【摘要】 连续体拓扑优化方法可以从力学本质上提升结构的性能,为设计人员提供多样性的创新性设计,近年来得到了快速发展.该领域在线性问题上发展已经较为成熟,已经成功应用到很多工程结构的高性能设计.但实际工程中会涉及大量非线性问题,如果将其近似为线性问题,往往会产生较大误差,甚至得到错误的结果,可能会导致重大的工程安全事故.在航空航天、机械工程、海洋工程、高速列车、建筑工程等重要工程领域需求驱动的背景下,非线性连续体拓扑优化方法近年来取得了引人注目的进展.本文系统地综述了涉及材料非线性、几何非线性和边界非线性三种类型的连续体拓扑优化方法,并对现有典型方法进行讨论和评述.最后,指出了非线性连续体拓扑优化方法目前存在的困难(如数值分析精度差、计算效率低、局限于静力学领域等)以及未来的发展方向.(如大变形大应变问题、非线性动力学问题、大规模拓扑优化设计问题等).本研究综述可为非线性连续体拓扑优化领域的初学者提供较为全面的知识梳理,同时也为从事相关领域学者提供应有的帮助.更多还原

【Abstract】 The continuum topology optimization method can extensively improve the structural performance from the mechanical essence, which can provide designers with a variety of innovative design candidates. Due to these advantages and significant help to engineering, the continuum topology optimization method has been rapidly developed in recent years. This field has been developed relatively mature in dealing with linear topology optimization design problems. And it has been successfully applied to the high-performance design of all sorts of engineering structures. However, a large number of nonlinear issues are inherently involved in practical engineering. If they are assumed as linear problems,significant errors will often generate, and even wrong results may be obtained. This may ultimately lead to substantial engineering safety accidents. Under the demand-driven background of important engineering fields such as aerospace,mechanical engineering, marine engineering, high-speed trains, and architectural engineering, nonlinear continuum topology optimization methods have made remarkable progress in recent years. This paper aims to systematically review three types of nonlinear continuum topology optimization methods involving material nonlinearity, geometric nonlinearity, and boundary nonlinearity, with the typical methods comprehensively discussed and reviewed. Finally, the current difficulties(e.g., the poor numerical analysis accuracy, the low computational efficiency, limited to the field of statics, etc.) and future development directions(e.g., the large deformation and large strain problems, the nonlinear dynamic problems, the large-scale topology optimization design problems, etc.) of nonlinear continuum topology optimization methods are highlighted. This research review can provide a comprehensive knowledge sorting for beginners in the field of nonlinear continuum topology optimization. Moreover, it can also provide due help for scholars engaged in nonlinear continuum topology optimization methods.更多还原