This paper investigates nonlinear damage response and ultimate collapse of laminates under in-plane and lateral pressure loadings. The in-plane loading was in the form of end-shortening strain, while the lateral pressure was sinusoidal. The plates had initial geometric imperfection to which simply-supported boundary conditions were applied. Ritz techniques with nonlinear strain terms in kinematic relations as well as the first-order shear deformation theory were applied. Hashin and Rotem failure criteria were used for failure analysis. Two models were also employed for degradation of material properties in the plates. The complete ply degradation model was implemented along with the ply region degradation model, in which stiffness reduction was applied only to one region of the ply in which failure had occurred. Note that the stiffness degradation after the failure was investigated as both instantaneous and linear models. In both complete ply and region ply degradation models with instantaneous degradation of material properties, at any location in a ply or region, which has exceeded the given stress criterion, the corresponding stiffness properties are instantaneously degraded throughout that ply or region but with linear material degradation model, the stiffness diminishes gradually and linearly. Finally, the results were then validated against the findings of different references as well as finite element analysis. According to the results, it was seen that in the ply region degradation model, last ply failure loads are generally larger than those of the complete ply degradation model.

中文翻译：

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使用线性材料退化模型和半解析技术预测不完美层压板的非线性损伤响应

本文研究了平面内和横向压力载荷下层压板的非线性损伤响应和最终坍塌。面内载荷为端部缩短应变形式，而侧向压力为正弦曲线。这些板具有初始几何缺陷，对其应用了简支边界条件。应用了运动学关系中具有非线性应变项的 Ritz 技术以及一阶剪切变形理论。Hashin 和Rotem 失效准则用于失效分析。还采用了两个模型来降低板中的材料特性。完整的层退化模型与层区域退化模型一起实施，其中刚度降低仅应用于发生失效的层的一个区域。请注意，失效后的刚度退化作为瞬时模型和线性模型进行了研究。在具有材料特性瞬时退化的完整层和区域层退化模型中，在已超过给定应力标准的层或区域中的任何位置，相应的刚度特性在整个层或区域中瞬时退化，但具有线性材料退化模型中，刚度逐渐线性减小。最后，根据不同参考文献的发现以及有限元分析对结果进行了验证。根据结果​​，可以看出在层区退化模型中，最后一层失效载荷通常大于完全层退化模型的载荷。