A general approach for solving three-dimensional transient nonlinear inverse heat conduction problems in irregular complex structures

Abstract

A novel general approach is proposed for solving three-dimensional transient nonlinear inverse heat conduction problems in irregular complex structures. The complex-variable-differentiation method (CVDM) is introduced into the commercial finite element method (FEM) software ABAQUS, for solving three-dimensional inverse heat conduction problems for the first time. First, the complex variable finite elements are set up, and the complex variable FEM is innovatively developed through the user element subroutine (UEL) in ABAQUS. Then, the key parameters in the Levenberg-Marquardt algorithm for solving inverse problems – sensitivity matrix coefficients – are accurately evaluated by utilizing the CVDM and ABAQUS standard solvers with the UEL. Finally, several numerical tests are carried out to verify the performances of the new approach for solving the three-dimensional transient nonlinear inverse heat conduction problem in an irregular complex structure.