[Brunei University Ph.D. Thesis]. UK:Brunel University,2001
[109]刘军,姚杨,王清勤.地下建筑围护结构传热的模拟与分析.见：全国暖通空调制冷2004年学术年会.兰州：2004
[110]Falconer D R, Sowell E F. Electronic tables for the ASHRAE load calculation manual. ASHRAE Transactions,1993,99(1):193-200
[111]Seem J E, Klein S A, Beckman W A, et al. Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer. Journal of Heat Transfer,1989,111(1):5-12
[112]McQuiston F C, Parker J D, Spitler J D. Heating, ventilating, and air-conditioning analysis and design.4th Ed. New York:John Wiley & Sons, Inc.,2000,1-30
[113]Incropera F P, DeWitt D P. Introduction to Heat Transfer.3rd ed. New York: Wiley,1996,1-47
[114]章熙民,任泽霈,梅飞鸣.传热学.第三版.北京：中国建筑工业出版社,1993,3-18
[115]Ceylan H T, Myers G E. Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs. ASME Journal of Heat Transfer,1980,102(1): 115-120
[116]Jiang Y. State-Space Method for the Calculation of Air-Conditioning Loads and the Simulation of Thermal Behavior of the Room. ASHRAE Transactions,1982. 88(2):122-138
[117]Seem J E. Modeling of Heat Transfer in Buildings:[The University of Wisconsin Madison Ph.D. Thesis]. Madison, Wisconsin, US:The University of Wisconsin Madison,1987
[118]陈友明,周娟,王盛卫.基于系统辨识的多层墙体z-传递函数计算方法.湖南大学学报：自然科学版.2004.31(5)：82-87
[119]Wang S. Chen Y. A simple procedure for calculating thermal response factors and conduction transfer functions of multilayer walls. Applied Thermal Engineering.2002.22(3):333-338
[120]Chen Y. Wang S. A new procedure for calculating periodic response factors based on frequency domain regression method. International Journal of Thermal Sciences.2005,44(4):382-392
[121]朱林.暖通与空调常用数据手册.第二版.北京：中国建筑工业出版社2002,1-100
[122]Myers G E. Analytical Methods in Conduction Heat Transfer.1 st ed. New York: McGraw-Hill.1971,1-38
[123]Hittle D C, Bishop R. An improved root-finding procedure for use in calculating transient heat flow through multilayered slabs. International Journal of Heat and Mass Transfer,1983,26(1):1685-1693
[124]郭萍.马继涌.大范围收敛迭代法在计算墙体传递函数极点中的应用.哈尔滨建筑大学学报,1999,32(5)：109-110
[125]Mitalas G P. Comments on the Z-Transfer Function Method for Calculating Heat Transfer in Buildings. ASHRAE Transactions,1978,84(1):667-674
[126]Wang S. Chen Y. Transient heat flow calculation for multilayer constructions using a frequency-domain regression method. Building and Environment,2003, 38(1):45-61
[127]Chen Y, Zhou J, Spitler J D. Verification for transient heat conduction calculation of multilayer building constructions. Energy and Buildings,2006, 38(4):340-348
[128]Spitler J D, Rees S J, Xiao D. Development of an analytical verification test suite for whole building energy simulation programs-building fabric. RP-1052, 2001.
[129]Kossecka E. Relationships Between Structure Factors, Response Factors, and Z-Transfer Function Coefficients for Multilayer Walls. ASHRAE Transactions, 1998,104(1A):68-77
[130]Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering,1994,37(2):229-256
[131]Nayroles B, Touzot G, Villon P. Generalizing the finite element method:diffuse approximation and diffuse elements. Computational Mechanics,1992,10(5): 307-318
[132]Belytschko T. Gu L, Lu Y Y. Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering.1994,2(3A):519-534
[133]Belytschko T. Lu Y Y. Gu L. et al. Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures,1995. 32(17-18):2547-2570
[134]Krysl P. Belytschko T. Analysis of thin plates by the element-free Galerkin method. Computational Mechanics.1995,17(1-2):26-35
[135]Krysl P. Belytschko T. Analysis of thin shells by the Element-Free Galerkin method. International Journal of Solids and Structures,1996,33(20-22): 3057-3080
[136]Cingoski V, Miyamoto N, Yamashita H. Element-free Galerkin method for electromagnetic field computations. IEEE Transactions on Magnetics,1998, 34(5):3236-3239
[137]Li G, Belytschko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations,2001,18(1-2):62-78
[138]Singh I V. Sandeep K, Prakash R. Heat transfer analysis of two-dimensional fins using meshless element free Galerkin method. Numerical Heat Transfer Part A-Applications,2003,44(1):73-84
[139]Singh I V, Sandeep K, Prakash R. The element free Galerkin method in three dimensional steady state heat conduction. International Journal of Computational Engineering Science,2002,3(3):291-303
[140]Singh I V, Sandeep K, Prakash R. Application of meshless element free Galerkin method in two-dimensional heat conduction problems. Computer Assisted Mechanics and Engineering Sciences,2004,11(4):265-274
[141]Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation,1981,37(155):141-158
[142]Belytschko T, Krongauz Y, Fleming M, et al. Smoothing and accelerated computations in the element free Galerkin method. Journal of Computational and Applied Mathematics,1996,74(1-2):111-126
[143]Belytschko T, Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method. Computers & Structures,1999,71(2):173-195
[144]Dolbow J, Belytschko T. An introduction to programming the meshless Element Free Galerkin method. Archives of Computational Methods in Engineering, 1998,5(3):207-241
[145]李庆扬,王能超,易大义.数值分析.第三版.武汉：华中科技大学出版社.1986,180-181
[146]Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method. Computational Mechanics,1995,17(3):186-195
[147]Singh I V. A numerical solution of composite heat transfer problems using meshless method. International Journal of Heat and Mass Transfer.2004. 47(10-11):2123-2138
[148]Shu H M, Huang Z Q, Li C W. Study of a new weight function in the meshless method and its application (in Chinese). Journal of Hefei University of Technology (Natural Science),2007,30(11):1489-1493
[149]Krysl P, Belytschko T. ESFLIB:A library to compute the element free Galerkin shape functions. Computer Methods in Applied Mechanics and Engineering, 2001,190(15-17):2181-2205
[150]Rao B N, Rahman S. An efficient meshless method for fracture analysis of cracks. Computational Mechanics,2000,26(4):398-408
[151]Zhu T, Atluri S N. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics,1998,21(3):211-222
[152]Lu Y Y, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1994,113(3-4):397-414
[153]Fernandez-Mendez S, Huerta A. Imposing essential boundary conditions in mesh-free methods. Computer Methods in Applied Mechanics and Engineering, 2004,193(12-14):1257-1275
[154]Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering,1996,131(1-2):133-145
[155]Gunther F C, Liu W K. Implementation of boundary conditions for meshless methods. Computer Methods in Applied Mechanics and Engineering,1998, 163(1-4):205-230
[156]Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering,1997,40(16): 2953-2974
[157]Ozisik M N.热传导.俞昌铭.第一版.北京：高等教育出版社,1983, 398-533
[158]Moaveni S.有限元分析—ANSYS理论与应用.工崧.第二版.北京：电子工业出版社,2005,189-191
[159]建筑工程常用数据系列手册编写组.暖通空调常用数据手册.第二版.北京：中国建筑工业出版社,2001,1-7
[160]Weitzmann P, Kragh J, Roots P. et al. Modelling floor heating systems using a validated two-dimensional ground-coupled numerical model. Building and Environment,2005,40(2):153-163
[161]McAdams W H. Heat Transmission.3nd Ed. New York:McGraw-Hill.1954. 1-500
[2]陈友明.王盛卫.建筑围护结构非稳定传热分析新方法.第一版.北京：科学出版社,2004,69-317
[3]Claridge D E. Design methods for earth-contact heat transfer. In:Advances in solar energy (ed. Boer K). Boulder, Colorado:American Solar Energy Society, 1987.305-350
[4]Shipp P H. Basement, Crawlspace and Slab-on-Grade Thermal Performance. In: Proceeding of the ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of Buildings Ⅱ. Las Vegas, Nevada:1982,160-179
[5]Claesson J, Hagentoft C. Heat loss to the ground from a building—Ⅰ. General theory. Building and Environment,1991,26(2):195-208
[6]Bahnfleth W P, Pedersen C O. A Three-Dimensional Numerical Study of Slab-on-Grade Heat Transfer. ASHRAE Transactions,1990,96(2):61-72
[7]Rees S J, Spitler J D, Davies M G, et al. Qualitative comparison of North American and U.K. cooling load calculation methods. HVAC and R Research, 2000.6(1):75-99
[8]Romine T B. Cooling load calculation. Art or science. ASHRAE Journal,1992, 34(1):14-24
[9]彦启森,赵庆珠.建筑热过程.第一版.北京：中国建筑工业出版社,1986,1-180
[10]James J. Cooling Load Analysis of A Bank. ASHVE Transactions,1937,43(1): 327-344
[11]Kratz A P, Konzo S. Study of Summer Cooling in the Research Residence at the University of Illinois. ASHVE Transactions,1933,39(1):95-118
[12]Houghten F C, Blackshaw J C, Pugh E M, et al. Heat Transmission as Influenced by Heat Capacity and Solar Radiation. ASHVE Transactions,1932, 38(1):232-284
[13]Gilkey H T, Bahnfleth D R, Roose R W. Cooling a Small Residence House with a Two-Horse Power Mechanical Condensing Unit. ASHVE Transactions,1953, 59(1):283-304
[14]Mackey C O, Wright L T. Periodic Heat Flow-Homogeneous Walls or Roofs. ASHVE Transactions,1944,50(1):293-312
[15]Mackey C O, Wright L T. Periodic Heat Flow-Composite Walls or Roofs. ASHVE Transactions,1946,52(1):283-296
[16]Stewart J P. Solar Heat Gains Through Walls and Roofs for Cooling Load Calculations. ASHVE Transactions,1948,54(1):361-388
[17]ASHRAE. Handbook of Fundamentals.1967, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[18]Carrier Air Conditioning Company. Handbook of Air-Conditioning System Design.1st ed. New York:McGraw-Hill,1965,1-40
[19]Brisken W R, Reque S G. Heat Load Calculations by Thermal Response. ASHVE Transactions,1956,62(1):391-424
[20]Mitalas G P, Stephenson D G. Room Thermal Response Factors. ASHRAE Transactions,1967,73(1):Ⅲ.2.1-Ⅲ.2.10
[21]Stephenson D G, Mitalas G P. Calculation of heat conduction transfer functions for multi-layer slabs. ASHRAE Transactions,1971,77(2):117-126
[22]ASHRAE. Handbook of Fundamentals.1972, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[23]Rudoy W, Duran F. Development of an Improved Cooling Load Calculation Method. ASHRAE Transactions,1975,81(2):19-69
[24]Sowell E F. Load Calculations for 200,640 Zones. ASHRAE Transactions,1988, 94(2):716-736
[25]Spitler J D, Mcquiston F C, Lindsey K L. The CLTD/SCL/CLF Cooling Load Calculation Method. ASHRAE Transactions,1993,99(1):183-192
[26]Pedersen C O, Fisher D E, Liesen R J. Development of a Heat Balance Procedure for Calculating Cooling Loads. ASHRAE Transactions,1997,103(2): 459-468
[27]Spitler J D, Fisher D E, Pedersen C O. The Radiant Time Series Cooling Load Calculation Procedure. ASHRAE Transactions,1997,103(2):503-515
[28]Spitler J D, Fisher D E. Development of Periodic Response Factors for Use with the Radiant Time Series Method. ASHRAE Transactions,1999,105(2): 491-509
[29]ASHRAE. Handbook of Fundamentals.2001, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[30]ASHRAE. Handbook of Fundamentals.2005, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[31]ASHRAE. Handbook of Fundamentals.2009, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[32]Chantrasrisalai C. Fisher D E, Iu I, et al. Experimental Validation of Design Cooling Load Procedures:the Heat Balance Method. ASHRAE Transactions, 2003.109(2):160-173
[33]Iu I S, Chantrasrisalai C, Eldridge D S. et al. Experimental Validation of Design Cooling Load Procedures:the Radiant Time Series Method. ASHRAE Transactions.2003.109(2):139-150
[34]Burch D M, Seem J E, Walton G N, et al. Dynamic Evaluation of Thermal Bridges in a Typical Office Building. ASHRAE Transactions,1992,98(1): 291-301
[35]Hittle D C. A Comparison of Building Energy Use Calculation with Actual and Synthesized Weather Data. ASHRAE Transactions.1979,85(2):167-189
[36]CIBSE. CIBSE GUIDE A3:Thermal properties of building structures.1st ed. London:The Chartered Institution of Building Services Engineers,1986,1-101
[37]Hittle D C, Pedersen C O. Calculating Building Heating Loads Using the Frequency Response of Multi-layered slabs. ASHRAE Transactions,1981, 87(2):545-568
[38]丁国良,张春路.空调动态负荷计算的新型谐波法.上海交通大学学报,1996,30(8)：100-103
[39]Davies M G. Current Methods to Handle Wall Conduction and Room Internal Heat Transfer. ASHRAE Transactions,1999,105(2):142-150
[40]Stephenson D G, Mitalas G P. Cooling Load Calculations by Thermal Response Factor Method. ASHRAE Transactions,1967,73(1):Ⅲ.1.1-Ⅲ.1.7
[41]Mitalas G P. Calculation of Transient Heat Flow through Walls and Roofs. ASHRAE Transactions,1968,74(2):182-188
[42]Kusuda T. Thermal Response Factors for Multi-Layer Structures of Various Heat Conduction Systems. ASHRAE Transactions,1969,75(1):246-271
[43]Spitler J D, Fisher D E. On the Relationship Between the Radiant Time Series and Transfer Function Methods for Design Cooling Load Calculations. HVAC&R Research,1999,5(2):123-136
[44]Mitalas G P, Arseneault J G. Fortran IV program to calculate z-transfer functions for the calculation of transient heat transfer through walls and roofs. In:Use of Computers for Environmental Engineering Related to Buildings. Gaithersburg, MD:NBS Building Science Series,1971
[45]ASHRAE. Handbook of Fundamentals.1977, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[46]ASHRAE. Handbook of Fundamentals.1981, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[47]ASHRAE. Handbook of Fundamentals.1985, Atlanta:American Society of Heating. Refrigerating, and Air-Conditioning Engineers, Inc.
[48]Peavy B A. A Note on Response Factors and Conduction Transfer Functions. ASHRAE Transactions,1978,84(1):688-690
[49]Hittle D C. Calculating Building Heating And Cooling Loads Using the Frequency Response of Multilayered Slabs:[University of Illinois PH.D. Thesis]. Urbana Champaign:University of Illinois,1981,221
[50]Stephenson D G. Ouyang K. Frequency domain analysis of the accuracy of Z-transfer function for walls. In:CIB 5th International Symposium. Bath, England:1986
[51]Harris S M, McQuiston F C. A Study to Categorize Walls and Roofs on the Basis of Thermal Response. ASHRAE Transactions,1988,94(2):688-714
[52]ASHRAE. Handbook of Fundamentals.1989, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[53]ASHRAE. Handbook of Fundamentals.1993, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[54]ASHRAE. Handbook of Fundamentals.1997, Atlanta:American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
[55]Ouyang K, Haghighat F. A procedure for calculating thermal response factors of multi-layer walls—State space method. Building and Environment,1991,26(2): 173-177
[56]李灏,张春路,丁国良.计算墙体反应系数的模型降价方法.上海交通大学学报,1998,32(7)：14-17
[57]丁国良,张春路,王险峰等.状态空间法计算墙体Z传递函数.暖通空调,1997,27(02)：15-17
[58]Davies M G. Solutions to Fourier's equation and unsteady heat flow through structures. Building and Environment,1995,30(3):309-321
[59]Davies M G.A Time-Domain Estimation of Wall Conduction Transfer Function Coefficients. ASHRAE Transactions,1996,102(1):328-343
[60]Davies M G. Wall transient heat flow using time-domain analysis. Building and Environment,1997,32(5):427-446
[61]陈友明,王盛卫.计算多层墙体响应系数的频域回归方法.湖南大学学报：自然科学版,2000,27(5)：71-77
[62]左政,陈友明.用频域回归方法计算圆柱形墙体的瞬时热流.湖南大学学报：自然科学版,2001(S1)：1-8
[63]Wang S, Chen Y. A novel and simple building load calculation model for building and system dynamic simulation. Applied Thermal Engineering.2001. 21(6):683-702
[64]Chen Y, Wang S. Frequency-domain regression method for estimating CTF models of building multilayer constructions. Applied Mathematical Modelling. 2001,25(7):579-592
[65]Macey H H. Heat loss through a solid floor. Journal of Institution of Fuel.1949. 22:369-371
[66]Latta J K, Boileau G G. Heat losses from house basements. Canadian Builders, 1969,19(10):39-42
[67]Delsante A E, Stokes A N, Walsh P J. Application of Fourier transforms to periodic heat flow into the ground under a building. International Journal of Heat and Mass Transfer,1983,26(1):121-132
[68]Delsante A E. Theoretical calculations of the steady-state heat losses through a slab-on-ground floor. Building and Environment,1988,23(1):11-17
[69]Hagentoft C. Steady-state heat loss for an edge-insulated slab:Part Ⅰ. Building and Environment,2002,37(1):19-25
[70]Hagentoft C. Periodic heat loss for an edge insulated slab:Part Ⅱ:A mixed boundary value problem. Building and Environment,2002,37(1):27-34
[71]Hagentoft C, Claesson J. Heat loss to the ground from a building—Ⅱ. Slab on the ground. Building and Environment,1991,26(4):395-403
[72]Hagentoft C. Heat losses and temperature in the ground under a building with and without ground water flow—Ⅱ. Finite ground water flow rate. Building and Environment,1996,31(1):13-19
[73]Hagentoft C. Heat losses and temperature in the ground under a building with and without ground water flow—Ⅰ. Infinite ground water flow rate. Building and Environment,1996,31 (1):3-11
[74]曹宝山.触地围护结构传热问题的分析研究.天津城建学院学报,1994(4)：7-24
[75]谈莹莹,闫晓娜.地下区域动态传热研究.科技创新导报,2008(32)：201-205
[76]谈莹莹.建筑墙体简化传热模型及触地结构传热计算方法研究：[湖南大学 硕士学位论文].长沙：湖南大学,2006
[77]Kusuda T, Bean J W. Simplified Methods for Determining Seasonal Heat Loss from Uninsulated Slab-on-Grade Floors. ASHRAE Transactions.1984,90(1B): 611-631
[78]Shen L S, Ramsey J W. An investigation of transient. two-dimensional coupled heat and moisture flow in the soil surrounding a basement wall. International Journal of Heat and Mass Transfer.1988.31(7):1517-1527
[79]Shen L S, Ramsey J W. A Simplified Thermal Analysis of Earth-Sheltered Buildings Using a Fourier-Series Boundary Method. ASHRAE Transactions. 1983,89(1B):438-448
[80]Krarti M, Claridge D E, Kreider J F. ITPE technique applications to time-varying two-dimensional ground-coupling problems. International Journal of Heat and Mass Transfer,1988,31(9):1899-1911
[81]Krarti M, Claridge D E, Kreider J F. The ITPE technique applied to steady-state ground-coupling problems. International Journal of Heat and Mass Transfer, 1988,31(9):1885-1898
[82]Krarti M, Choi S. Optimum insulation for rectangular basements. Energy and Buildings,1995,22(2):125-131
[83]Choi S, Krarti M. Thermally optimal insulation distribution for underground structures. Energy and Buildings,2000,32(3):251-265
[84]Chuangchid P, Krarti M. Foundation heat loss from heated concrete slab-on-grade floors. Building and Environment,2001,36(5):637-655
[85]程宝义,袁艳平,茅靳丰等.建筑材料热特性对地下工程围护结构热行为的影响.暖通空调,2004,34(12)：15-18
[86]Kusuda T, Achenbach P R. Numerical Analyses of the Thermal Environment of Occupied Underground Spaces with Finite Cover Using a Digital computer. ASHRAE Transactions,1963,69:439-451
[87]Davies G R. Thermal analysis of earth covered buildings. In:Proceedings of 4th National Passive Solar Conference. Kansas City:1979,744-748
[88]Ambrose C W. Modelling losses from slab floors. Building and Environment, 1981,16(4):251-258
[89]Xie X N, Jiang Y, Xia J J. A new approach to compute heat transfer of ground-coupled envelope in building thermal simulation software. Energy and Buildings,2008,40(4):476-485
[90]谢晓娜.建筑模拟软件中楼地动态传热问题的处理.见：2005年全国暖通空 调专业委员会空调模拟分析学组学术交流会.北京：2005
[91]谢晓娜,江亿DeST的热物理模型中地下部分传热研究.见：全国暖通空调制冷2004年学术年会.兰州：2004
[92]谢晓娜.建筑能耗模拟用楼地和热桥传热计算方法研究：[清华大学学位论文].北京：清华大学,2006
[93]谢晓娜,宋芳婷,张晓亮等.建筑环境设计模拟分析软件DeST第11讲与地面相邻区域动态传热问题的处理.暖通空调,2005,35(6)：55-63
[94]燕达.谢晓娜,宋芳婷等.建筑环境设计模拟分析软件DeST第一讲建筑模拟技术与DeST发展简介.暖通空调,2004,34(7)：48-56
[95]Szydlowski R F, Kuehn T H. Analysis of Transient Heat Loss in Earth-sheltered structures. Underground Space,1981,5(4):237-246
[96]Saxhof B, Poulsen K E. Foundations for Energy Conservation Houses:A Thermal Analysis based on Examples from Five Low-energy Houses at Hjorteker. Low-Energy House Project, Report No 130,1982.
[97]Rock B A. Sensitivity Study of Slab-on-Grade Transient Heat Transfer Model Parameters. ASHRAE Transactions,2004,110(1):177-184
[98]Wang F S. Mathematical modelling and computer simulation of insulation systems in below grade applications. In:Proceedings of the ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of Buildings Ⅰ. Orlando, Florida:ASHRAE,1979,456-471
[99]Mitalas G P. Calculation of Below-Grade Residential Heat Loss:Low-rise residential building. ASHRAE Transactions,1987,93(1):743-783
[100]Mitalas G P. Calculation of Basement Heat Loss. ASHRAE Transactions,1983, 89(1B):420-437
[101]Bligh T P, Willard T E. Modeling the thermal performance of earth-contact buildings, including the effect of phase change due to soil freezing. Computers & Structures,1985,21(1-2):291-318
[102]Deru M P. Ground-coupled heat and moisture transfer from buildings: [Colorado State University Ph.D. Thesis]. Fort Collins, Colorado, US:Colorado State University,2001
[103]Deru M, Judkoff R, Neymark J. Whole Building Energy Simulation with a Three-Dimensional Ground-Coupled Heat Transfer Model. ASHRAE Transactions,2003,109(1):557-565
[104]Mihalakakou G, Santamouris M, Asimakopoulos D, et al. On the ground temperature below buildings. Solar Energy,1995,55(5):355-362
[105]Adjali M H, Davies M, Littler J. Three-dimensional earth-contact heat flows:A comparison of simulated and measured data for a buried structure. Renewable Energy,1998,15(1-4):356-359
[106]Zoras S, Davies M, Wrobel L C. Earth-contact heat transfer:improvement and application of a novel simulation technique. Energy and Buildings,2002,34(4): 333-344
[107]Zoras S, Davies M, Adjali M H. A novel tool for the prediction of earth-contact heat transfer:a multi-room simulation. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2001,215(4):415-422
[108]Zoras S. A Novel Tool for the Prediction of Building Earth-contact Heat Transfer:[Brunei University Ph.D. Thesis]. UK:Brunel University,2001
[109]刘军,姚杨,王清勤.地下建筑围护结构传热的模拟与分析.见：全国暖通空调制冷2004年学术年会.兰州：2004
[110]Falconer D R, Sowell E F. Electronic tables for the ASHRAE load calculation manual. ASHRAE Transactions,1993,99(1):193-200
[111]Seem J E, Klein S A, Beckman W A, et al. Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer. Journal of Heat Transfer,1989,111(1):5-12
[112]McQuiston F C, Parker J D, Spitler J D. Heating, ventilating, and air-conditioning analysis and design.4th Ed. New York:John Wiley & Sons, Inc.,2000,1-30
[113]Incropera F P, DeWitt D P. Introduction to Heat Transfer.3rd ed. New York: Wiley,1996,1-47
[114]章熙民,任泽霈,梅飞鸣.传热学.第三版.北京：中国建筑工业出版社,1993,3-18
[115]Ceylan H T, Myers G E. Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs. ASME Journal of Heat Transfer,1980,102(1): 115-120
[116]Jiang Y. State-Space Method for the Calculation of Air-Conditioning Loads and the Simulation of Thermal Behavior of the Room. ASHRAE Transactions,1982. 88(2):122-138
[117]Seem J E. Modeling of Heat Transfer in Buildings:[The University of Wisconsin Madison Ph.D. Thesis]. Madison, Wisconsin, US:The University of Wisconsin Madison,1987
[118]陈友明,周娟,王盛卫.基于系统辨识的多层墙体z-传递函数计算方法.湖南大学学报：自然科学版.2004.31(5)：82-87
[119]Wang S. Chen Y. A simple procedure for calculating thermal response factors and conduction transfer functions of multilayer walls. Applied Thermal Engineering.2002.22(3):333-338
[120]Chen Y. Wang S. A new procedure for calculating periodic response factors based on frequency domain regression method. International Journal of Thermal Sciences.2005,44(4):382-392
[121]朱林.暖通与空调常用数据手册.第二版.北京：中国建筑工业出版社2002,1-100
[122]Myers G E. Analytical Methods in Conduction Heat Transfer.1 st ed. New York: McGraw-Hill.1971,1-38
[123]Hittle D C, Bishop R. An improved root-finding procedure for use in calculating transient heat flow through multilayered slabs. International Journal of Heat and Mass Transfer,1983,26(1):1685-1693
[124]郭萍.马继涌.大范围收敛迭代法在计算墙体传递函数极点中的应用.哈尔滨建筑大学学报,1999,32(5)：109-110
[125]Mitalas G P. Comments on the Z-Transfer Function Method for Calculating Heat Transfer in Buildings. ASHRAE Transactions,1978,84(1):667-674
[126]Wang S. Chen Y. Transient heat flow calculation for multilayer constructions using a frequency-domain regression method. Building and Environment,2003, 38(1):45-61
[127]Chen Y, Zhou J, Spitler J D. Verification for transient heat conduction calculation of multilayer building constructions. Energy and Buildings,2006, 38(4):340-348
[128]Spitler J D, Rees S J, Xiao D. Development of an analytical verification test suite for whole building energy simulation programs-building fabric. RP-1052, 2001.
[129]Kossecka E. Relationships Between Structure Factors, Response Factors, and Z-Transfer Function Coefficients for Multilayer Walls. ASHRAE Transactions, 1998,104(1A):68-77
[130]Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering,1994,37(2):229-256
[131]Nayroles B, Touzot G, Villon P. Generalizing the finite element method:diffuse approximation and diffuse elements. Computational Mechanics,1992,10(5): 307-318
[132]Belytschko T. Gu L, Lu Y Y. Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering.1994,2(3A):519-534
[133]Belytschko T. Lu Y Y. Gu L. et al. Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures,1995. 32(17-18):2547-2570
[134]Krysl P. Belytschko T. Analysis of thin plates by the element-free Galerkin method. Computational Mechanics.1995,17(1-2):26-35
[135]Krysl P. Belytschko T. Analysis of thin shells by the Element-Free Galerkin method. International Journal of Solids and Structures,1996,33(20-22): 3057-3080
[136]Cingoski V, Miyamoto N, Yamashita H. Element-free Galerkin method for electromagnetic field computations. IEEE Transactions on Magnetics,1998, 34(5):3236-3239
[137]Li G, Belytschko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations,2001,18(1-2):62-78
[138]Singh I V. Sandeep K, Prakash R. Heat transfer analysis of two-dimensional fins using meshless element free Galerkin method. Numerical Heat Transfer Part A-Applications,2003,44(1):73-84
[139]Singh I V, Sandeep K, Prakash R. The element free Galerkin method in three dimensional steady state heat conduction. International Journal of Computational Engineering Science,2002,3(3):291-303
[140]Singh I V, Sandeep K, Prakash R. Application of meshless element free Galerkin method in two-dimensional heat conduction problems. Computer Assisted Mechanics and Engineering Sciences,2004,11(4):265-274
[141]Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation,1981,37(155):141-158
[142]Belytschko T, Krongauz Y, Fleming M, et al. Smoothing and accelerated computations in the element free Galerkin method. Journal of Computational and Applied Mathematics,1996,74(1-2):111-126
[143]Belytschko T, Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method. Computers & Structures,1999,71(2):173-195
[144]Dolbow J, Belytschko T. An introduction to programming the meshless Element Free Galerkin method. Archives of Computational Methods in Engineering, 1998,5(3):207-241
[145]李庆扬,王能超,易大义.数值分析.第三版.武汉：华中科技大学出版社.1986,180-181
[146]Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method. Computational Mechanics,1995,17(3):186-195
[147]Singh I V. A numerical solution of composite heat transfer problems using meshless method. International Journal of Heat and Mass Transfer.2004. 47(10-11):2123-2138
[148]Shu H M, Huang Z Q, Li C W. Study of a new weight function in the meshless method and its application (in Chinese). Journal of Hefei University of Technology (Natural Science),2007,30(11):1489-1493
[149]Krysl P, Belytschko T. ESFLIB:A library to compute the element free Galerkin shape functions. Computer Methods in Applied Mechanics and Engineering, 2001,190(15-17):2181-2205
[150]Rao B N, Rahman S. An efficient meshless method for fracture analysis of cracks. Computational Mechanics,2000,26(4):398-408
[151]Zhu T, Atluri S N. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics,1998,21(3):211-222
[152]Lu Y Y, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1994,113(3-4):397-414
[153]Fernandez-Mendez S, Huerta A. Imposing essential boundary conditions in mesh-free methods. Computer Methods in Applied Mechanics and Engineering, 2004,193(12-14):1257-1275
[154]Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering,1996,131(1-2):133-145
[155]Gunther F C, Liu W K. Implementation of boundary conditions for meshless methods. Computer Methods in Applied Mechanics and Engineering,1998, 163(1-4):205-230
[156]Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering,1997,40(16): 2953-2974
[157]Ozisik M N.热传导.俞昌铭.第一版.北京：高等教育出版社,1983, 398-533
[158]Moaveni S.有限元分析—ANSYS理论与应用.工崧.第二版.北京：电子工业出版社,2005,189-191
[159]建筑工程常用数据系列手册编写组.暖通空调常用数据手册.第二版.北京：中国建筑工业出版社,2001,1-7
[160]Weitzmann P, Kragh J, Roots P. et al. Modelling floor heating systems using a validated two-dimensional ground-coupled numerical model. Building and Environment,2005,40(2):153-163
[161]McAdams W H. Heat Transmission.3nd Ed. New York:McGraw-Hill.1954. 1-500