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

CHEN Shenshen; HU Ying; ZHANG Wei; WANG Fangxin

doi:10.21656/1000-0887.450222

Volume 46 Issue 6

Jun. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(6): 791-799

CHEN Shenshen, HU Ying, ZHANG Wei, WANG Fangxin. A Cell-Based Smoothed Radial Point Interpolation Method for Upper Bound Limit Analysis[J]. Applied Mathematics and Mechanics, 2025, 46(6): 791-799. doi: 10.21656/1000-0887.450222

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

doi: 10.21656/1000-0887.450222

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

Received Date: 2024-07-31
Rev Recd Date: 2024-09-04
Publish Date: 2025-06-01

Abstract

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.

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References

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