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...

In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and th...

here the box at the top right-hand corner of the article or click Receive free email alerts when new articles cite this article-sign up in Conservation laws have been recently obtained by requiring that a positive definite functional of the stress gradient (the Euler–Lagrange equations of which are the Beltrami–Michell compatibility conditions) be invariant under certain transformations. Here t...

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non-trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of com...

In Schramm & Kayser (1995) we introduced the complex Beltrami Equation as an appropriate framework for the analysis of arclets in cluster lensing. Corresponding real formalisms have been developed by Kaiser and Schneider & Seitz (this volume, compare also the references in Schramm & Kayser 1995). Here, we show how the solutions of the Beltrami differential equation can be used to identify multi...

In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...