1) in a curvilinear coordinate domain solved by a C language program.
This paper introduced the Sinc-Galerkin method for the Poisson problem in one type of curvilinear coordinate domain.
Then, the generalized Hooke's law for isotropic materials as provided in Sokolnikoff (4) in curvilinear coordinates becomes:
Inclusion of the effect of thermal expansion in the generalized Hooke's Law in curvilinear coordinates can be derived by use of the mixed thermal expansion coefficient tensor.
Derivation of a Viscoelastic Constitutive Model in Curvilinear Coordinates
A virtual work expression in general curvilinear coordinates was developed by Sokolnikoff  and can be derived by taking the dot product of the integrand of the stress equilibrium equation with a virtual displacement vector having covariant displacement components and then integrating the expression over the volume.