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Major simplifications of the corresponding rigorous thermal and thermo-mechanical analyses are applied in this chapter. Transient temperature fields are replaced by fixed temperature profiles. The ‘computationally efficient’ (CE) methods introduce further simplifications where transverse and longitudinal thermal strains are derived from approximations embodied in the mismatched thermal strain and transverse contraction strain algorithms. In the CE ‘analytical’ approach, these strains are applied to linear elastic, small strain models, using conventional strength of materials techniques. In the CE ‘computational’ approach, the strains are applied to linear-elastic, large-strain, finite-element models. Various hybrid stepwise methods are also shown, where a measure of sequential description is included, together with the use of elasto-plastic, finite-element computation.

Results from weld simulations and experiments for fillet-weld procedures are brought together to provide information on distortion in stiffened plate fabrications. The results of thermocouple and thermographic studies are used to expand on thermal aspects, described initially for small-scale fabrications in Chapter 7 . Computationally efficient solution methods are applied to large-scale fabrication cases and the results compared with experiments. Special attention is given to application of the transverse contraction strain (TCS) algorithm and ways in which it can be fine-tuned to match different models of transverse constraint. Modelling methods for multiple parallel stiffeners are given and the results of full-scale experiments are compared with the results of a computational case study in which different sequences of stiffener attachment were applied.

Modelling strategies and results from previous chapters are brought together in a comprehensive treatment of butt welding procedures. Various practical issues are treated, including effects on distortion of initial out-of-flatness, disposition of supports, tacking assembly and clamping of components. In the case of clamping, it is shown that excessively constrained clamping strategies can lead to greater levels of distortion than if the components are relatively unconstrained. The outcomes of the various simulation methods for prediction of residual stresses in butt welds are described. Effects in multiple longitudinal butt welds where there are interactions between several welds in an assembly are shown.

Distortion and residual stress are driven by the thermal gradients generated by the moving heat source. Heat energy enters the workpiece through the fusion zone primarily and procedures are provided to model heat input as a lumped source, including the effects of weld filler deposition and losses due to convection and radiation. Alternative three-dimensional and two-dimensional thermal models are given. Stiffener fillet welding involves more conduction routes and a double-sided fillet stiffener weld is treated. Methods to determine welding thermal efficiency are given, with values for different processes. The characteristics of thermal cutting are discussed.

Information from all preceding chapters in the book is applied to support design and manufacturing strategies, showing how simulation can be applied to explore alternative design configurations and manufacturing sequences. In terms of design, configuration and manufacturing sequence questions in the fabrication of multi-stiffened plates are examined. Studies also include the use of multiple welding heads, where computation is applied to show that an optimum spacing can be established, avoiding the risk of buckling. Simulation is also applied to investigate three techniques that have been proposed to mitigate distortion.

Contrasting approaches to control and reduction of distortion are described. A method based on the use of artificial neural networks (ANNs) uses statistical techniques to interpret observations of distortions and to discover interactions between different input parameters. The section on computational simulation is based on mathematical modelling of the physical processes in welding. Several processes that can be applied along with the welding operation or in the post-welding phase are described. Thermal and mechanical methods include transient thermal tensioning, roller tensioning, intense cooling in the trailing region behind the weld and the use of special weld filler metal.

The opening chapter contrasts a welding design and fabrication strategy based on trial and error with one that is guided by quantitative welding simulation methods. An outline is given of the main contributing factors to the development of computational welding mechanics as a discipline and the possibilities that such studies offer for interpreting welding phenomena such as distortion during fabrication. The importance of establishing simple models is emphasised and a first mention is made of simplified computational methods. The content of the following chapters is briefly described and the relationships between each of the chapters in the sequence are explained.

A first introduction to welding mechanics is given, based at this stage on uncoupled analytical solutions for thermal and thermomechanical behaviour. Rosenthal’s well-known quasi-static solution for the temperature field caused by a fast-moving, concentrated heat source is used to demonstrate the influence of different material properties and welding process conditions on the temperature fields. An approximate thermo-mechanical solution due to Okerblom is used to demonstrate the roles of the thermal dilatation of the material being welded and the heat input on welding deformations. This solution is also used to illustrate the development of residual stress fields and the potential for buckling.

Experimental strategies and techniques underpinning this book are described and the role of practical studies is highlighted. Thermal investigation of welding heat input and conduction in the workpiece is based on thermocouple arrays and thermography. Welding and measurement rigs to create industrial-scale structures are described. The arrangement integrates welding with thermal and deformation measurements to minimise workpiece handling errors. A special deformation-smoothing procedure is given that ensures appropriate interpolation between point deformation measurements and leads to profiles that can be differentiated to provide accurate surface slopes and curvatures. The use of different statistical measures of out-of-plane deformation is discussed.

The overall industrial context of thin, stiffened-plate fabrication is outlined. A typical fabrication sequence is described, showing the various stages where distortion issues can arise. Stock quality and flatness have a strong influence on outcomes. Some high-risk factors for distortion are identified, which could be removed by better management of the design and fabrication process. Cause and effect are not always easily related in many cases and application of quantitative modelling tools could often resolve ambiguity and improve distortion outcomes. The chapter closes with a brief description of methods used to rectify any distortion that may have arisen.

The many different physical phenomena present in welding operations are described. It is shown that the many interactions between these can be simplified to a smaller number, similarly for material properties. An outline of thermal computation approaches is given. Thermo-mechanical computational approaches are described, ranging from ‘reduced solution’ methods, where substantial simplifications are made, to full elasto-plastic methods that make greater demands on computing resources. The advantages of reduced solutions are exemplified through a butt-welding simulation treated via a ‘computationally efficient’ method based on the Okerblom approach and two variants of a hybrid method.