弹性薄壳大变形分析的杂交应力法

本文基于增量余能原理,导出了用于板壳几何非线性分析的假定应力杂交模型。根据单元体边界和内部位移的协调内插以及满足单元体内应力平衡的应力分布假定,列出了有限元的公式,而最后的矩阵公式中只包含节点的未知位移。由此我们建立了3节点、15个自由度的三角形扁壳单元。考虑到计算量的原因,我们对这种单元的应力平衡条件进行了简化处理,仅采用部分满足应力平衡方程的非一致模式。有关公式都是在当前的拉格朗日坐标系统中建立的。数值计算结果表明,用杂交应力模式来分析板壳结构的大变形是很有效的。

Large Deflection Analysis of Thin Elastic Shells by Hybrid Stress Method

Based on the principle of incremental complemental energy,a stress hybrid model is developed for the geometrically nonlinear analysis of plates and shells. According to the compatibility of both interior and boundary displacements for an element and the assumption of the stress distribution satisfying the stress equilibrium at the interior of the element,we derive finally the finite element formulas in matrix which include only the nodal unknown displacements.Then, a three-node triangular shallow shell element with fifteen degrees of freedom is established.Eor the convenience in numerical solution,we simplify the stress equilibrium equation of the shell element,and utilize only an inconsistent model satisfying partially the stress equilibrium equation.Formulas about the shell element are derived in the updated Lagrangian coordinate system.Numerical examples demonstrate that the stress hybrid model used to analyse the large deflection of plates and shells is very efficient.