# A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems

Chen, Haofeng and Shu, D.W. (1999) A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems. International Journal of Pressure Vessels and Piping, 76 (2). pp. 105-112. ISSN 0308-0161 (https://doi.org/10.1016/S0308-0161(98)00130-6)

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## Abstract

The determination of lower bound limit load of 3-D structures is by no means an easy task, especially for complex configurations and loading systems. In our previous work, a numerical method of upper bound limit analysis for 3-D structures with multi-loading systems was proposed. This method combines FEM and mathematical programming technique in an iterative procedure. In the present article, on the basis of the nature of the iterative procedure for upper bound limit analysis, the statically admissible stress fields, which satisfies the equilibrium equation and boundary conditions, are constructed using some intermediate variables obtained by upper bound limit analysis procedure. Moreover, a mathematical programming formulation is set up for the static limit analysis of 3-D structures under multi-loading systems and a direct iterative algorithm used to determine the lower bound limit load multiplier is proposed, which depends on the static theorem of plasticity. The numerical examples are given to demonstrate the applicability of the procedure.

#### ORCID iDs

Chen, Haofeng ORCID: https://orcid.org/0000-0001-6864-4927 and Shu, D.W.;
• Item type: Article 36398 DateEvent1999Published mathematical programming, iterative algorithm, limit analysis , loading path , Mechanical engineering and machinery, Mechanics of Materials, Materials Science(all), Mechanical Engineering Technology > Mechanical engineering and machinery Faculty of Engineering > Mechanical and Aerospace Engineering Pure Administrator 14 Dec 2011 11:37 06 Jan 2024 18:30 https://strathprints.strath.ac.uk/id/eprint/36398