Thermoelastic equilibrium of a rectangular parallelepiped with nonhomogeneous symmetry and antisymmetry conditions on its faces (Q2709763)

The author discusses a boundary value problem of linear homogeneous isotropic thermoelastostatics for a rectangular parallelepiped \(0\leq x_i\leq a_i\) \((i=1,2,3)\) in which the normal displacement, tangent stress components, and the normal heat flux (or the normal stress, tangent displacements, and the temperature) are prescribed on each side of the parallelepiped. The boundary data satisfy suitable compatibility conditions on the edges of the parallelepiped. Using a displacement representation in terms of three harmonic functions, the author presents a Fourier series solution to the problem. Since the method relies heavily on finding solutions to boundary value problems for two-dimensional rectangular regions, an application of the method to a boundary value problem for three-dimensional parallelepiped would be useful. The reviewer also notes that a traction boundary value problem of thermoelastostatics for a rectangular parallelepiped is not covered by the method; additionally, the statement in the author's abstract that ``normal stress and tangential stresses'' are prescribed on the boundary is misprinted.