PSI - Issue 25

Romanin Luca et al. / Procedia Structural Integrity 25 (2020) 149–158 Author name / Structural Integrity Procedia 00 (2019) 000–000

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 Robust in terms of design changes such as thickness and weld throat  It takes advantage of common type of element (generic FEM code)  Joint deformations decoupling At the same time, some disadvantages are intrinsically present in the method:  Residual stresses could not be predicted. As a matter of fact, since pre-strain and pre-curvature are assigned, no stress field arises in the case of welding without clamps. For a shell element, the stress-strain relationship in terms of the mid-plane strains and the plate curvature is presented in Eq. 1. � � � �� � � �� � � � � 1 00 �� � � � �� �� ��� ��� � � � � � � �� � � ∆ � � � �� (1) The contribution due to pre-strain and pre-curvature is subtracted to the calculated strain and thus does not affect shell stresses.  Shell modelling could not recreate all the type of welded joint  The method is insensitive to welding sequence. This is because the model is completely linear elastic, the order in which the load is applied does not influence the numerical results. The problem has to be reformulated mathematically as a series of single-objective optimization problems, each optimization problem is defined by a fitness function which has to be minimized or maximized. Every deformed joint is stored as a six size vector � � , ∆ � , � , ∆ � , ��� , ∆ ��� � representing the equivalent load parameters. The best solution is the one which minimize the error between the FE solution and experimental data according to Eq. 2. Each point and each coordinate has a equal weight. ��� ��� � ∑ �� ���,� ���������⃗ � � ��,� �������⃗� � ��� (2) The transversal shrinkage components are obtained analytically from the decomposition of residual deformations. Remembering that the virtual weld bead region width has been set to 20 mm to simplify the pre-processing phase, Eq. 3 could be used to obtain . � ∆� ����� �� (3) where is the pre-strain to be applied as an equivalent load and ∆ ����� the reference for the residual deformation in the transverse direction. In the case of a T joint the equation is applied for each side of the joint for a total of three times. For calibrating the thermal gradient across the thickness, Particle Swarm Optimizer (PSO) has been chosen because it could be applied for fitness functions which are not derivable. As matter of fact, a non-linear version of this simplified method is being developed where the choice of the optimization algorithm plays an important role. As for the transversal shrinkage, each joint side is optimized singularly, taking advantage of linear superposition. For each side, the reference angular deformation is calculated from extracting the angular coefficient of a linear regression of the deformed shape. The PSO minimizes the difference between the actual and the reference angular deformation. 3. Validation of a Megastructure Steel Connection A welding process simulation of a megastructure joint has been carried out by usion the proposed Virtual Weld Bead method and validated by experimental measurements. Particular welded joint types are addressed that, to the authors best knowledge, are not yet modelled in literature with numerical simplified methods (Fig. 5). The weight of the megastructure connection is 11000 kg and that of the filler material used is more than 150 kg. In fact, the assembly consists of around 140 welds obtained with more than 700 runs. By using the CWM, with a very optimistic solution time of 1 hour per weld run, a total time of 29 days would be necessary. Several points against the use of a complex model could be brought to the attention. First of all, for a small batch, the simulation cost exceeds that of repairing operations. Moreover, there could be a strict time constraint between the end of the design and the start of production, which is often one-of-a-kind, and distortions problems should be identified before this phase.