基于互补模型的弹塑性桁架结构灵敏度分析过程

提出了一个用于弹塑性结构灵敏度分析的方法,称为NCP函数法。通过引入NCP函数,弹塑性结构分析的互补模型被等价为方程组形式;利用直接法对等价的方程组模型关于设计变量直接求导,建立了用于弹塑性灵敏度分析的线性方程组模型。新的灵敏度分析模型精确刻画了材料性质发生变化时灵敏度系数的不连续性,并避免了通过迭代过程来确定灵敏度系数的跳跃量。针对桁架结构的数值试验显示了算法的特点及其有效性。

DESIGN SENSITIVITY ANALYSIS OF ELASTOPLASTIC TRUSS STRUCTURES BY COMPLEMENTARITY FORMULATION

A computational procedure named NCP function method for sensitivity analysis of elastoplastic structures is developed based on the complementarity formulation of elastoplastic structural analysis. By introducing the NCP function, a system of nonlinear equations is formulated for the complementary node. The design sensitivity formula of elastoplastic structures is derived by directly differentiating the nonlinear equations with respect to the design variables. Discontinuities of the design sensitivity coefficients at material transition points can be accurately described, and the iterative procedures to compute the jumps of the sensitivity coefficients are no longer needed in the newly proposed sensitivity analysis model. Numerical results demonstrating the validity of the approach are reported.