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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Reduction of excessive energy in the four-noded membrane quadrilateral element. Part Ⅱ: Near incompressibility and J_2 plasticity
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Reduction of excessive energy in the four-noded membrane quadrilateral element. Part Ⅱ: Near incompressibility and J_2 plasticity

机译：减少四节点膜四边形单元中的过多能量。第二部分：不可压缩性和J_2可塑性

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摘要

The elemental formulation presented in Part Ⅰ of this study [E. Paraskevopoulos, D. Talaslidis, Reduction of excessive energy in the four-noded membrane quadrilateral element. Part Ⅰ: Linear theory-compressible materials, Comput. Methods Appl. Mech. Engrg. 194 (2005) 3771-3796] is extended in a straightforward manner to problems with nearly incompressible materials and to J_2 plastic flow-problems. Sources of excessive energy resulting from the incompressibility constraint as well as the coupling between the deviatoric components of strain are examined and conclusions are drawn concerning the selection of appropriate approximations for the field variables. A modified version of the Hu-Washizu principle is employed that utilizes the orthogonality between deviatoric and volumetric terms and incorporates part of the plane strain conditions. Furthermore, satisfaction of the patch test is analytically verified. In deriving the weak form of the equations governing the J_2 plasticity problem, attention is focused on a straightforward extension of the linear problem without reference to additional postulates. In case of J_2 plasticity, the current formulation incorporates an important modification that leads to further simplifications: the continuous, linear functions employed for the approximations are replaced by the Heaviside function. Finally, results of numerical examples and comparisons with other formulations are presented.
机译：本研究的第一部分介绍了元素配方[E. Paraskevopoulos，D。Talaslidis，减少四节点膜四边形单元中的过多能量。第一部分：线性理论可压缩材料，计算。方法应用。机甲gr 194（2005）3771-3796]以直接的方式扩展到几乎不可压缩的材料和J_2塑料流动问题的问题。研究了由不可压缩性约束以及应变的偏分量之间的耦合所导致的过多能量的来源，并得出了关于为场变量选择适当近似值的结论。使用了Hu-Washizu原理的改进版本，该原理利用了偏项和体积项之间的正交性，并合并了部分平面应变条件。此外，通过分析验证了补丁测试的满意度。在推导控制J_2可塑性问题的方程的弱形式时，注意力集中在线性问题的简单扩展上，而不涉及其他假设。在具有J_2可塑性的情况下，当前的配方进行了重要的修改，从而导致进一步的简化：用于近似的连续线性函数被Heaviside函数代替。最后，给出了数值示例的结果以及与其他公式的比较。

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