减缩积分和假设应力法在消除自锁上的等效性

Equivalence of Reduced Integration and Assumed Stress Method on Eliminating Locking.

本文以板弯曲单元为例,将位移法和应力杂交法导得的有限元平衡方程写成统一的形式,(K_b+αK_s)q=F,指出减缩积分和假设应力法消除自锁的原因是一致的,即使剪切应变能引入的约束K_(s_q)=0为Kirchhoff约束。并通过对自由度和约束的讨论给出产生零能模式的条件。最后以数例证明减缩积分和假设应力法避免自锁的等效性。本文对构造有效的通用单元有一定的指导意义。

The unified formulae of the finite element equilibrium equations, (Kb+αKs) q = F, is derived for both displacement method and hybrid stress method. It is demonstrated that the reason of eliminating locking of reduced integration and assumed stress method is identical, i.e., the constraints infroduced by shear-strain energy Ksq = 0 only give rise to Kirchhoff constraints. The conditions for existence of zero energy modes are given via detection of degree of freedom and constraints. Finally, numerical examples are given to present the equivalenee of reduced integration and assumed stress method on eliminating locking. The paper may be guidance for constructing efficient general elements.