Resumen de Proper generalized decomposition solutions for composite laminates parameterized with fibre orientations for fast computations
Karim Mohamed Shaker Ibrahim El Ghamrawy
Composite materials are gaining popularity as an alternative to classical materials in many different applications. Moreover, their design is even more flexible due to the potential of additive manufacturing. Thus, one can produce a tailored composite laminate with the optimal values of some design parameters providing the desired mechanical performance. In this context, having a parametric numerical model for the mechanical response of the composite laminate is essential to compute the optimal parameters. Generally, solving a mechanical model using mesh-based techniques in 3D is computationally expensive and at some point it could become infeasible when the problem is multidimensional. Furthermore, if the problem under consideration is an application requiring multiple queries such as optimization, inverse problems,or uncertainty quantification, the direct problem is solved numerous times increasing drastically the computational burden. In the present thesis, the design parameters under consideration are the angles describing the orientation of the reinforcement fibers in different layers or patches of the composite laminates. We present the Tsai-Wu failure criterion as the objective function of the optimization problem. The use of a Model Order Reduction (MOR) technique is advocated to alleviate the mentioned computational burden. Namely, we resort to the Proper Generalized Decomposition (PGD) to obtain the generalized solution of the structure mechanical response. Particularly, we obtain a 3D computational vademecum which provides laminate failure index and safety factor that depend explicitly on the fiber orientation. The PGD vademecum provides also sensitivities for a gradient-based optimization algorithm. The potentiality and efficiency of the presented approach is demonstrated through some numerical tests. Finally, a coupling between the proposed methodology and clustering techniques is presented to enhance the overall performance of the model.
