A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
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In the present paper, a method for the modelling of the mechanical behaviour of composite plates, especially hybrid laminates and sandwich plates, is proposed. The chosen method is the computational homogenisation, or the so-called FE^2, for plates. The principle is to split the considered problem into two scales: on the one hand, the two-dimensional FE computation of a plate is performed on the macroscale. On the other hand, a three-dimensional FE problem is computed on the mesoscale, which enables the discretisation of the layers organisation. From each integration point of the macroscale, the deformations are projected to the Representative Volume Element (RVE) on the mesoscale, where a Dirichlet boundary value problem is solved. Finally, the homogenisation of the stresses is conducted to define the stress resultants of the macroscale. The proposed method presents the advantage to take into account any material behaviour without any transformation of the constitutive laws, even non-linear ones. Furthermore, the new projection strategy, presented in this work, considers the thickness change of the plate, which enables a resolution of the Poisson locking. The method is illustrated by the simulation of the mechanical behaviour of both sandwich plate and of hybrid laminate.