Nuclear Engineering and Design 64 (1981) 49-80 North-Holland Publishing Company A SOLUTION PROCEDURE FOR THERMO-ELASTIC-PLASTIC AND CREEP PROBLEMS

The application of the finite element method to the inelastic analysis of structures and continua has received considerable attention over the last fifteen years [ 1-21 ]. To a large extent, this effort has been motivated by the need to safety and economically predict material response under conditions of extreme mechanical and thermal loading. Some examples are the design and analysis of pressure vessels, ships, and aircraft, as well as the study of metal forming, welding, and nuclear weapon effects on soils and structures. Based on extensive experience, the solution of problems with inelastic material behavior has proven to be much more difficult than the analysis of linear elastic behavior. The currently available solution procedures can be quite costly, unstable, and inaccurate. In addition, the models of inelastic material behavior in current engineering use are not always suitable for complex loading conditions. All of these factors have placed a severe constraint on the routine use of inelastic finite element analysis. The cost of inelastic analysis is particularly high in three-dimensional calculations. However, a more critical factor is that considerable user knowledge and judgment are involved in selecting an appropriate solution strategy. In practice, this situation almost always means that obtaining a reliable solution requires some, if not extensive, numerical experimentation. There is surely a need for solution techniques with increased accuracy and stability properties as well as self-adaptive algorithms that adjust computational strategy as the solution proceeds. Our objective in this paper is to present the development, analysis, and testing of,a solution procedure for the finite element analysis of thermo-elastic-plastic and creep problems with temperature-dependent material properties. The solution procedure is based on a one-parameter integration method (the a-method) for a system of ordinary differential equations. This integration method, which contains the well-known Euler forward and backward methods, was previously proposed and analyzed for the finite element analysis of certain heat conduction [22,23] and viscoplasticity [3,4,6] problems. In this paper we use the a-method as the basis of an effective algorithm for the analysis of significantly more complex thermo-elastic-plastic and creep problems. We first summarize in section 2 the formulation of the thermo-elastic-plastic and creep material model. Section 3 contains the development of the finite element solution procedure and a theoretical analysis of its stability charac teristics. The procedure has been implemented in the finite element computer program ADINA [21 ] and in section 4 we present and discuss the solutions for three test problems. The conclusions are contained in section 5.