Document Type : Research Paper


Department of Civil Engineering, Enugu State University of Science & Technology, Enugu State, Nigeria


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 usually used to achieve a solution. Stress-based formulation and displacement-based formulation methods are two common simplified methods for solving elasticity problems.This work adopted a stress-based formulation for a three dimensional elasticity problem. In this work, the Maxwell's stress functions for solving three dimensional problems of elasticity theory were derived from fundamental principles. It was shown that the three Maxwell stress functions identically satisfy all the three differential equations of static equilibrium when body forces were ignored. It was further shown that the three Maxwell stress functions are solutions to the six Beltrami-Michell stress compatibility equations if the Maxwell stress functions are potential functions. It was also shown that the Airy's stress functions for two dimensional elasticity problems are special cases of the Maxwell stress functions.


Main Subjects

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Volume 49, Issue 2
December 2018
Pages 342-350
  • Receive Date: 07 October 2018
  • Revise Date: 27 October 2018
  • Accept Date: 28 October 2018