Nonlinear heat transfer and thermo mechanical stress analysis using finite elements. - Pennington, Derek Steven (Department of Mechanical Engineering, 2014)
This thesis deals with the development, implementation and testing of numerical procedures for the heat transfer and thermo-mechanical analysis of sol id continua. Steady state conduction heat transfer is developed as a particular case of the general field equation. Internal heat generation and the boundary conditions of specified temperatures, flux, convection. and radiation are included. The stress - strain - temperature relationships for a corresponding body are not coupled to the heat transfer relationships for steady state conditions. The heat transfer problem is thus solved prior to, and independently of, the mechanical problem. The resulting temperature field is adopted for the solution of the thermal deformation problem. Finite element formulations using a common discretization are developed for these problems using Galerkin' s method. The formulations are implemented in an existing temperature independent nonlinear finite element stress analysis code. Four, eight and nine noded isoparametric continuum finite elements with the option of the plane stress, plane strain and axisymetric cases are utilized. Nonlinear heat transfer due to temperature dependent thermal conductivity and/or internal heat generation is solved using an iterative method based on the Newton-Raphson algorithm. Thermal deformations and stresses are determined by calculating equivalent nodal loads corresponding to the thermal strains which result from the temperature field. These are then applied to the mechanical model. The implementation is illustrated by three examples whose solutions compare favourably with analytical solutions taken from the literature.