连续体结构综合优化设计  

Integration Optimization Design of Continuum Structure

作　　者：傅晓锦[1,2] 

机构地区：[1]上海电机学院机械学院,上海200245 [2]绍兴文理学院工学院,绍兴312000

出　　处：《机械工程学报》2012年第1期128-134,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金(50675206);浙江省自然科学基金(Y106847;Y1090153);上海市自然科学基金(11ZR1413800);上海电机学院重点培育(10C102;10C431);上海市教育委员会重点学科建设(J51902)资助项目

摘　　要：以连续体为对象的优化解法所求得的优化结果,经常只是反映最佳传力途径的具有锯齿状边界的某个区域。基于此,将拓扑优化、形状优化、有限元分析和计算机辅助几何设计有机地集成在一起,提出一种基于隐含边界描述的水平集连续体结构拓扑和形状渐进综合优化设计方法,将形状导数与拉格朗日乘子法引入到优化敏度分析中,控制水平集函数的动态运动,从而间接地实现结构边界的动态演化;用B样条曲线曲面逼近拓扑优化后的结构体边界,将前一优化过程所得到的反映传力途径的概念解上升为具有光顺边界,并被参数化了的物理解;在形状优化中,设计变量定义为B样条曲线或曲面的控制顶点的运动,建立边界节点移动速度场计算方法和边界形状调整方法,寻求较快的搜索方向,以合理速度分布,使结构变为最佳。通过一个典型算例证明所研究方法的有效性。The optimization result which is got by optimization algorithm aimed at continuum structure only reflect the saw-shaped boundary area owning best force-passed path.Based on this,topology optimization,shape optimization,finite element analysis and computer aided geometric design are integrated effectively.A new evolutionary integrated optimization algorithm of topology and shape for continuum structure is presented based on level set method of implicit boundary representation.The shape derivative analysis and Lagrangian multipliers are applied to sensitivity analysis of optimization to dominate the dynamic evolvement for the embedded level set function and further to control the movement of structural boundary with the flexibility of handing structure changes.B-spline curve and curved surface are used to approach continuum structure boundary after topology optimization,which transform the concept solution that reflects force passing path got by the above optimization process to the parametrical precision solution.In the shape optimization,the control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization,and then the corresponding calculation algorithm of boundary movement velocity field and the method of boundary shape adjustment for the boundary node are set up.Finding the fast look for orientation,the shape turns into best by the rational velocity assign.The effectiveness of the method is illustrated by example.

关 键 词：拓扑优化 B样条 形状优化 水平集方法 形状导数 

分 类 号：O241[理学—计算数学] TH122[理学—数学]