Nonlinear finiteelement heat conduction analysis with direct implicit time integration
Abstract
A finiteelement procedure is described that utilizes conjugate base functions and a modified form of the secant method for solving the discretized equations. Since a variational formulation involving conjugate bases provides a consistent diagonal capacitance matrix, time integration can be performed directly from nodal forces rather than by use of a global conductance matrix. By utilizing an iterative procedure, implicit time integration is achieved with nodal forces computed from information associated with elements connected to a given node. The result is that the algorithm has the simplicity normally associated with explicit time integration and the unconditional stability of an implicit time integrator. Furthermore, computational effort is automatically concentrated in the region where the dependent variable is changing most. The procedure holds considerable promise for largescale nonlinear heat conduction problems.
 Publication:

Numerical Heat Transfer
 Pub Date:
 September 1981
 Bibcode:
 1981NumHT...4..377S
 Keywords:

 Conductive Heat Transfer;
 Finite Element Method;
 Numerical Integration;
 Thermodynamics;
 Algorithms;
 Conjugates;
 Galerkin Method;
 Iterative Solution;
 Fluid Mechanics and Heat Transfer