A study on improvement of the trial function in p-Ritz method

Abstract

In the p--Ritz method using a power function for the basis functions, effect of round-off errors in the erasing operation is increased because condition number of the stiffness matrix is large. The purpose of this study is to improve the trial function of p--Ritz method in order to apply this method to the bending analysis of plates. Orthogonal polynomials, such as the Legendre polynomial or Chebyshev polynomials of first kind is used for the basis functions. Furthermore, in selecting the displacement field, all terms of the expansion terms up to given number are used without omitting the higher order terms. The improved p--Ritz method is applied to the bending and free vibration analysis of plates based on the first order shear deformation theory, the accuracy and applicability of this method is investigated.