杆系结构形态创构方法研究
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摘要
结构形态创构是建筑与结构交叉领域新兴研究方向之一，是从结构分析出发，寻求多种“良好”建筑形状的理论方法，对建筑与结构设计的进一步发展有较深的意义。杆系结构类型众多，在实际工程中应用广泛，杆系结构形态创构方法的研究具有较高的应用价值，有助于建筑形式的多样化。本文以结构优化理论为基础，考虑建筑空间制约条件，以结构刚度最大化为设计目标，提出了兼顾形状、拓扑和截面的杆系结构形态创构方法。方法中考虑了程序通用性，使方法能够用于各种杆系结构的形态创构。本文主要开展以下几个方面工作：
1.建立了杆系结构的节点调整方法
从应变能和节点坐标的关系出发，推导了节点移动应变能敏感度表达式，并考虑空间制约条件，得到了受约束节点移动应变能敏感度表达式。详细分析了节点移动应变能敏感度的特性，提出了根据应变能对节点坐标的敏感程度逐步调整节点来实现结构刚度最大化的杆系结构形状创构方法。为了提高进化效率，进一步研究了节点移动方向的修正方法，对杆系结构形状创构方法进行了改进。研究发现在应该能收敛阶段，节点移动敏感度趋于零，此阶段的结构具有对初始缺陷不敏感的特点。
2.提出了兼顾拓扑和形状的杆系结构拓扑形态创构方法
为了评价每个单元在整个结构中抵抗荷载的贡献程度，定义了单元增减应变能敏感度，并将其作为衡量单元承载效率高低的指标。利用单元增减应变能敏感度的特性，研究了单元增减的策略，并结合节点调整，提出了兼顾结构拓扑与形状的创构方法。该方法通过直接地消除低效单元和在高效单元附近增加单元，实现了结构的拓扑变化，并通过节点调整修正拓扑变化过程中的节点位置和结构形状。由于单元可增可减，方法的初始结构既可以简单也可复杂，可灵活选择。在结构形态确定后，在方法中还引入了截面优化，使方法可以兼顾形状、拓扑和截面，完善了方法。方法适用广泛，能够用于平面及空间中的各类杆系结构的形态创构。
3.在杆系结构形态创构方法中考虑了建筑空间制约条件
为增强本文方法的实用性，采用B样条曲线（曲面）等来表达建筑要求所提出的空间制约条件，并在应变能敏感度的推导过程中给予反应，使方法所产生的结构能够满足建筑要求。此外，还利用初始结构对最终结构的影响，在初始结构确定时以不同的杆件布置手段来体现空间制约条件。由于初始结构是结构演化的起点，同时也为新杆件生成提供基本的可能空间，对建筑空间制约条件的实现起重要作用。还通过对不同应用场合下的空间制约条件的处理，增强了方法的实用性，同时也丰富了结构形态创构方法的内容。
4.研究方法在平面及空间结构中的应用
为了探讨方法的适用性，对平面及空间结构中的桁架型结构，树状型结构，桥梁型结构等进行了大量算例应用实践。算例展现了方法广泛的适用性和实用性。针对不同支座条件，不同初始结构条件、不同创构策略以及不同结构类型的杆系结构进行形态创构。考察了进化过程中结构形态变化和力学性能变化，总结了创构策略对结构形态变化的影响和方法的特点。方法所得结构形式具有以轴力传递荷载的几何特征，结构形式多呈现优美的弧状，这有利于建筑造型中美学意图的实现。同时，所得结构形式符合力学概念，可为结构力学教育和结构设计提供参考。
5.研究并总结了方法所得结构的力学性能
从大量算例的力学量的变化可知，兼顾拓扑与形状的杆系结构形态创构方法可以使结构向刚度提高、弯矩降低的方向演化，最终结构将以轴力为主要传递荷载方式。方法中的节点调整对结构力学性能的改善贡献较多。对节点调整前后结构的稳定性进行验算，结果表明调整后结构不仅可提高结构刚度，且可提高极限承载力和改善初始节点偏差对结构的影响。虽然以应变能作为目标函数，但可同时改善多项力学性能指标：结构刚度，结构极限承载力，结构力学性能的稳定性等，这些力学性能在演化过程中具有同时改善的趋势。
文中方法用Fortran语言编程实现，用ANSYS有限元软件考察了方法所得结构的一些力学性能。本文还获得了一套杆系结构形态创构程序。
Structural morphogenesis is a new research direction of the interdiscipline ofarchitecture and structural enginnering. Based on structural analysis, structuralmorphogenesis methods are a series of thoeries and methods to seek a variety ofgood architectural shape. This study can promote the development of thearchitectural and structural design. Framed structures have many types and a widerange of applications in engineering. Therefore, the research on framed structuralmorphogenesis method has important application value and is helpful to diversifythe architectural forms. Based on the structural optimization theories, this structuralmorphogenesis method is put forward for the shape, topology and sizingoptimizition of framed structures under architectural space constraints aiming tomaximize the structural stiffness. The method can be applied to the structuralmorphogenesis of various framed structures. This paper mainly focused out thefollowing tasks:
1. The nodal adjustment method for framed structures
The expressions of nodal strain energy sensitivity are derived from therelationship between strain energy and the nodal coordinates. Moreover, theexpressions of strain energy sensitivity of nodes under the spatial constraints weregotten. The shape morphogenesis method of framed structure, which took themaximization of structural stiffness as the design objective, was put forward throughgradual nodal adjustment after the analysis of the properties of nodal strain energysensitivity. In order to increase the efficiency of the method, the method foramending the direction of nodal shift was studied further and the shapemorphogenesis method of framed structure was improved. It was found that thenodal strain energy sensitivity tended to zero in the convergence stage, and then thecorresponding structures were less sensitive to the initial defect.
2. topology morphogenesis method of framed strucutres combining shapeand topology optimization
To evalue the contribution degree of each element in the whole structure toresisting loads, the elemental strain energy sensitivity for addition and eliminationwas defined and taken as the efficiency index for bearing loads. The topology andshape morphogenesis method of the framed structures including the nodaladjustment was put forward after the strategy study of elemental addition andelimination and the analysis of the properties of the elemental strain energysensitivity. This method realised the topology change through the direct eliminationof inefficient elements and addition of new elements near the highly efficient elements and the nodal position and structural shape were amended by the nodaladjustment during the topology change. The initial structure may be simple orcomplex because the elements may be added or eliminated in this method. After thestructural shape was fixed, the size optimization was introduced to make thismorphogenesis method integrate the shape, topology and size optimization. Thismethod can be used for the morphogenesis of all kinds of framed strucutres in planeor space.
3. Architectural space constraints considered in this mehtod
To enhance the usefulness of this method, the architectural spatial constraintsfrom the architectural requirements were expressed by B-spline curves and surfaces,etc.,and were reflected in the strain energy sensitivity to make the structures derivedform this method meet the architectural requirements. In addtion, the architecturalspatial constraints were embodied by the intial strucutres which were set through thedifferent layout of rods according to the influence of the initial structure on finalstructure. Since the initial structure was the starting point of the structural evlotionand provided the basic posssible allowable space for the generation of new rods, theinitial strucutres had an important role on the realization of the architectural spatialconstraints. This paper perfected the program fuctions of the method in a variety ofspatial constraints for different application situations. This further enhanced thepracticality of the method, and also enriched the theory of structural morphology.
4. Application in the plane and spatial structures for this method
In order to discuss the applicability fo the method, a number of applicationexamples were carried out such as trusses, tree-like structures, bridges, etc. in theplane and spatial structures. Numerical examples demonstrated the wideapplicability and practicality of this method. The morphorgenesis of these structureswas about the different support condition, different initial structures, differentmorphorgenesis strategyies and different structural types. The changes of structuralshape and mechanical behaviors in the evolutionary process were investigated tosummarize the properties of the method and the inflence of the morphorgenesisstrategyies on the change of strucutral shape. The strucutral shape derived from themethod had the geometrical characters which transferred loads to supports mainlyby the axis force. These strucutral shapes often appeared beatiful arc shape and thiswas benificial for the realization of artistic intention of architechtural shape.Moreover, the structural forms derived from this method conformed to mechanicalconcepts, which could be provided for the education of structural mechanics andstructural design as reference.
5. The summary of mechanical properties of the structures by this method
From the change of mechanical quantities in the numerial examples, thetopology and shape morphogenesis method of framed structures can make the structure evolve in the direction of the decline of strain energy and bending moment,and the finial structure would transfer loads with axis force. The nodal adjustmenthad great contribution to the improvement of structural mechanical behaviors. Bychecking stability of the structures in the evolutionary process, it was found that thenodal adjustment can not only improve the structural stiffness and ultimate load, butalso less influence by the initial nodal defect. This illustrated that the method takingstrain energy as the objective function can increase the structural rigidity and thestructure of ultimate load; Moreover, the structures derived by the method are lesssensitive to the initial defect. These mechanical quantities will be improvedsimaltinously in the optimization process.
The proposed method was coded in Fortran language, and finite elementcommercial software ANSYS was used in the calculation of some structuralmechinical behaviors. In addtion, this paper got the program of the morphogenesisof framed strucutres.
1.建立了杆系结构的节点调整方法
从应变能和节点坐标的关系出发，推导了节点移动应变能敏感度表达式，并考虑空间制约条件，得到了受约束节点移动应变能敏感度表达式。详细分析了节点移动应变能敏感度的特性，提出了根据应变能对节点坐标的敏感程度逐步调整节点来实现结构刚度最大化的杆系结构形状创构方法。为了提高进化效率，进一步研究了节点移动方向的修正方法，对杆系结构形状创构方法进行了改进。研究发现在应该能收敛阶段，节点移动敏感度趋于零，此阶段的结构具有对初始缺陷不敏感的特点。
2.提出了兼顾拓扑和形状的杆系结构拓扑形态创构方法
为了评价每个单元在整个结构中抵抗荷载的贡献程度，定义了单元增减应变能敏感度，并将其作为衡量单元承载效率高低的指标。利用单元增减应变能敏感度的特性，研究了单元增减的策略，并结合节点调整，提出了兼顾结构拓扑与形状的创构方法。该方法通过直接地消除低效单元和在高效单元附近增加单元，实现了结构的拓扑变化，并通过节点调整修正拓扑变化过程中的节点位置和结构形状。由于单元可增可减，方法的初始结构既可以简单也可复杂，可灵活选择。在结构形态确定后，在方法中还引入了截面优化，使方法可以兼顾形状、拓扑和截面，完善了方法。方法适用广泛，能够用于平面及空间中的各类杆系结构的形态创构。
3.在杆系结构形态创构方法中考虑了建筑空间制约条件
为增强本文方法的实用性，采用B样条曲线（曲面）等来表达建筑要求所提出的空间制约条件，并在应变能敏感度的推导过程中给予反应，使方法所产生的结构能够满足建筑要求。此外，还利用初始结构对最终结构的影响，在初始结构确定时以不同的杆件布置手段来体现空间制约条件。由于初始结构是结构演化的起点，同时也为新杆件生成提供基本的可能空间，对建筑空间制约条件的实现起重要作用。还通过对不同应用场合下的空间制约条件的处理，增强了方法的实用性，同时也丰富了结构形态创构方法的内容。
4.研究方法在平面及空间结构中的应用
为了探讨方法的适用性，对平面及空间结构中的桁架型结构，树状型结构，桥梁型结构等进行了大量算例应用实践。算例展现了方法广泛的适用性和实用性。针对不同支座条件，不同初始结构条件、不同创构策略以及不同结构类型的杆系结构进行形态创构。考察了进化过程中结构形态变化和力学性能变化，总结了创构策略对结构形态变化的影响和方法的特点。方法所得结构形式具有以轴力传递荷载的几何特征，结构形式多呈现优美的弧状，这有利于建筑造型中美学意图的实现。同时，所得结构形式符合力学概念，可为结构力学教育和结构设计提供参考。
5.研究并总结了方法所得结构的力学性能
从大量算例的力学量的变化可知，兼顾拓扑与形状的杆系结构形态创构方法可以使结构向刚度提高、弯矩降低的方向演化，最终结构将以轴力为主要传递荷载方式。方法中的节点调整对结构力学性能的改善贡献较多。对节点调整前后结构的稳定性进行验算，结果表明调整后结构不仅可提高结构刚度，且可提高极限承载力和改善初始节点偏差对结构的影响。虽然以应变能作为目标函数，但可同时改善多项力学性能指标：结构刚度，结构极限承载力，结构力学性能的稳定性等，这些力学性能在演化过程中具有同时改善的趋势。
文中方法用Fortran语言编程实现，用ANSYS有限元软件考察了方法所得结构的一些力学性能。本文还获得了一套杆系结构形态创构程序。
Structural morphogenesis is a new research direction of the interdiscipline ofarchitecture and structural enginnering. Based on structural analysis, structuralmorphogenesis methods are a series of thoeries and methods to seek a variety ofgood architectural shape. This study can promote the development of thearchitectural and structural design. Framed structures have many types and a widerange of applications in engineering. Therefore, the research on framed structuralmorphogenesis method has important application value and is helpful to diversifythe architectural forms. Based on the structural optimization theories, this structuralmorphogenesis method is put forward for the shape, topology and sizingoptimizition of framed structures under architectural space constraints aiming tomaximize the structural stiffness. The method can be applied to the structuralmorphogenesis of various framed structures. This paper mainly focused out thefollowing tasks:
1. The nodal adjustment method for framed structures
The expressions of nodal strain energy sensitivity are derived from therelationship between strain energy and the nodal coordinates. Moreover, theexpressions of strain energy sensitivity of nodes under the spatial constraints weregotten. The shape morphogenesis method of framed structure, which took themaximization of structural stiffness as the design objective, was put forward throughgradual nodal adjustment after the analysis of the properties of nodal strain energysensitivity. In order to increase the efficiency of the method, the method foramending the direction of nodal shift was studied further and the shapemorphogenesis method of framed structure was improved. It was found that thenodal strain energy sensitivity tended to zero in the convergence stage, and then thecorresponding structures were less sensitive to the initial defect.
2. topology morphogenesis method of framed strucutres combining shapeand topology optimization
To evalue the contribution degree of each element in the whole structure toresisting loads, the elemental strain energy sensitivity for addition and eliminationwas defined and taken as the efficiency index for bearing loads. The topology andshape morphogenesis method of the framed structures including the nodaladjustment was put forward after the strategy study of elemental addition andelimination and the analysis of the properties of the elemental strain energysensitivity. This method realised the topology change through the direct eliminationof inefficient elements and addition of new elements near the highly efficient elements and the nodal position and structural shape were amended by the nodaladjustment during the topology change. The initial structure may be simple orcomplex because the elements may be added or eliminated in this method. After thestructural shape was fixed, the size optimization was introduced to make thismorphogenesis method integrate the shape, topology and size optimization. Thismethod can be used for the morphogenesis of all kinds of framed strucutres in planeor space.
3. Architectural space constraints considered in this mehtod
To enhance the usefulness of this method, the architectural spatial constraintsfrom the architectural requirements were expressed by B-spline curves and surfaces,etc.,and were reflected in the strain energy sensitivity to make the structures derivedform this method meet the architectural requirements. In addtion, the architecturalspatial constraints were embodied by the intial strucutres which were set through thedifferent layout of rods according to the influence of the initial structure on finalstructure. Since the initial structure was the starting point of the structural evlotionand provided the basic posssible allowable space for the generation of new rods, theinitial strucutres had an important role on the realization of the architectural spatialconstraints. This paper perfected the program fuctions of the method in a variety ofspatial constraints for different application situations. This further enhanced thepracticality of the method, and also enriched the theory of structural morphology.
4. Application in the plane and spatial structures for this method
In order to discuss the applicability fo the method, a number of applicationexamples were carried out such as trusses, tree-like structures, bridges, etc. in theplane and spatial structures. Numerical examples demonstrated the wideapplicability and practicality of this method. The morphorgenesis of these structureswas about the different support condition, different initial structures, differentmorphorgenesis strategyies and different structural types. The changes of structuralshape and mechanical behaviors in the evolutionary process were investigated tosummarize the properties of the method and the inflence of the morphorgenesisstrategyies on the change of strucutral shape. The strucutral shape derived from themethod had the geometrical characters which transferred loads to supports mainlyby the axis force. These strucutral shapes often appeared beatiful arc shape and thiswas benificial for the realization of artistic intention of architechtural shape.Moreover, the structural forms derived from this method conformed to mechanicalconcepts, which could be provided for the education of structural mechanics andstructural design as reference.
5. The summary of mechanical properties of the structures by this method
From the change of mechanical quantities in the numerial examples, thetopology and shape morphogenesis method of framed structures can make the structure evolve in the direction of the decline of strain energy and bending moment,and the finial structure would transfer loads with axis force. The nodal adjustmenthad great contribution to the improvement of structural mechanical behaviors. Bychecking stability of the structures in the evolutionary process, it was found that thenodal adjustment can not only improve the structural stiffness and ultimate load, butalso less influence by the initial nodal defect. This illustrated that the method takingstrain energy as the objective function can increase the structural rigidity and thestructure of ultimate load; Moreover, the structures derived by the method are lesssensitive to the initial defect. These mechanical quantities will be improvedsimaltinously in the optimization process.
The proposed method was coded in Fortran language, and finite elementcommercial software ANSYS was used in the calculation of some structuralmechinical behaviors. In addtion, this paper got the program of the morphogenesisof framed strucutres.
引文
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