An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids

Abstract

a b s t r a c tThis paper presents an analytical approach to solve the plane elasticity and thermoelasticity problems for inhomogeneous, orthotropic planes, half-planes, and strips. Solution of the problems is reduced to the governing Volterra integral equation formulated for the key function and accompanied by the corresponding integral conditions. By making use of the resolvent-kernel technique, the governing equation is solved and the solution to the original problem is presented in explicit form.

Steady-State Heat Transfer and Thermo-Elastic Analysis of Inhomogeneous Semi-Infinite Solids

“…Herein we employ the resolvent-kernel algorithm (Pogorzelski, 1966;Porter & Stirling, 1990) in the same manner as it has been done in , 2009a. This method allows us to obtain the explicit-form analytical solution that is convenient for analysis.…”

“…where To solve equation (39), we employ the resolvent-kernel solution technique (Tokovyy & Ma, 2009a) …”

“…The analytical, semi-analytical, and numerical methods for solving the heat conduction and thermoelasticity problems in inhomogeneous solids attract considerable attention in recent years. The overview of the relevant literature is given in our publications , 2008a, 2009a. On the other hand, determination of temperature gradients, stresses and deformations is usually an intermediate step of a complex engineering investigation.…”

“…By following this solution strategy, the one-dimensional thermoelasticity problem for a radially-inhomogeneous cylinder has been analyzed (Vihak & Kalyniak, 1999;Kalynyak, 2000). In the same manner, the two-dimensional elasticity and thermoelasticity problems for inhomogeneous cylinders, strips, planes and semi-planes were solved in (Tokovyy & Rychahivskyy, 2005;, 2008a, 2009a. The same method has also been extended for three-dimensional problems , 2010a.…”

Elastic crack-tip stress field in a semi-strip

“…In [26] the overview of recent advanced methods for rapid calculation of notch stress intensity factors under mixed mode loadings was presented. The analytical approach for plane elastic and thermoelastic problems for inhomogeneous, orthotropic planes, half-planes and strips was presented in [27].…”