A Simplified Kinematic Method for 3D Limit Analysis
A Simplified Kinematic Method for 3D Limit Analysis
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3D 极限分析的简化运动学方法
DOI：
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发表时间：
2016
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：
J. Hambleton;S. Sloan
极限分析的运动学（上限）方法是一种强大的技术，用于评估通常非常接近真实极限载荷的极限载荷的严格界限。虽然二维（例如平面应变）问题的通用计算技术已经很成熟，但适用于三维问题的方法相对不发达且未得到充分利用，这在很大程度上是由于解析解计算的繁琐性以及数值方法所需的大量计算时间。本文提出了一种用于三维极限分析的简单公式，该公式考虑了服从莫尔-库仑屈服条件的材料和由平面速度不连续性分隔的滑动刚性块组成的塌陷机制。该方法的一个关键优点是它对最少数量的未知数的依赖，可以大大减少处理时间。尽管扩展到其他几何形状很简单，但本文特别关注四面体块。对于任意但固定的块排列，计算产生最小上限的未知块速度的过程被表示为二阶锥规划问题，可以使用广泛可用的优化代码轻松解决。本文以一个简单的例子和关于工作扩展的评论作为结尾。
The kinematic (upper bound) method of limit analysis is a powerful technique for evaluating rigorous bounds on limit loads that are often very close to the true limit load. While generalized computational techniques for two-dimensional (e.g., plane strain) problems are well established, methods applicable to three-dimensional problems are relatively underdeveloped and underutilized, due in large part to the cumbersome nature of the calculations for analytical solutions and the large computation times required for numerical approaches. This paper proposes a simple formulation for three-dimensional limit analysis that considers material obeying the Mohr-Coulomb yield condition and collapse mechanisms consisting of sliding rigid blocks separated by planar velocity discontinuities. A key advantage of the approach is its reliance on a minimal number of unknowns, can dramatically reduce processing time. The paper focuses specifically on tetrahedral blocks, although extension to alternative geometries is straightforward. For an arbitrary but fixed arrangement of blocks, the procedure for computing the unknown block velocities that yield the least upper bound is expressed as a second-order cone programming problem that can be easily solved using widely available optimization codes. The paper concludes with a simple example and remarks regarding extensions of the work.