数学规划加权残值法分析薄板与薄壳的几何非线性问题

使用数学规划加权残值涯分析了薄板大挠度及薄壳的非线性稳定问题。在两者应变协调方程严格满足的情况下,论证并利用平衡方程的单调性,建立数学规划问题,首先得到无布载荷四边简支方板中心挠度的最小上界及最大下界,经典Ｌｅｖｙ解位基其间。

ANALYSIS OF GEOMETRICALLY NONLINEAR PROBLEMS OF PLATE AND SHELL BY MATHEMATICAL PROGRAMMING MWR

Mathematical programming MWR is applied to study the problems of large deflection of thin plate and nonlinear stability of thin shell. While the compatibility equations in both cases are satisfied, the monotonicities of the equilibrium equations are analyzed and the corresponding mathematical programming problems are established. First, for a square plate hinged at four edges being subjected to uniformly distributed load, the center deflections of minimum upper bound and maximum lower bound are obtained for the first tirne. It shows that the Levy's solution is in the bound. Second, the "reversal" phenomenon in monotonicity in the nonlinear equilibrium equation of thin shell is revealed. The possibility of determining the jumping point of a structure according to MP-MWR and the "reversal" phenomenon is investigated and a new method is proposed for calculating the critical load of a structure.Taking the mean value of minimum upper bound and maximun lower bound as the approxi-mate solution, we can obtain a more accurate and error-known result with less arnount of work.