Elzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions

GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

ON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

Differential Transform Method to two-dimensional non-linear wave equation

In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Time-Discontinuous Finite Element Analysis of Two-Dimensional Elastodynamic Problems using Complex Fourier Shape Functions

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.