finite element method IMPORTANT QUSTIONS

2019

This paper is concerned with the analysis of simply supported beam using MATLAB programming language and structural analysis program SAP2000. The beam was discretized into rectangular elements using finite element method. Three patterns of different dimensions and numbers of rectangular elements were used to verify the results of vertical displacements and stresses obtained by MATLAB and SAP 2000.The development of four noded isoparametric quadrilateral membrane elements in MATLAB programming language is presented. The membrane elements developed are plane strain condition. The considered patterns were analyzed as shell elements using SAP2000. A finite element program is also developed using MATLAB to check the accuracy of the developed elements.

An analysis for programing a 20 by 20 rectangular nine-node element in the finite element framework is presented linearly. The main goals are computation the stress and strain planes. Handy solution is indicated for a simple geometry. Then, the objectives of the major geometry are obtained through programing in Matlab software. Apparently, the important aspects comprise nodal displacements, deformation and stiffness matrices, nodal forces and stress and strain planes in this investigation. The methods applied in the procedure are based on Lagrangian family, explicit isoparametric systems and Gaussian function. First of all, the interpolation polynomials for General Lagrange solid nine-node element have been carried out and it contributes to the nodes to be arbitrarily along the corresponding edges. Then, the displacement vector is determined through finite elements method. Afterwards, the stiffness matrix is obtained by the integration from shape functions and displacement matrix an...