Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries

A finite element method formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and combined thermoelasticity continuum problems is presented. The present finite element method formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently overspecified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for two-dimensional problems are presented.