用边界元方法和复合形法求解三维结构的下限安定载荷

COMPUTATION OF LOWER BOUND SHAKEDOWN LOADS OF 3-D STRUCTURES BY BEM AND THE COMPLEX METHOD

基于安定分析的静力定理,建立了用常规边界元方法进行三维理想弹塑性结构安定分析的整套求解算法。下限安定分析所需的弹性应力场直接由边界元方法求出,所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,这些自平衡应力场基矢量通过边界元弹塑性迭代计算获取。安定分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题并通过复合形法直接求解。计算结果表明了算法的有效性。

Based on the lower bound theorem of shakedown analysis, a solution procedure for shakedown analysis of three-dimensional elastoplastic structures has been established using conventional boundary element method (BEM). The elastic stress field for lower bound shakedown analysis is computed directly by 3-D BEM. The self-equilibrium stress field is constructed by the linear combination of several self-equilibrium basis vectors which can be computed by elastic-plastic incremental iteration of 3-D BEM analysis. The lower bound shakedown analysis problem is finally reduced to a series of nonlinear programming sub-problems with relatively few optimal variables. The complex method is used to solve effectively the nonlinear programming sub-problems. Numerical results show the effectiveness of the present solution algorithm.