Node's residual descent method for steady-state thermal and thermoelastic analysis

Thermoelastic problems are prevalent in various practical structures, wherein thermal stresses are of considerable concern for product design and analysis. Solving these thermal and thermoelastic problems for intricate geometries and boundary conditions often requires numerical computations. This study develops a node's residual descent method (NRDM) for solving steady-state thermal and thermoelastic problems. The method decouples the thermoelastic problem into a steady-state thermal problem and an elastic boundary value problem with temperature loading. Numerical validation indicates that the NRDM exhibits excellent performance in terms of precision, iterative convergence, and numerical convergence. The NRDM can readily couple steady-state thermal analysis with linear elastic analysis to enable thermoelastic analysis, which verifies its capability of solving multiphysics field problems. Moreover, the NRDM achieves second-order numerical accuracy using a first-order generalized finite difference algorithm, reducing the star's connectivity requirements while enhancing the convergence rate of the traditional generalized finite difference method (GFDM). Furthermore, the NRDM addresses the numerical challenges of material nonlinearity by simply updating the node thermal conductivities during iterations, without requiring frequent incremental linearization as in the GFDM, thus achieving improved computational efficiency.