【摘要】 发展了一种利用水平集演化技术求解拓扑相关荷载作用下结构拓扑优化问题的数值方法。通过引入水平集函数,我们以隐含的方式对结构的拓扑和形状作了描述,从而把拓扑优化问题转化为了寻求最优水平集函数的数学规划问题。利用基于连续体概念的灵敏度分析技术,构造了用于驱动水平集演化的速度场。由于结构的边界可以用零水平集加以描述,因此利用适当的数学变换,我们可以方便地处理施加在结构上的拓扑相关荷载,这样就避免了以往算法中繁复的边界提取工作以及为了处理拓扑相关荷载所采取的特殊技巧。文末的数值算例表明了提出的优化方法在处理此类问题时所具有的独到的优越性。更多还原

【Abstract】 In the present paper,a new method of topology optimization of linearly elastic continuum structures subject to design-dependent loads is proposed.The new approach is developed in the context of level set method(LSM).By employing this approach,the structural topology can be represented by a level set function implicitly,thus the optimization of the structural topology is transferred to finding the optimal level set function of a higher dimension.As a result,the difficulties associated with the description of the boundary curve and application of the design-dependent load can be overcome in an efficient and robust way.Numerical examples demonstrate the advantage and the effectiveness of the proposed approach.更多还原