结构静态拓扑重分析的迭代组合近似方法

AN ITERATIVE COMBINED APPROXIMATION APPROACH FOR STRUCTURAL STATIC REANALYSIS OF TOPOLOGICALMODIFICATIONS^1

提出一种拓扑修改的静态重分析的迭代组合近似方法.这种方法基本上是两步法。首先,将新增加的自由度通过Guyan缩减方法凝聚到原始自由度上,形成凝聚方程.其次,用迭代组合近似方法求出原始自由度的近似位移,从而求出原结构自由度的位移.新增加自由度的位移可以通过恢复得到。通过板结构的加筋布局优化设计的数值例子表明,该方法对拓扑修改较大时仍可得到满意的结果。

This paper presents an iterative combined approximation (ICA) approach for structural static reanalysis of all types of topological modifications. The proposed procedure is basically an approximate two step method. First, the newly added degrees of freedom (DOFs) are assumed to be linked to the original DOFs of the modified structure by means of the Guyan reduction so as to obtain the condensed equation. Second, the displacements of the original DOFs of the modified structure are solved using the ICA approach. And the displacements of the newly added DOFs resulting from topological modification can be recovered. In order to illustrate the application of the present method, the layout optimal design of stiffeners in the plate-shell structure is given. In the layout optimization, the strain energy sensitivity of the element and the rejection ratio are introduced. In each iteration, a number of elements may be deleted. To save computational effort, the ICA is used to perform the reanalysis to update the modified displacements of the structure. The results show that the ICA method is effective for structural static reanalysis of the topological modifications oven though the large topological modifications are made, and it is easy to implement on a computer.