BEM Inverse Identification Of Boundary Conditions And Thermal Parameters And Geometry Shapes In Elasticity

Identification of boundary conditions, parameters and the unknown boundaryshapes is analyzed in this paper.1) The singular value decomposition (SVD),truncation at an optimal number, is analyzed for obtaining approximate solutions toill-conditioned linear algebraic systems of equations which arise from the boundaryelement method (BEM) discretization of an ill-posed boundary value problem inlinear elasticity. The regularization parameter, namely the optimal truncationnumber, is chosen according to the Fourier coefficients. The numerical resultsobtained confirm that the SVD+BEM produce a convergent and stable numericalsolution. The relationship between the deviation principle and Fourier coefficientmethod is analyzed in this paper.2) A two-dimensional inverse problem indetermining the heat transfer coefficients (parameters) utilizing the Gauss-Newtonmethod and the complex-variable-differentiation method is applied successfully inthe present study based on the measured temperature or the heat flux distributions.3) A steady-state two-dimensional shape identification problem to determine theunknown irregular boundary configurations by utilizing the conjugate method isdeveloped and examined in this study based on the simulated measured temperaturedistributions on the bottom surface.