考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

Elasto-Plastic Postbuckling Analysis of Orthotropic Plates Including Damage Effects

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程.基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解.数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响.数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略.

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion which is related to the spherical tensor of stress was proposed to describe the mixed hardening of damaged orthotropic materials, and the dimensionless form of which is isomorphic with the Mises criteflon for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations were established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates including damage effect were obtained, and the equations were solved by the finite difference method and iteration method. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.