On stress functions in classical elasticity

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...

Lecture Notes on Constant Elasticity Functions

1 CES Utility In many economic textbooks the constant-elasticity-of-substitution (CES) utility function is defined as: U (x, y) = (αx ρ + (1 − α)y ρ) It is a tedious but straightforward application of Lagrangian calculus to demonstrate that the associated demand functions are: x(p x , p y , M) = α p x σ M α σ p 1−σ x + (1 − α) σ p 1−σ y and y(p x , p y , M) = 1 − α p y σ M α σ p 1−σ x + (1 − α)...

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

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...

Integral Equations Formulation of Classical Elasticity

Convergence of Peridynamics to Classical Elasticity Theory

The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classica...