Non-Intrusive In-Plane-Out-of-Plane Separated Representation in 3D Parametric Elastodynamics

Claudia Germoso,Giacomo Quaranta,Francisco Chinesta,Jean Louis Duval

doi:10.3390/computation8030078

Claudia Germoso, Giacomo Quaranta + Show 2 more

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https://doi.org/10.3390/computation8030078

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Abstract

Mesh-based solution of 3D models defined in plate or shell domains remains a challenging issue nowadays due to the fact that the needed meshes generally involve too many degrees of freedom. When the considered problem involves some parameters aiming at computing its parametric solution the difficulty is twofold. The authors proposed, in some of their former works, strategies for solving both, however they suffer from a deep intrusiveness. This paper proposes a totally novel approach that from any existing discretization is able to reduce the 3D parametric complexity to the one characteristic of a simple 2D calculation. Thus, the 3D complexity is reduced to 2D, the parameters included naturally into the solution, and the procedure applied on a discretization performed with a standard software, which taken together enable real-time engineering.

Highlights

The finite element method (FEM) remains the major protagonist of SBE (Simulation BasedEngineering)
That is the case of problems defined in plate or shell domains, where the mesh size is almost determined by the domain thickness and the material and/or solution details to be represented
The procedure considers a non-intrusive formulation in order to overcome the difficulty related with the standard Proper Generalized Decomposition (PGD) algorithm when performing the in-plane-out-of-plane separated representation and, including parameters as extra coordinates

Summary

Introduction

The finite element method (FEM) remains the major protagonist of SBE It is largely considered for performing three-dimensional (3D) analyses, the number of degrees of freedom that certain models involve compromises the solution efficiency. That is the case of problems defined in plate or shell domains, where the mesh size is almost determined by the domain thickness and the material and/or solution details to be represented. The enormous number of degrees of freedom that such models involve makes the use of traditional discretization techniques difficult. A possibility to circumvent such difficulty consists of reducing the model complexity. In this sense simplified descriptions can be derived by introducing adequate kinematic and mechanic hypotheses, leading to usual shell, plate or beam theories

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