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

国家自然科学基金 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

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: 45
- HTML全文浏览量: 11
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-31
- 修回日期: 2024-09-04
- 刊出日期: 2025-06-01

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

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

HTML全文

图 1 受内压的厚壁圆筒

Figure 1. A cylinder subjected to internal pressure

下载: 全尺寸图片幻灯片

图 2 b/a=2.0时厚壁圆筒的背景网格划分

Figure 2. The background mesh for the cylinder, b/a=2.0

下载: 全尺寸图片幻灯片

图 3 极限载荷数值解与解析解比较

Figure 3. Comparison of numerical limit loads with analytical solutions

下载: 全尺寸图片幻灯片

图 4 α_ir=0.5时厚壁圆筒的背景网格划分

Figure 4. The background mesh for the cylinder, α_ir=0.5

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图 5 Cook梁

Figure 5. The Cook beam

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图 6 Cook梁的背景网格划分

Figure 6. The background mesh for the Cook beam

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图 7 极限状态下的塑性耗散功率分布云图

注为了解释图中的颜色，读者可以参考本文的电子网页版本.

Figure 7. The plastic dissipation work distribution in the limit state

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表 1 厚壁圆筒的极限载荷数值解

Table 1. Numerical limit loads for the cylinder

b/a	analytical solution	the present	error/%
2.0	0.800 4	0.801 8	0.174 9
2.5	1.058 0	1.058 8	0.075 6
3.0	1.268 6	1.273 5	0.386 3
3.5	1.446 6	1.453 5	0.518 7
4.0	1.600 8	1.605 7	0.306 1

下载: 导出CSV

表 2 不同畸变系数下厚壁圆筒的极限载荷

Table 2. Limit loads of the cylinder with different irregularity factors

irregularity factor	analytical solution	the present	error/%
0.1		0.801 8	0.174 9
0.2		0.803 5	0.387 3
0.3	0.800 4	0.806 6	0.774 6
0.4		0.807 5	0.887 1
0.5		0.808 3	0.987 0

下载: 导出CSV

表 3 Cook梁的极限载荷数值解

Table 3. Numerical limit loads of the Cook beam

Ciria et al. ^[27] uniform/adaptive mesh	Le et al. ^[26]	Zhou et al. ^[2] Laplace/Sibson	the present
0.396 4/0.401 6	0.395 6	0.400 8/0.399 5	0.396 2

下载: 导出CSV

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