Numerical solution of a two-dimensional quasi-static problem of thermoplasticity: residual thermal stress calculation for a multipass welding of heterogeneous steels

A two-dimensional mathematical model was developed for estimating the stresses in welded joints formed during multipass welding of multilayer steels. The basis of the model is the system of equations that includes the Lagrange variational equation of incremental plasticity theory and the variational equation of heat conduction, which expresses the principle of M. Biot. Variational-difference method was used to solve the problems of heat conductivity and calculation of the transient temperature field, and then at each time step — for the quasi-static problem of thermoplasticity. The numerical scheme is based on triangular meshes, which gives a more accuracy in describing the boundaries of structural elements as compared to rectangular grids.