拉压不同模量弹性结构分析中的对称性问题

Symmetry in elastic structural analysis based on different elastic moduli in tension and compression

基于对称和反对称问题中应力和位移分量满足的必要条件,分析了主方向上应力状态的对称和反对称特点,并用算例加以验证。研究表明材料的非线性导致拉压不同模量弹性结构的主应力的反对称性改变而对称性仍旧保持;同时,将复杂问题分解为对称和反对称问题并通过叠加原理获得解答的方法也会失效。由于不同模量弹性理论将其本构关系建立在主方向上,因此基于主方向的应力状态分析是研究的关键。

Symmetrical characteristics of elastic structures will change when different tension-compression moduli was employed. Based on the necessary conditions satisfied by stress and displacement, we analyzed symmetry and antisymmetry under the principal stress state using a computational example. The research indicates that antisymmetry of elastic structures in the magnitude and direction of principal stress will change due to the nonlinearity of materials while symmetry still holds, and the superposition theorem will fail when a complex problem is resolved into symmetric and antisymmetrie components. It is concluded that the principal stress state due to the bimodular constitutive model based on principal direction is key.