Analysis of Nonlinear Heat Conduction Problems with Temperature-Dependent Conductivity Using Peridynamic Differential Operator

Abstract

In this paper, a nonlocal approach for handling nonlinear heat conduction problems is developed using the peridynamic differential operator (PDDO). The boundary conditions and heat conduction equations are transformed from local differential form to nonlocal integral form by introducing peridynamic functions. The algebraic equations are established by the Lagrange multiplier method and variational analysis, which is solved with Newton–Raphson iterative method. Nonlinearities resulting from the temperature-dependence of material properties have been taken into account in irregular boundaries and cracked plates. Numerical examples demonstrate the effectiveness and accuracy of the PDDO for solving nonlinear heat conduction problems with temperature-dependent conductivity.