Brief History of Computational Welding Mechanics
Historically, arc welding began shortly after electrical power became available in the late 1800s. Serious scientific studies date from at least the 1930s. The failure of welded bridges in Europe in the 1930s and the American Liberty ships in World War II did much to stimulate research in welding in the 1940s.
In the USA, the greatest attention was focused on developing fracture mechanics and fracture toughness tests. This could be interpreted as a belief that welding was too complex to analyze and therefore they chose an experimental approach that relied heavily on metallurgical and fracture toughness tests. The steady state heat transfer analysis of Rosenthal was an exception .
Russia took a different approach. The books of Okerblom  and Vinokurov  are a rich record of the analysis of welded structures including multi-pass welds and complex structures.
Over time the main techniques for solving heat transfer problems were changing with growing computer capacity. The strategy for analyzing welds and numerical methods (finite difference and finite element analysis) began in the 1960s with the pioneering work of Hibbitt and Marcal , Friedman , Westby , Masubuchi  and Andersson . Marcal  made an early summary of experiences from welding simulation. Chihoski sought a theory to explain why welds cracked under certain conditions but not others [51, 52 and 53]. Basically, he imaged that the weld was divided into longitudinal strips and into transverse strips. He then computed the thermal expansion and contraction in each of these strips due to the temperature field of edge and butt welds. He concluded that a small intense biaxial compression stress field exists near the weld pool. Ahead of the compression field there may be a gap or a tensile stress field. Behind the compression field a tensile field or a crack can appear. The startling aspect of Chihoski’s theory was that by varying the welding procedure, the position of this compressive field could be controlled. To support this theory, Chihoski developed a Moire’fringing technique to measure displacements during edge and butt weld. Chihoski used his theory to understand and solve a number of common problems: cracks and microcracks, forward gapping, upset and part distortion, sudden changes in current demand and unexpected responses to welding gaps. He considered the position and pressure of hold down fingers; the influence of localized heating or cooling; and the effects of gaps. He argued that these parameters could be optimized to obtain crack free welds.
These authors consider Chihoski’s papers to be among the most important in computational welding mechanics because he combined experience in production welds with an insight into weld mechanics that enabled him to conceive a theory that rationalized his observations and predicted solutions to his problems.
The reviews by Karlsson [12 and 13], Smith , Radaj [18 and 19] and Goldak [1, 14, 15, and 16] include references to simulations performed up to 1992. The research in Japan is reviewed by Ueda [20 and 21] and Yurioka and Koseki . But Finite Element Analysis (FEA) methods gained a wide acceptance only over the last decade [10, 23, 24, 25, and 46].
The Moire’fringing technique of Chihoski is today one of the most powerful means of assessing FEA of stress and strain in welds (also see Johnson  for more on Moire’ fringing methods for measuring strain in welds.).
The use of finite difference methods is more a transition between analytical and finite element methods. The main advantage of the finite difference method is that it is rather simple and easily understandable physically [10 and 26].
The finite element method has achieved considerable progress and powerful techniques of solving thermal-mechanical manufacturing process such as welding [1, 27, 28, 29 and 30]. Runnemalm presents in a dissertation thesis  the development of methods, methodologies and tools for efficient finite element modeling and simulation of welding. The recently published dissertation of Pili - penko  presents the development of an experimental, numerical and analytical approach to the analysis of weldability.
Lindgren review’s [47, 48 and 49] summarized the direction for future research, which consists of three parts. Part 1  shows that increased complexity of the models gives a better description of the engineering applications. The important development of material modeling and computational efficiency are outlined in part 2 and 3 [48 and 49], respectively. Figure 1-4 shows the increase in the size of the computational models in welding simulation during the last decades.