基于空间映射的多工况下任意设计域内结构形态创构  

Multi-load structural morphogenesis within arbitrary design domains based on space mapping

作　　者：马振福 崔昌禹[2] 邱英杰 MA Zhenfu;CUI Changyu;QIU Yingjie(School of Civil and Hydraulic Engineering,Ningxia University,Yinchuan 750021,China;School of Civil Engineering,Harbin Institute of Technology,Harbin 150090,China)

机构地区：[1]宁夏大学土木与水利工程学院,宁夏银川750021 [2]哈尔滨工业大学土木工程学院,黑龙江哈尔滨150090

出　　处：《建筑结构学报》2024年第11期200-209,共10页Journal of Building Structures

基　　金：国家自然科学基金项目(51578185)。

摘　　要：空间形体的任意性以及荷载工况的多样性是真实物理环境中的建筑结构形态创构面临的难题。为解决该问题,基于空间映射理论,提出了考虑多工况的连续体结构形态创构方法,通过建立具有映射关系的正交参数空间,实现任意复杂设计域内自由形态结构的合理布置。引入连续性假定保证了应力在整个设计域参数空间中连续化分布,使得形态在结构整体层面双向迭代进化。采用广义平均距离确定所有工况下最不利应力分布状态的进化基准值,并提取对应的应力等值线(面),最终得到形状和拓扑自由的创构结果。通过二维和三维数值算例分析表明:在满足最大允许应力和位移等约束条件下,材料用量大幅减少,von Mises应力趋于均匀分布,结构形态兼顾各个单工况荷载的传力路径,证实了方法的有效性;所提出的基于空间映射的连续体结构形态创构方法,能够在多工况下的任意设计域内生成力学性能高效的自由形态结构。The challenges of morphogenesis in building structures in a physical environment include the arbitrariness of spatial forms and the variety of loading conditions.To this end,a morphogenesis method for continuum structures considering multi-load conditions was proposed based on the space mapping theory.By establishing an orthogonal parameter space with a mapping relationship,a reasonable arrangement of the free-form structure can be achieved in any complex design domain.The continuity assumption was introduced to ensure that the stresses were distributed continuously in the parameter space of the entire design domain,allowing the morphology to evolve iteratively in bi-directions at the global-structural level.The generalized mean distance was utilized to determine the evolutionary thresholds of the most unfavorable stress distribution state for all loading conditions.Subsequently,the corresponding stress isolines/isosurfaces are extracted,and ultimately,the structures free of form and topology were obtained.The 2D and 3D numerical examples demonstrate that the material volume is significantly reduced,and the von Mises stresses tend to be uniformly distributed under the constraints of maximum allowable stresses and displacements.The structural morphology considers the transmission paths of each individual load case,confirming the effectiveness of the method.The proposed space mapping-based morphogenesis method for continuum structures can generate free-form structures with efficient mechanical properties in any design domain under multi-load conditions.

关 键 词：连续体结构 形态创构 空间映射 多工况 参数空间 

分 类 号：TU311.41[建筑科学—结构工程]