R-adaptivity in Limit Analysis
R-adaptivity in Limit Analysis
复制标题
极限分析中的 R 自适应
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Sloan
中科院分区：
文献类型：
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作者：
José J. Muñoz;J. Hambleton;S. Sloan
直接法的目的是找到最大的载荷系数，由塑性材料制成的域可以承受之前，经历完全崩溃。它的解析解可以作为一个约束最大化问题，这是通过采取适当的离散化的相关领域，如应力或速度场计算解决。实际的离散解强烈依赖于这样的离散化，它由一组节点、元素和插值类型定义。在这里，我们诉诸于一个自适应的策略，旨在扰动的节点的位置，以提高离散最大化问题的解决方案。当考虑节点的位置时，优化问题变得高度非线性。我们近似这个问题作为两个交错的线性问题，一个写在应力变量（下限问题）或速度变量（上限问题），另一个相对于节点的位置。以这种方式，我们表明，对于一些简单的问题，计算的负载因子可以进一步提高，同时保持恒定数量的元素。
Direct methods aim to find the maximum load factor that a domain made of a plastic material can sustain before undergoing full collapse. Its analytical solution may be posed as a constrained maximisation problem, which is computationally solved by resorting to appropriate discretisation of the relevant fields such as the stress or velocity fields. The actual discrete solution is though strongly dependent on such discretisation, which is defined by a set of nodes, elements, and the type of interpolation. We here resort to an adaptive strategy that aims to perturb the positions of the nodes in order to improve the solution of the discrete maximisation problem. When the positions of the nodes are taken into account, the optimisation problem becomes highly non-linear. We approximate this problem as two staggered linear problems, one written in terms of the stress variable (lower bound problem) or velocity variables (upper bound problem), and another with respect to the nodal positions. In this manner, we show that for some simple problems, the computed load factor may be further improved while keeping a constant number of elements.