Development of Higher Order Shear element for the static analysis of composite lamina using mat lab

In this paper a higher order shear element, which is a 4 nodded quadrilateral element, is developed. This element is used for the static analysis of composite lamina. Using the Higher order shear deformation plate theory for basic displacement field equations, the B matrix, (Strain-Displacement relationship matrix) the D matrix (material matrix) and the resultant K (global stiffness matrix) are formulated. These B, D & K matrices were used in formulating the 4 nodded element with 3 degree of freedom at each node. This element was also formulated to incorporate 5 degrees of freedom per node to obtain increased accuracy in the analysis. MATLAB, a numerical analysis package, was used for the calculation of nodal displacements taking A. Ferreira [7] as basis for coding principles. The modeling was initially done for an isotropic material given by Chandraputla [5] then extending it for the composite lamina with different angles of orientations. Knowing the position of the quadrilateral in the coordinate system, geometrical dimensions, its material properties and the loads which it is being subjected to, the above said entity can be calculated. Developing a MATLAB code was meticulously done to make sure that all the formulations are rightly interpreted in the code. Eliminating rows and columns after removing corresponding constraints is one such example. This code is helpful in eliminating all the paper work that is needed to solve problems in FEM based on theory used and can obtain results as accurate and precise as possible. Complete terminology, sample problem included in this report ensures that any person novice to FEM and its formulation in MATLAB will understand the code and can successfully implement it for future purposes.