极限上限分析的区域光滑径向点插值法

陈莘莘; 胡英; 张玮; 王方鑫

doi:10.21656/1000-0887.450222

极限上限分析的区域光滑径向点插值法

doi: 10.21656/1000-0887.450222

陈莘莘^1, ,,
胡英¹,
张玮¹,
王方鑫²

1. 华东交通大学土木建筑学院，南昌 330013;
2. 扬州大学建筑科学与工程学院，江苏扬州 225127

基金项目:

国家自然科学基金(12172131；12162014)；江西省主要学科学术和技术带头人培养计划(20225BCJ22010)；江苏省自然科学基金(BK20220554)

详细信息

作者简介:
陈莘莘（1975—），男，教授，博士(通讯作者. E-mail: chenshenshen@tsinghua.org.cn).

通讯作者:
陈莘莘（1975—），男，教授，博士(通讯作者. E-mail: chenshenshen@tsinghua.org.cn).

中图分类号: TB115
计量
- 文章访问数: 10
- HTML全文浏览量: 2
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-31
- 修回日期: 2024-09-04
- 网络出版日期: 2025-06-30

A Cell-Based Smoothed Radial Point Interpolation Method for Upper Bound Limit Analysis

1. School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, P.R.China;
2. College of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, P.R.China

Funds:

The National Science Foundation of China(12172131；12162014)

摘要

摘要: 基于极限分析的上限定理，建立了用区域光滑径向点插值法进行理想刚塑性结构极限分析的整套求解算法.为了能方便地施加本质边界条件，采用径向点插值法构造机动容许的速度场.通过引入广义梯度光滑技术，将复杂的域内积分转换为简单的光滑域边界积分，避免了对形函数的求导.考虑了材料的塑性不可压条件，并针对平面应力和平面应变问题采用不同方式进行处理.将极限上限分析问题归结为满足一系列等式约束的塑性耗散功率最小化问题，从而可采用标准的二阶锥规划对该问题进行求解，这样既提高了求解效率，又提高了求解精度.数值算例结果表明，该文所提方法能对理想刚塑性结构的极限载荷乘子给出令人满意的结果，并且计算结果对网格畸变十分不敏感.
- 无网格法 /
- 区域光滑径向点插值法 /
- 极限上限分析 /
- 广义梯度光滑技术 /
- 二阶锥规划
Abstract: Based on the upper bound theorem of limit analysis, a solution procedure for limit analysis of structures made of rigid-perfectly plastic material was proposed with the cell-based smoothed radial point interpolation method (CS-RPIM). To impose the essential boundary conditions directly, the RPIM was utilized to construct a kinematically admissible velocity field. The plastic incompressibility conditions of plane stress and plane strain problems were treated respectively with 2 different methods. The upper bound problem was formulated mathematically through minimization of the dissipation power subject to a set of equality constraints and this minimization problem can be transformed into a standard 2nd-order cone programming one, which can be easily solved with the primal-dual interior point method. Numerical examples demonstrate that, the proposed method can provide reasonable and satisfactory upper bound limit load multipliers for rigid-perfectly plastic structures. In addition, the computational results are very insensitive to the mesh distortion.
- meshless method /
- cell-based smoothed radial point interpolation /
- upper bound limit analysis /
- generalized gradient smoothing technique /
- 2nd-order cone programming

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