Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial di...

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

A new method (the sinh–sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and...

This paper investigates natural frequencies of free transverse vibrations prestressed beams, and the governing equations vibration in related literatures are discussed corrected. The differential quadrature methods (DQ) applied directly to corrected get values frequency numerically. Under simple supported boundary conditions, model beam numerically studied, physical parameters analyzed respecti...

The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L2 and the H1 norms are proved. The numerical solution obtained from the finite element method with quadrature formula is shown to be unique for a sufficien...