Modeling of Variable Angle Tow Composites based on a Variable Separation Method
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We are interested in the modeling of the Variable Angle Tow composite plates (VAT) that allows us to enlarge the range of possibilities to design optimal structures. Indeed, the fibers are not constrained to a straight line but can follow a curvilinear path. Thus, it calls for an efficient numerical tool to modelise such structures. Previous studies have shown the need of a Layerwise approach [1]. Classical equivalent single layer methods fail to provide accurate stresses without the use of a post-processing computation through the integration of the equilibrium equations. Alternatively, refined approaches based on Reissner’s Mixed Variational Theorem (RMVT) formulation yields satisfactory results [2]. In the present work, a reduced order modeling approach, namely the Proper Generalized Decomposition, is addressed to analyse VAT composite plates. Classically, the present approach is based on the separated representation of the unknown displacements. In this way, the three displacements are written under the form of a sum of products of 2D and 1D functions because of in-plane and out-of-plane coordinates separation. In this particular framework, a CUF (Carrera’s Unified Formulation) formulation is adapted to keep the separability feature of the approach. Finally, the deduced non-linear problem implies the resolution of two coupled linear 2D and 1D problems alternatively. An interesting feature of this approach lies on the possibility to have a higher order through-the-thickness expansion and to refine the description of the mechanical quantities without increasing the computational cost. Numerical tests are performed on a variety of composite / sandwich plates. The efficiency of the proposed methods is shown. The accuracy of the results is assessed by comparing with a layerwise fourth-order reference solution and 3D FEM results.