To ascertain the extent of deformation due to the thermal cycles caused by welding it calls for solving a complex thermal elasto-plastic problem, which is non-linear and involves plastic deformation of the medium at high temperature varying in both time and space. Analytical solutions turned out to be inadequate. At the same time conventional numerical techniques proved to be highly time consuming and thereby prohibitively expensive in real life situations. The concept of pseudolinear equivalent constant rigidity system was developed in this investigation for thermo-mechanical analysis of plates undergoing variation of rigidity due to a continuously changing temperature profile as is encountered in welding situations. The initial non-linear problem with modulus varying with temperature was transformed into a pseudolinear equivalent system of constant rigidity that was solved by applying linear analysis. The numerical results compared very well with those of the experimental ones. The present method was found to be computationally more efficient and simpler to model compared to FEM for solving similar thermo-elasto-plastic nonlinear problems. The analysis procedure presented in this work and the results thus obtained, holds a great promise for analyzing the complicated thermo-elasto-plastic problems as encountered in real life situations. © 2008 Elsevier Inc. All rights reserved.
Adak, M., & Mandal, N. R. (2009). Pseudolinear equivalent constant rigidity concept for analyzing welding residual deformation. Applied Mathematical Modelling, 33(4), 2096–2108. https://doi.org/10.1016/j.apm.2008.05.024