优化设计中单元最优剖分的数学模型和程序实现方法

用有限元法进行建筑物优化设计过程中,建筑物的形状和几何尺寸在不断变化.建筑物变化后,原来的单元会出现重叠或锐化畸形,计算结果就会失真.因此,必须重新调整节点坐标,改善单元形状.笔者提出的牵制覆盖法就是应用最优控制的数学模型获得网格单元的最优剖分,保证位移和应力计算结果的准确,最终实现建筑物的最优设计.

Method of Mathematical Model and Program in Optimal Unit Division of Optimal Design

When optimal designing a structure with finite unit method,the shape and geometry dimension of the structure will be changed gradually.After that,original unit will overlap and become sharp abnormality and the calculation result will be distorted.We must readjust coordinate of the node,then the shape of unit will be improved.In this article,the writer brings a new method named hold and cover Method,which can obtain optimal division of the grid unit with mathematical model of optimal control.The method can keep the precision of the result of the stress calculation and the displacement,and finally can get the optimal design of the structure.