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基于一个含面内初应力薄板问题的修正的Hellinger-Reissner变分原理,导出了一个十二自由度矩形杂交应力弯曲板元。并首次将杂交应力模型用于求解各向同性以及加筋平板的弹塑性欧拉屈曲问题。计算中,将Sturm序列方法与0.618加载法相结合以确定临界应力。材料性质采用Stowell塑性屈曲理论及Ramberg-Osgood应力应变关系加以反映。 计算结果与解析解、实验值均符合良好。而且比多数已知有限元解精确。这表明,用杂交应力模型求解平板的弹塑性欧拉屈曲问题可行,方便,可以获得满意结果:本文导出的单元精度高、收敛快。
Based on a modified Hellinger-Reissner variational principle with an in-plane initial stress plate problem, a 12-degree-of-freedom rectangular hybrid stress bending plate element is derived. For the first time, the hybrid stress model was used to solve the elastoplastic Euler buckling problems for isotropic and stiffened plates. In the calculation, the Sturm sequence method is combined with the 0.618 loading method to determine the critical stress. The material properties are reflected by the Stowell plastic buckling theory and the Ramberg-Osgood stress-strain relationship. The calculated results are in good agreement with the analytical solutions and experimental values. And it is more accurate than most known finite element solutions. This shows that using the hybrid stress model to solve the elasto-plastic Euler buckling problem of flat plates is feasible and convenient, and satisfactory results can be obtained: The unit derived in this paper has high accuracy and rapid convergence.