INTRODUCTION OF SHELL ELEMENT FOR FINITE ELEMENT ANALYSIS USING GRAPH-THEORETICAL FORCE METHOD

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Karimi I.; Masoudi M.S.

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Journal Paper

Paper Information

Journal: International Journal of Optimization in Civil Engineering Year:2024 | Volume:14 | Issue:1 Page(s): 115-138

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Information Journal Paper

Title

INTRODUCTION OF SHELL ELEMENT FOR FINITE ELEMENT ANALYSIS USING GRAPH-THEORETICAL FORCE METHOD

Author(s)

Karimi I. | Masoudi M.S. | Issue Writer Certificate

Keywords

Finite element force method

graph theory

shell element

null basis matrix

flexibility matrix.

Abstract

The main part of finite element analysis via the force method involves the formation of a suitable null basis for the equilibrium matrix. For an optimal analysis, the chosen null basis matrices should exhibit sparsity and banding, aligning with the characteristics of sparse, banded, and well-conditioned flexibility matrices. In this paper, an effective method is developed for the formation of null bases of finite element models (FEMs) consisting of shell elements. This leads to highly sparse and banded flexibility matrices. This is achieved by associating specific graphs to the FEM and choosing suitable subgraphs to generate the self-equilibrating systems (SESs) on these subgraphs. The effectiveness of the present method is showcased through two examples.

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