渐进优化法的一种高阶棋盘格式抑制方法

A kind of high ordered checkerboard pattern suppressing algorithm of progressive optimization method

棋盘格现象是固定有限元网格的连续体结构在拓扑优化中一种常见的现象,特别是用一阶有限单元建模时。已有的研究表明,棋盘格现象是有限元分析误差所致。在渐进结构优化设计的各种优化判据下都存在这一现象。棋盘格的存在使优化结果的解释变得困难,后处理时提取适合于加工的几何模型变得非常困难。为了避免棋盘格现象,在文献[13]的灵敏度再分配的过滤技术基础上,提出了一种灵敏度高阶再分配的过滤技术。这种高阶过滤技术不需要对有限元网格进行重新划分,也不需要增加结构重分析的计算量。给出较多的算例,证明了该方法的实用性。

The phenomenon of checkerboard is a kind of common phenomenon in structural topologic optimization of continuous body of fixed finite element lattice especially when modeling with the first ordered finite element. The existed research shows that the checkerboard phenomenon is caused by the analytical error of finite element. This phenomenon is all existed under various kinds of optimization criterion of the progressive structural optimization design. The existence of checkerboard lattice let the interpretation of the optimal results become difficult, and let the collection of geometric model suitable for processing during post-treatment become very difficult. For the sake of avoiding the phenomenon of checkerboard lattice, a kind of filtration technique for the high ordered redistribution of sensitivity was put forward on the basis of filtration technique of sensitivity redistribution in document[13]. This kind of high ordered filtering technique needs neither carrying out re-differentiation to the finite element lattice nor increasing the amount of calculation for reanalysis of structure. More computational examples have been presented and the practicality of this algorithm was verified.