An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis
An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis
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DOI：
10.1016/j.cma.2014.12.014
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发表时间：
2015-03
影响因子：
7.2
通讯作者：
H. Nguyen-Xuan;G. Liu
中科院分区：
文献类型：
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作者：
H. Nguyen-Xuan;G. Liu
本文讨论了三次气泡函数在运动学定理框架内基于边缘的有限元法 (ES-FEM) 公式中的关键作用，用于预测结构的塑性倒塌载荷。我们证明了气泡函数可以通过非零系数 alpha 进行缩放，而体积锁定则被完全消除。基于这一发现，本方法被设计为具有非常小的值，并且气泡函数在单元的中心处最大。这可能导致统一分区的丧失。为了便于参考，本方法被称为α bES-FEM。本方法的显着优点在于对可在全塑性范围内发生的体积无锁定的严格处理。 α bES-FEM 通过使用三角形网格，工作效率很高。它实现了塑性极限分析包的简单性和计算效率。在 α bES-FEM 的情况下，锁定问题可以通过两种方案方便地解决：（1）在三角形单元的原始网格上用三次气泡函数丰富的通常分段线性位移，以及（2）通过与网格中的边缘相关的对偶网格的应变率投影算子。有限元极限分析的优化公式以二阶锥规划（SOCP）的形式编写。可以有效地利用成熟的内点求解器。使用少量积分点的α bES-FEM能够有效地解决大规模优化问题。此外，还导出了基于替代耗散指标的自适应网格划分程序，以进一步提高解决方案的质量，而无需显着增加模型的自由度数量。数值结果表明了该方法的鲁棒性。
This paper deals with critical roles of cubic bubble functions for the edge-based finite element method (ES-FEM) formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures. We show that the bubble function can be scaled by a non-zero coefficient alpha, while the volumetric locking is entirely eliminated. Based on this finding, the present method is designed, in a very small value, with a bubble function that is maximum at the center of the element. This can lead to the loss of the partition of unity. For easy reference, the present method is termed as α bES-FEM. The significant advantage of the present method lies in the rigorous treatment of the volumetric locking-free that can occur in the fully plastic range. The α bES-FEM works well with high efficiency by using triangular meshes. It achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses. In case of α bES-FEM, the locking issue can be solved conveniently by two schemes:(1) the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and (2) a projection operator of strain rates through a dual mesh associated with the edges in the mesh. The optimization formulation of finite element limit analysis is written in the form of a second-order cone programming (SOCP). The well-established interior-point solvers can be exploited efficiently. The α bES-FEM using a small number of integration points enables to solve the large-scale optimization problems efficiently. In addition, an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model. Numerical results show the robustness of the proposed method.