RT - Journal Article
T1 - Efficient finite element analysis using graph-theoretical force method tetrahedron elements
JF - IJCE
YR - 2014
JO - IJCE
VO - 12
IS - 2
UR - http://ijce.iust.ac.ir/article-1-1123-en.html
SP - 249
EP - 269
K1 - hree dimensional elements
K1 - Tetrahedron elements
K1 - Higher order elements
K1 - Finite element method
K1 - Force method
K1 - Null basis matrix
K1 - Flexibility matrix
K1 - Graph Theory.
AB - Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method.
LA eng
UL http://ijce.iust.ac.ir/article-1-1123-en.html
M3
ER -