Shakedown analysis of a hollow sphere by interior-point method with non-linear optimization
Shakedown analysis of a hollow sphere by interior-point method with non-linear optimization
复制标题
采用非线性优化内点法对空心球进行安定分析
DOI：
10.1016/j.ijmecsci.2020.105515
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发表时间：
2020-06
影响因子：
7.3
通讯作者：
Shao J. F.
中科院分区：
文献类型：
--
作者：
Zhang J;Oueslati A.;Shen W. Q.;De Saxce G.;Nguyen A. D.;Zhu Q. Z.;Shao J. F.
本工作通过基于梅兰定理的直接数值方法研究了多孔材料的安定安全域。考虑载荷域的临界加载路径而不是整个历史，将静态安定条件转化为以安定限制因子为目标函数的大尺寸优化问题，并离散化为由von Mises矩阵组成的三维模型。在空心球模型的极限分析中，我们考虑纯静水载荷和偏载荷来在虚拟弹性体中产生参考弹性应力，以捕获压缩/拉伸和剪切效应的效果。通过使用基于内点法的非线性优化器IPOPT，有效地解决了所提出的优化问题，不仅提供了安定极限载荷系数，而且还提供了极限状态的残余应力分布。将所建立的方法应用于轴对称和非轴对称循环加载以及两个自变量加载，以发现加载条件和固体基体特性对多孔介质（空心球）安定安全域的影响。对所得结果进行了说明，并与文献中的参考解决方案以及增量式逐步有限元计算的结果进行了充分比较。本方法已通过比较研究进行了访问和验证。
The shakedown safety domain of porous materials is investigated in this work by a direct numerical method based on Melan’s theorem. Considering the critical loading path of the load domain instead of the whole history, the statical shakedown condition is transformed to a large size optimization problem, of which the objective function is the shakedown limit factor, with the discretization of a three dimensional model composed of von Mises matrix. As in limit analysis of the hollow sphere model, we consider pure hydrostatic and deviatoric loads to produce the reference elastic stresses in the fictitious elastic body, for the purpose of capturing the effects of compressive/tensile and shear effects. By the use of a non-linear optimizer IPOPT based on the interior-point method, the proposed optimization problem is solved efficiently, providing not only the shakedown limit load factor, but also the distribution of residual stresses for the limit state. The established method is applied to axisymmetric and non-axisymmetric cyclic loadings, as well as the two independent variable loadings, in order to discover the influence of the loading condition and the solid matrix characteristics on the shakedown safety domain of porous medium (hollow sphere). The obtained results are illustrated and fully compared with reference solutions from literature and with the one from the incremental step-by-step FEM computations. The present method has been accessed and validated by the comparative study.
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影响因子：
7.3
作者：
M. A. Belouchrani;D. Weichert
通讯作者：
M. A. Belouchrani;D. Weichert
影响因子：
2.4
作者：
J. Mandel
通讯作者：
J. Mandel
DOI：
--
发表时间：
2008
期刊：
Algorithmic Oper. Res.
影响因子：
--
作者：
Igor Griva;D. Shanno;R. Vanderbei;Hande Y. Benson
通讯作者：
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DOI：
10.1016/j.ijsolstr.2005.06.042
发表时间：
2006-05
影响因子：
3.6
作者：
C. Bouby;G. Saxcé;Jean-Bernard Tritsch
通讯作者：
C. Bouby;G. Saxcé;Jean-Bernard Tritsch
DOI：
10.2307/3611266
发表时间：
1950
期刊：
--
影响因子：
--
作者：
R. Hill
通讯作者：
R. Hill