TY - JOUR
ID - 68654
TI - ON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY
JO - Journal of Computational Applied Mechanics
JA - JCAMECH
LA - en
SN - 2423-6713
AU - Ike, Charles
AD - Department of Civil Engineering, Enugu State University of Science & Technology, Enugu State, Nigeria
Y1 - 2018
PY - 2018
VL - 49
IS - 2
SP - 342
EP - 350
KW - Maxwell stress functions
KW - Beltrami-Michell stress compatibilty equations
KW - Differential equations of equilibrium
KW - Airy's stress potential functions
DO - 10.22059/jcamech.2018.266787.330
N2 - 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.
UR - https://jcamech.ut.ac.ir/article_68654.html
L1 - https://jcamech.ut.ac.ir/article_68654_a7d2b37ca577349ae19817f017646b11.pdf
ER -