Mathematical models for heat conduction with point source and beam bending with concentrated force include singular Delta function in the source term.Barycentric Lngrange interpolation is used to approximate unknown functions.Barycentric interpolation collocation method and barycentric interpolation Galerkin method for singular source problems are presented using relation between delta function and derivative of Heaviside function and integrated property of delta function.Formulations of the method are given in detail.Two one-dimensional examples and a two-dimensional example are shown.It demonstrates effectiveness and precision of the methods.

To overcome shortcomings of traditional inverse analysis method (TIAM), a fast and reliable searching scheme is used to find elements passing through die entrance radius during deformation process. An efficient stress-strain relation for continuous uniaxial tensile test is introduced to update stress distributions. Constitutive equations avoid complexity of incremental FEM based stress/strain updating algorithms, and effects of die entrance radius on deformation history are considered. Numisheet'93 square box drawing benchmark demonstrates that the constitutive equations significantly enhance prediction of stress distribution compared with incremental FEM based software DYNAFORM.