空间网格结构的鲁棒性理论与试验研究
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摘要
网格结构是空间结构中应用最为广泛的结构形式,具有跨度大、构件多、破坏后果严重的特点,但目前设计时较少考虑结构受到意外干扰时的性能,而近年来人为事故和自然灾害对其破坏性愈加突出,结构倒塌事件时有发生。增强结构的鲁棒性可以降低其对干扰的敏感性,提高结构抵抗不相称破坏的能力。目前,结构鲁棒性缺乏有效的数值表达和可行的设计方法,且研究对象主要为桁架、框架结构,在空间网格结构领域较为少见。因此,对空间网格结构的鲁棒性理论进行系统研究,具有十分重要的理论意义和工程价值。
本文从结构鲁棒性定量评价指标、典型空间网格结构的鲁棒性、基于鲁棒性的优化设计方法和模型试验等几个层次展开研究。具体内容如下：
借鉴H∞最优的思想,针对线性结构系统,根据定性描述的结构鲁棒性定义,从结构自身的属性出发,建立了H∞结构鲁棒性定量评价指标。通过单自由度体系和桁架结构的算例,阐释了H∞鲁棒性指标的性质、物理意义,以及影响结构鲁棒性的因素,验证了本文提出的评价指标的合理性和有效性。
针对非线性结构系统,引入L2性能准则,利用凸集模型表达不确定性干扰,给出考虑弹塑性的结构鲁棒性计算公式,进而分析弹塑性、冗余度以及外部荷载和结构自身的不确定性与鲁棒性的关系。以上两部分研究为基于鲁棒性的结构分析与设计提供了理论基础。
采用线性H∞结构鲁棒性评价指标,选取常见的扇形三向网格、肋环斜杆型和肋环型单层球面网壳结构,以及单向斜杆正交正放网格和三向网格的单层圆柱面网壳结构,通过参数分析,研究了几何尺寸、网格形式对单层网壳结构鲁棒性的影响。通过逐步概念移除构件,分析了构件的重要性,进而搜索了影响鲁棒性的关键路径。最后针对某双层网壳结构工程实例,讨论了不同的支承形式对鲁棒性的影响。
对地震作用下不同形式的网架结构进行大规模数值计算,分析了其动力失效模式及特征,发现网架结构各失效模式之间存在模糊性。利用模糊C-均值聚类方法将网架动力失效模式归为三类：失稳型局部失效、强度型整体失效和强度型局部失效,得到了各失效模式的典型数字特征,给出了分析地震作用下网格结构鲁棒性的步骤。
以H∞结构鲁棒性指标为目标,采用基于多精英选择的遗传算法,从截面层次研究了结构鲁棒性优化设计方法。以平面和三维桁架结构为例,验证了提出的方法,并探索遗传算法中种群个体数的合理取值。针对典型的单层球面和圆柱面网壳结构进行了截面优化,得到了较为合理的截面布置,并通过与承载力和位移指标比较,验证了优化结果。
采用SIMP模型描述材料的刚度,以结构鲁棒性为优化目标,从拓扑层次研究了结构鲁棒性优化设计方法。将结构鲁棒性设计转化成连续体拓扑优化问题,通过平面应力模型验证了方法的可行性和合理性。以球面壳和双曲面壳为例,得到了网壳结构的鲁棒构型,为网格结构的拓扑优化提供了有效的手段。
分别按照鲁棒设计和常规设计,制作了两个单层球面网壳结构模型,通过静力和冲击试验,制造不同的干扰场景,分析了不同结构设计方案的鲁棒性,验证了H∞鲁棒性指标的合理性。结果表明,通过连续体拓扑优化进行鲁棒设计,能够有效地提高结构鲁棒性。
本文系统地研究了空间网格结构的鲁棒性,初步建立了空间网格结构的鲁棒性设计理论和设计原则,为有效防止该类结构的不相称破坏提供理论依据和设计方法。
As the most widely used spatial structure form, spatial latticed structures have the features of large span, multi-components, and serious destruction consequences. But during the design procedure, little consideration is taken on the accidental interference. In recent years, spatial latticed structures increasingly suffer from man-made accidents and natural disasters, and collapse events have occurred sometimes. Enhancing the structural robustness can reduce its susceptibility to interference, and increase the resistance capacity to disproportionate destruction. Now the research of structural robustness is mainly focused on trusses and frame structures, while the study on spatial latticed structures is rare, and effective numerical expression and feasible design method are lack. The research of the robustness of spatial latticed structures is valuable for theory and engineering.
This paper conducts research from several levels, including quantitative evaluations of structural robustness, the robustness of the typical spatial latticed structures, and optimization design methods based on robustness. The specific contents are as follows:
Taking basis in robust H∞, control theory and the attributes of structures, a framework for quantitative assessing structural robustness is proposed according to the qualitative statement. Taking a SDOF system and truss structures as examples, properties and physical interpretation of the H∞, structural robustness index were clarified, and factors affecting structural robustness were studied. The results indicate that H∞structural robustness index can effectively and reasonably reflect structural robustness.
For nonlinear systems, the uncertainties were expressed by convex model, and specific formula for elastic-plastic structural robustness was given, using L2norm as an evaluation of signal. Influence of elastic-plastic, redundancy and the uncertainties of loads and structural attributes were analyzed. The above two parts of research lay foubdation for structure analysis and design based on robustness.
For the typical spherical latticed shells, including Kiewitt dome, Schwedler dome and ribbed type, and cylindrical latticed shells, including one-way orthogonal grid and three-way grid, influence of geometric parameters and grid configurations on the robustness of single-layer reticular shells were analyzed through parametric analysis. Then the components importance indices were calculated by component removal method. Furthermore the critical path for robustness was obtained. Finally, taking an engineering practice for example, the impact of different forms of supports to robustness was discussed.
Based on large scale numerical calculations for different forms of spaec grid structures subjected to earthquake, dynamic failure modes and characteristics were analyzed, which showd fuzziness. Using fuzzy C-means method, the failure modes were classified into three categories: instability based progressive collapse, strength based overall collapse and strength based progressive collapse, and the numerical prototypes of failure modes were obtained. Finally the steps to analyze robustness of spatial latticed structures subjected to earthquake are proposed.
Setting H∞, structural robustness indicators as the target, size level structural robustness optimization was investigated, using the genetic algorithm based on multi-elitist selection. The proposed method was verified by the examples of planar and three-dimensional truss structures, and the reasonable number of individuals in populations of genetic algorithm was explored either. Typical single-layer spherical and cylindrical latticed shell structures were optimization then, and reasonable cross-section arrangements were obtained. The results were verified by the robustness indicators based on bearing capacity and displacement.
Using the SIMP material model to describe the stiffness of material, topology level structural robustness optimization was investigated. Robustness based design of spatial latticed structures is formulated as a continuum topology optimization problem, where the structural robustness is considered as the optimization objective. The feasibility and rationality of the method were verified by the plane stress model. As an example, robustness configurations of a single-layer spherical and a hyperboloid shell were obtained by robustness based structural design, which could provide an effective method for the topology optimization of spatial latticed structures.
Two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that robustness based structural design improves structural robustness effectively.
This paper systematically studied the robustness of spatial latticed structures. The research results can preliminarily provide theoretical basis and design methods to effectively prevent the disproportionate consequences.
本文从结构鲁棒性定量评价指标、典型空间网格结构的鲁棒性、基于鲁棒性的优化设计方法和模型试验等几个层次展开研究。具体内容如下：
借鉴H∞最优的思想,针对线性结构系统,根据定性描述的结构鲁棒性定义,从结构自身的属性出发,建立了H∞结构鲁棒性定量评价指标。通过单自由度体系和桁架结构的算例,阐释了H∞鲁棒性指标的性质、物理意义,以及影响结构鲁棒性的因素,验证了本文提出的评价指标的合理性和有效性。
针对非线性结构系统,引入L2性能准则,利用凸集模型表达不确定性干扰,给出考虑弹塑性的结构鲁棒性计算公式,进而分析弹塑性、冗余度以及外部荷载和结构自身的不确定性与鲁棒性的关系。以上两部分研究为基于鲁棒性的结构分析与设计提供了理论基础。
采用线性H∞结构鲁棒性评价指标,选取常见的扇形三向网格、肋环斜杆型和肋环型单层球面网壳结构,以及单向斜杆正交正放网格和三向网格的单层圆柱面网壳结构,通过参数分析,研究了几何尺寸、网格形式对单层网壳结构鲁棒性的影响。通过逐步概念移除构件,分析了构件的重要性,进而搜索了影响鲁棒性的关键路径。最后针对某双层网壳结构工程实例,讨论了不同的支承形式对鲁棒性的影响。
对地震作用下不同形式的网架结构进行大规模数值计算,分析了其动力失效模式及特征,发现网架结构各失效模式之间存在模糊性。利用模糊C-均值聚类方法将网架动力失效模式归为三类：失稳型局部失效、强度型整体失效和强度型局部失效,得到了各失效模式的典型数字特征,给出了分析地震作用下网格结构鲁棒性的步骤。
以H∞结构鲁棒性指标为目标,采用基于多精英选择的遗传算法,从截面层次研究了结构鲁棒性优化设计方法。以平面和三维桁架结构为例,验证了提出的方法,并探索遗传算法中种群个体数的合理取值。针对典型的单层球面和圆柱面网壳结构进行了截面优化,得到了较为合理的截面布置,并通过与承载力和位移指标比较,验证了优化结果。
采用SIMP模型描述材料的刚度,以结构鲁棒性为优化目标,从拓扑层次研究了结构鲁棒性优化设计方法。将结构鲁棒性设计转化成连续体拓扑优化问题,通过平面应力模型验证了方法的可行性和合理性。以球面壳和双曲面壳为例,得到了网壳结构的鲁棒构型,为网格结构的拓扑优化提供了有效的手段。
分别按照鲁棒设计和常规设计,制作了两个单层球面网壳结构模型,通过静力和冲击试验,制造不同的干扰场景,分析了不同结构设计方案的鲁棒性,验证了H∞鲁棒性指标的合理性。结果表明,通过连续体拓扑优化进行鲁棒设计,能够有效地提高结构鲁棒性。
本文系统地研究了空间网格结构的鲁棒性,初步建立了空间网格结构的鲁棒性设计理论和设计原则,为有效防止该类结构的不相称破坏提供理论依据和设计方法。
As the most widely used spatial structure form, spatial latticed structures have the features of large span, multi-components, and serious destruction consequences. But during the design procedure, little consideration is taken on the accidental interference. In recent years, spatial latticed structures increasingly suffer from man-made accidents and natural disasters, and collapse events have occurred sometimes. Enhancing the structural robustness can reduce its susceptibility to interference, and increase the resistance capacity to disproportionate destruction. Now the research of structural robustness is mainly focused on trusses and frame structures, while the study on spatial latticed structures is rare, and effective numerical expression and feasible design method are lack. The research of the robustness of spatial latticed structures is valuable for theory and engineering.
This paper conducts research from several levels, including quantitative evaluations of structural robustness, the robustness of the typical spatial latticed structures, and optimization design methods based on robustness. The specific contents are as follows:
Taking basis in robust H∞, control theory and the attributes of structures, a framework for quantitative assessing structural robustness is proposed according to the qualitative statement. Taking a SDOF system and truss structures as examples, properties and physical interpretation of the H∞, structural robustness index were clarified, and factors affecting structural robustness were studied. The results indicate that H∞structural robustness index can effectively and reasonably reflect structural robustness.
For nonlinear systems, the uncertainties were expressed by convex model, and specific formula for elastic-plastic structural robustness was given, using L2norm as an evaluation of signal. Influence of elastic-plastic, redundancy and the uncertainties of loads and structural attributes were analyzed. The above two parts of research lay foubdation for structure analysis and design based on robustness.
For the typical spherical latticed shells, including Kiewitt dome, Schwedler dome and ribbed type, and cylindrical latticed shells, including one-way orthogonal grid and three-way grid, influence of geometric parameters and grid configurations on the robustness of single-layer reticular shells were analyzed through parametric analysis. Then the components importance indices were calculated by component removal method. Furthermore the critical path for robustness was obtained. Finally, taking an engineering practice for example, the impact of different forms of supports to robustness was discussed.
Based on large scale numerical calculations for different forms of spaec grid structures subjected to earthquake, dynamic failure modes and characteristics were analyzed, which showd fuzziness. Using fuzzy C-means method, the failure modes were classified into three categories: instability based progressive collapse, strength based overall collapse and strength based progressive collapse, and the numerical prototypes of failure modes were obtained. Finally the steps to analyze robustness of spatial latticed structures subjected to earthquake are proposed.
Setting H∞, structural robustness indicators as the target, size level structural robustness optimization was investigated, using the genetic algorithm based on multi-elitist selection. The proposed method was verified by the examples of planar and three-dimensional truss structures, and the reasonable number of individuals in populations of genetic algorithm was explored either. Typical single-layer spherical and cylindrical latticed shell structures were optimization then, and reasonable cross-section arrangements were obtained. The results were verified by the robustness indicators based on bearing capacity and displacement.
Using the SIMP material model to describe the stiffness of material, topology level structural robustness optimization was investigated. Robustness based design of spatial latticed structures is formulated as a continuum topology optimization problem, where the structural robustness is considered as the optimization objective. The feasibility and rationality of the method were verified by the plane stress model. As an example, robustness configurations of a single-layer spherical and a hyperboloid shell were obtained by robustness based structural design, which could provide an effective method for the topology optimization of spatial latticed structures.
Two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that robustness based structural design improves structural robustness effectively.
This paper systematically studied the robustness of spatial latticed structures. The research results can preliminarily provide theoretical basis and design methods to effectively prevent the disproportionate consequences.
引文
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