|نویسندگان||A Kaveh - MS Massoudi - MJ Massoudi|
|نشریه||Periodica Polytechnica. Civil Engineering|
|نوع مقاله||Full Paper|
|رتبه نشریه||علمی - پژوهشی|
|کشور محل چاپ||مجارستان|
Abstract. Formation of a suitable null basis for equilibrium matrix is the main part of finite elements analysis via force method. Foran optimal analysis, the selected null basis matrices should be sparse and banded corresponding to produce sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of null bases of finite element models (FEMs) consisting of rectangular plane stress and plane strain serendipity family 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. The efficiency of the present method is illustrated through three examples.
tags: Finite elements,Force method,Null basis,Flexibility matrix,Graph theory,Plane stress,Plane strain,Rectangular elements,Serendipity family elements