DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY  

作　　者：WANG Lin-xiang Roderick V. N. Melnik 

机构地区：[1]MCI, Faculty of Science and Engineering, University of Southern Denmark, Sonderborg, DK-6400, Denmark [2]Center for Coupled Dynamics ＆ Complex Systems, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, Canada, N2L3C5

出　　处：《Applied Mathematics and Mechanics(English Edition)》2006年第9期1185-1196,共12页应用数学和力学（英文版）

摘　　要：An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.

关 键 词：THERMOELASTICITY TWO-DIMENSIONAL differential-algebraic solvers 

分 类 号：O343.6[理学—固体力学] O155[理学—力学]