#MATLAB TRIGONOMETRIC SYSTEM OF EQUATIONS SOLVER CODE#

#MATLAB TRIGONOMETRIC SYSTEM OF EQUATIONS SOLVER CODE#

In this code the entire stiffness matrix with all zero terms is stored in computer memory and then the Gaussian elimination procedure is used to solve the resulting system of linear equations. Implementation of Efficient FE solver in MatlabР”Р‡or solving the problem described above the Matlab code presented in the book by Ferreira is used. Dependence of the shear force Qy = Qx at the corner y = 0, x = 0 ofР”Р„ll these results suggest that having the mesh with large number of elements is strongly desired in the analysis of the simply-supported plate, especially in case of the plate with SS-B type of boundary conditions. Indeed, with 150-200 elements along each side of the plate we can obtain a reasonably good approximation to the value of the shear force at the corner.Р”Тђ0 100 150 200 250 300 number of elements along the sideР”Р‡ig. We see here that situation with the convergence of the shear force results is slightly better compared to the shear force at the center of the side. Zero, but for the SS-B plate this force is not zero. For the SS-A plate the shear force is equal to 3 shows the shear force Qy at the corner of the plate y = 0, x = 0. The square plate, subjected to uniform transverse pressure of magnitude 1, on the number of elementsР”Р‡ig. Dependence of the shear force Qy at the center of the side y = 0 of These are SS-A and SS-B types of boundary conditions and they are different in how the angles of rotations Р”РЋ, U^y^ 1, shear force is shown for y=0, x=1/2Р”В 50 100 150 200 250 300 350 400 number of elements along the sideР”Р‡ig. In we analyzed bending moments in simply-supported plate and we showed that for this type of plate two kinds of boundary conditions are possible in case one uses the Mindlin plate theory. For better accuracy of the solution for moderately thick and thick plates it is recommended to use Mindlin plate theory. In contrast, in the theory of thin plates (Kirchhoff plate theory) the vertical element of the plate always remains perpendicular to the mid-surface of the plate and therefore the shear deformations are zero. Recall that in the theory of thick plates (Mindlin plate theory) the transverse normal can rotate in such a way that after rotation it does not remain perpendicular to the mid-surface of the plate and thus the shear deformations are not zero. Various extensions of the classical theory can be found in references. Keywords: simply-supported plate, Mindlin plate theory, sparse solver, Matlab, finite element methodР”В¬lassical theory of thick plates and plates of moderate thickness is presented in references. The performance of this solver is so good that even for fine meshes considered the CPU time is small enough. This solver is tested on fine meshes consisting of a large number of linear rectangular finite elements.

Rogacheva Moscow State Civil Engineering University, MoscowР”Р„bstract: In this paper we describe efficient Matlab-based implementation of the finite element solver for the problem of bending of Mindlin plates. РїВ»С—Fast Matlab-based Finite Element Solver for the Problem of Bending ofР”Р„lexander P.

Matlab trigonometric system of equations solver