基于动响应约束的结构材料优化设计

发布时间：2018-10-14 20:16

【摘要】：针对于随机荷载作用下动响应为约束的结构材料优化问题,基于结构拓扑优化思想,提出了一种变动响应约束的结构材料优化方法。采用分式有理式和幂函数识别结构材料单元特性参数,以微观单元拓扑变量倒数为设计变量,导出了频率及振型对微观单元设计变量的一阶导数,进而得到了随机荷载作用下结构均方响应的一阶近似展开式。结合变约束限的思想,建立了以结构质量作为目标函数,均方响应作为约束条件的连续体微结构拓扑优化近似模型,并采用对偶方法进行求解。对典型结构进行了考虑单个和多个动响应约束的结构材料优化设计,优化所得结果验证了该方法的有效性和可行性。
[Abstract]:Based on the idea of structural topology optimization, a structural material optimization method with variable response constraints is proposed for the optimization of structural materials constrained by dynamic response under random loads. The fractional rational formula and power function are used to identify the characteristic parameters of structural material element, and the reciprocal of micro element topology variable is taken as design variable. The first derivative of frequency and mode shape to micro element design variable is derived. Furthermore, the first order approximate expansion of the mean square response of the structure under random loads is obtained. Combined with the idea of variable constraint limits, an approximate model of topology optimization for continuum microstructures with structural mass as objective function and mean square response as constraint condition is established and solved by dual method. The optimization design of structural materials with single and multiple dynamic response constraints is carried out for typical structures. The results show that the proposed method is effective and feasible.
【作者单位】：中南大学土木工程学院;长沙学院土木建筑工程系;长沙理工大学桥梁工程安全控制省部共建教育部重点实验室科研平台;长沙理工大学汽车与机械工程学院;
【基金】：国家自然科学基金项目(11372055) 湖南省教育厅科学研究项目(15C0119;14C0098) 长沙理工大学桥梁工程安全控制省部共建教育部重点实验室开放基金项目(13KB07)
【分类号】：TU31

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