AUTOMATED RITZ METHOD FOR THE ANALYSIS OF LAMINATED ANISOTROPIC PLATES

Most of the available functional form solutions of anisotropic plates are available for cases involving simple boundary conditions such clamped and simply supported edges. The proposed method which is based on the well-known Ritz method offers an alternative semi-analytical solution in terms of simple polynomials. As per Ritz method, the trial functions are required to satisfy the essential (geometric) boundary conditions and therefore free edges can be accommodated by the method. However, large number of polynomials is needed in order to get the required convergence which cannot be handled by the standard Ritz method due to the huge number of symbolic integrals to be computed. This difficulty is overcome by casting the method in a matrix form the elements of which are derived using indicial notation and integrated using a symbolic Mathematica code. The code is capable of accommodating a large number of polynomials as required by the accuracy and convergence of the solution. Several numerical examples are presented to verify the accuracy and efficiency of the proposed method.