A finite element method (FEM) formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and thermoelasticity continuum problems is presented. The present FEM 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 over-specified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for 2-D problems are presented.

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