TY - JOUR
ID - 75011
TI - Elzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions
JO - Journal of Computational Applied Mechanics
JA - JCAMECH
LA - en
SN - 2423-6713
AU - Ike, Charles Chinwuba
AD - Dept of Civil Engineering, Enugu State University of Science and Technology,
Enugu State, Nigeria
Y1 - 2020
PY - 2020
VL - 51
IS - 2
SP - 302
EP - 310
KW - Elzaki transform method
KW - Airy stress potential function
KW - stress compatibility equation
KW - line load of infinite extent
KW - elastic half plane
KW - two dimensional elasticity problem
DO - 10.22059/jcamech.2020.296012.472
N2 - 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 to a fourth order ordinary differential equation (ODE). The general solution for the Airy stress potential function in the Elzaki transform space was obtained by solving the ODE. By inversion, the general solution for the Airy stress potential function was obtained in the physical domain space variables in terms of four unknown integration constants. Normal stresses and shear stress fields were also determined for the general case of 2D elasticity problems. The Flamant problem was solved as a particular illustration of 2D elasticity problems. The stress boundary conditions and the requirement of equilibrium of the internal stress resultants and the external forces were used simultaneously to determine the four constants of integration. The Airy stress potential function and the normal and shear stress fields were thus completely determined. The principle of superposition was used to obtain the elasticity solutions for the stress fields in the elastic half plane due to strip load of infinite extent, and solutions for horizontal stresses on smooth rigid retaining walls due to strip loads and parallel line load of infinite extent acting on the elastic half plane.
UR - https://jcamech.ut.ac.ir/article_75011.html
L1 - https://jcamech.ut.ac.ir/article_75011_f6f0b3d9c814d755500501f72295f07c.pdf
ER -