基于自适应多点约束逼近的二级结构优化方法研究

 本文对结构优化设计提出了一种二级逼近方法。基于优化过程中所得到的若干点上临界约束函数值及其一阶导数,构造出显式近似函数逼近原约束函数。该近似函数的非线性程度由自适应方法控制,使之在其展开域内接近真实约束函数;由此建立逼近原结构优化问题的第一级显式非线性序列近似问题。为处理其中每个子问题,建立逼近它的第二级序列近似问题,然后采用对偶方法对其求解。算例表明本文方法具有收敛迅速稳定的特点。

TWO-LEVEL STRUCTURE OPTIMIZATION METHOD BASED ON ADAPTIVE MULTI-POINT CONSTRAINT APPROACHING

A two-level approaching method for structural optimal design is proposed. Based upon the values and the first-order derivatives of the critical constraint functions at the points obtained in the procedure of optimization, the explicitly approximate functions approaching the primal constraint functions have been made up, and the nonlinearity of them is controlled to be near to those of the constraint functions in their expansive domains with a adaptive method, from the above principle the first-level nonlinearly explicit approximate problems approaching the primal problem are established. In order to handle each of them, the second-level approximate problems is formed, which are then solved by using dual theory. The results of given examples show that the present method is of a rapidly stable convergence.