数学规划加权残值法分析薄板与薄壳的几何非线性问题  

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

作　　者：焦永树[1] 赵志岗[2] 

机构地区：[1]河北工业大学动力机械工程系,天津300132 [2]天津大学力学与工程测试系,天津300072

出　　处：《固体力学学报》1997年第1期17-24,共8页Chinese Journal of Solid Mechanics

摘　　要：使用数学规则加权残值法（MP－MWR）分析了薄板大挠度及薄亮的非线性稳定问题．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，首先得到均布载荷四边商支方极中心挠度的最小小界及最大下界，经典Levy解位于其间，其次，文中首次揭示了薄壳非线性平衡方程单调性的"逆变"现象，探讨了用MP－MWR及"逆变"现象确定结构跳跃点的可能性，为计算其临界载荷提供了一个新方法。若取最小上界及最大下界的平均值作为近似解可用较少的工作量得到误差界可知的高精度计算结果．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.

关 键 词：数学规划 加权残值法 薄板 薄壳 几何非线性 

分 类 号：O343[理学—固体力学]