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Efficient force method for tetrahedron finite element analysis using mathematical optimization technique

Maryam Daei (Department of Civil Engineering, University of Isfahan, Isfahan, Iran)
S. Hamid Mirmohammadi (Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran)

Engineering Computations

ISSN: 0264-4401

Article publication date: 18 April 2017




The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases vectors. As the null bases for an indeterminate structure are not unique, for an optimal analysis, the selected null bases should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrix. This paper aims to present an efficient method for the formation of optimal flexibility matrix of finite element models comprising tetrahedron elements via mathematical optimization technique.


For this purpose, a linear mixed integer programming model is presented for finding sparse solution of underdetermined linear system, which is correspond to sparse null vector. The charged system search algorithm is improved and used to find the best generator for formation of null bases.


The efficiency of the present method is illustrated through some examples. The proposed method leads to highly sparse, banded and accurate null basis matrices. It makes an efficient force method feasible for the analysis of finite element model comprising tetrahedron elements.


The force method, in which the member forces are used as unknowns, can be appealing to engineers. The main problem in the application of the force method is the formation of a self-stress matrix corresponding to a sparse flexibility matrix. In this paper, the highly sparse, banded and accurate null basis matrices gains by using mathematical optimization technique.



Daei, M. and Mirmohammadi, S.H. (2017), "Efficient force method for tetrahedron finite element analysis using mathematical optimization technique", Engineering Computations, Vol. 34 No. 2, pp. 447-470.



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