This is an attempt for mathematical formulation and general analytical solution of the most generalized thermal bending problem in the Cartesian domain. The problem has been formulated in the context of non-homogeneous transient heat equation subjected to Robin’s boundary conditions. The general solution of the generalized thermoelastic problem has been discussed for temperature change, displacements, thermal stresses, deflection, and deformation. The most important feature of this work is any special case of practical interest may be readily obtained by this most generalized mathematical formulation and its analytical solution. There are 729 such combinations of possible boundary conditions prescribed on parallelepiped shaped region in the Cartesian coordinate system. The key idea behind the solution of heat equation is to transform the original initial and boundary value problem into eigenvalue problem through the Strum-Liouville theory. The finite Fourier transform has been applied with respect to space variables by choosing suitable normalized kernels. The well-posedness of the problem has been discussed by the existence, uniqueness, and stability of series solutions obtained analytically. The convergence of infinite series solutions also been discussed.
Kulkarni, V. S. and Parab, Vinayaki
Generalized problem of thermal bending analysis in the Cartesian domain,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
1, Article 9.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss1/9