|نویسندگان||A Kaveh - MS Massoudi|
|نشریه||International Journal of Civil Engineering|
|نوع مقاله||Full Paper|
|رتبه نشریه||علمی - پژوهشی|
|کشور محل چاپ||ایران|
Abstract. 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.
tags: Force method,Flexibility matrix,Graph theory,Three dimensional elements,Tetrahedron elements,Higher order elements,Finite element method,Null basis matrix