A numerical homogenisation method for sandwich plates based on a plate theory with thickness change

Abstract

Nowadays composite plates are widely used, especially in the transport industry. Their importance derives from their relatively low weight and good mechanical properties, but their behaviour is complex and cannot be obtained from a simple mixture rule properly. In the scope of this work, the considered composite plate is composed of a complex assembly of metal layers and carbon fibers reinforced polymers (CFRP) layers. Whereas the CFRP can be considered as anisotropic elastic, the metal layers have an elasto-plastic material behaviour. In this case, the possibility to use the classical plate theory is excluded, because the classical plate theory can only regard small deformations and linear material behaviour. For this reason, the modelling of the mechanical behaviour of the composite plate is based on a numerical homogenisation. The underlying principle is a numerical multi-scale consideration of the composite plate: on the one hand, the macroscale is considered as a Finite Element computation of a plate which is following a plate theory including a thickness change, i. e. a seven degrees of freedom approach. On the other hand, the mesoscale is obtained with a three-dimensional modelling which explicitly takes into account the stacking order and the material behaviour of the different layers. From each integration point of the macroscale, the deformations are projected on the boundaries of a Representative Volume Element (RVE) of the mesoscale. In this scale, a boundary value problem is solved, and the macroscopic forces, moments and shear forces are obtained as resultants from the mesoscopic stresses.

A multiscale projection approach for the coupled global–local structural analysis of photovoltaic modules

“…Towards a proper estimation of stresses in the unit cell, a coupling of global and local scales is required. In principle, approaches to scale coupling of plates or shells to 3D continua can be found in the literature, often referred to as FE 2 , see [47,48,49,50]. Common to these approaches is the use of FOSDT at global scale, which is not appropriate to solve structural problems for photovoltaic modules [9].However, these approaches have the objective to deliver effective material properties for the global scale.…”

A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory

“…[16,17]. However, numerical techniques are required to estimate the effective transverse shear deformation in the inelastic range [18,19]. It should be mentioned that for laminates with extreme differences in the stiffness of layers the FSDT fails to predict the deformation properties of the laminate correctly, as shown for example in [4,7] for beams and in [20,21] for plates.…”

Application of the first-order shear deformation theory to the analysis of laminated glasses and photovoltaic panels

“…[4]. To estimate the effective transverse shear deformation in the inelastic range, various numerical techniques are available [16,17].…”