Numerical solution of Lower bound theorem

DOI

10.2991/978-94-6463-316-0_23How to use a DOI?

Keywords

Lower bound theorem; Numerical solution; Node equilibrium equations; Limit load; Plastic stress field; Degree of relative freedom

Abstract

A numerical solution for solving plastic stress field based on the lower bound theorem is proposed in this paper. The method uses the node equilibrium equations rather than the element equilibrium equations. The equilibrium differential equations over the area of element around the node are transformed into the equilibrium integral equations along the boundary by Green’s theorem. A linear programming model is developed with the variables of nodes stresses, linearized objective functions, equilibrium equations, stress boundary conditions and yield criteria constraints. The lower bound limit load and plastic stress field can be computed from the model. The further analysis shows that it is necessary only for the element equilibrium equations to introduce the node unique to a particular element, which will cause the model suitable only for the lower bound limit load, not for the plastic stress field. For the node equilibrium equations, it is not necessary to introduce the node unique to a particular element. The model with the node equilibrium equations is suitable for both the lower bound limit load and the plastic stress field. One example for the lower bound limit load and the plastic stress field illustrates the capability of the numerical solution proposed in this paper.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Hao Wu
AU  - Zhipei Zhang
PY  - 2023
DA  - 2023/12/14
TI  - Numerical solution of Lower bound theorem
BT  - Proceedings of the 2023 5th International Conference on Civil Engineering, Environment Resources and Energy Materials (CCESEM 2023)
PB  - Atlantis Press
SP  - 201
EP  - 218
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-316-0_23
DO  - 10.2991/978-94-6463-316-0_23
ID  - Wu2023
ER  -