PSI - Issue 31

M.L. Larsen et al. / Procedia Structural Integrity 31 (2021) 70–74 M.L Larsen, V. Arora, H.B. Clausen/ Structural Integrity Procedia 00 (2019) 000–000

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to crack initiation, Maddox (1991). With the increasing computational performance, more and more research into structural optimization considering fatigue constraints has been performed, Oest et al. (2017) and Suresh et al. (2019). However, these methods are often based on a single fatigue criterion and thus these methods do not allow for easy implementation and analysis of other fatigue criteria and estimation methods. In this paper, a framework for shape optimization of a welded plate considering different fatigue estimation methods have been developed. The optimal shape of a weld in the structure has been analysed based on the nominal stress approach and the following fatigue estimation methods (criteria): IIW (Hobbacher (2016)), EC3 (Eurocode 3(2007)), the Findley Criterion (Findley (1959)) and the Modified Wöhler Curve Method (Susmel (2009)). The Findley criterion and the MWCM are implemented using the critical plane approach. The results show that the framework is capable of optimizing the structure using the different fatigue criteria without additional work to the optimization framework. Furthermore, the results show that the critical plane approach is not suitable for fatigue analysis using the nominal stress approach. 2. Optimization framework The shape optimization framework has been developed based on the HyperWorks (2019) finite element software in combination with code produced with MATLAB (2020). The key difference between this developed framework and other published optimization approaches is that the described framework uses the finite difference approach for response gradient estimation. This means that n+1 finite element analyses are required in each optimization iteration, where n corresponds to the number of design variables. The developed optimization framework leads to slower optimization, compared to methods where the finite difference approach is not used, but allows the user to include a variety of different fatigue criteria (or other criteria) without requiring prior complex gradient calculations. This, furthermore, allows the user to include different fatigue approaches and stress estimation methods, without having to completely rewrite or add additional code to the FE and/or optimization software. 3. Optimization of weld orientation in plate structure In this paper a case study is performed on a simple plate structure using the developed optimization framework. The plate is shown in Fig. 1 and consists of two parts that are assumed to be welded together. The dimensions of the plate are: 100 mm in width and 400 mm in total length. The thickness of both parts is 10 mm. The weld between the two parts is assumed to be a double-sided butt weld with properties corresponding to a FAT-90 class S-N curve, see EC3. The plate material is assumed to be regular steel with Youngs modulus of 210 GPa and Poisson’s ratio of 0.3. A total of 1600 first order shell elements are used in the finite element model of the plate.

Fig. 1. Plate FE model used in optimization study.

The FE model of the plate is made using the Altair OptiStruct software. The weld orientation is controlled by two shape parameters as shown in Fig. 1. These parameters allow the weld to be rotated up to 45 degrees, still keeping the weld straight. These two parameters are used as design variables in the optimization framework. The plate is fixed at the left edge and a uniaxial load, F x , is applied at the right edge as shown in Fig. 1. Sinusoidal loading is applied in