Multilayered Plate Model with “Adaptive” Representation of Displacements and Temperature Across the Thickness and Fixed D.O.F.

Abstract

A new multilayered zig-zag plate model for analysis of thermo-elastic problems is developed. It a priori fulfils the boundary conditions and the stress contact conditions on interlaminar shear and normal stresses and the continuity of the heat flux and temperature at the layer interfaces, as prescribed by the elasticity theory and heat conduction equation. The functional d.o.f. are the mid-plane displacements and shear rotations, like for classical plate models, and the temperature at the upper and lower bounding faces. A non-classical feature, a high-order piecewise variation of the transverse displacement is assumed across the thickness aimed at accurately describing the transverse normal stress, as it has a significant bearing for keeping equilibrium in thermo-elastic problems. Also non classical feature, the representation of displacements and temperature can be different from point to point across the thickness, to adapt to the variation of solutions. This refinement is obtained by keeping the number of functional d.o.f. unchanged, since the coefficients of the hierarchic contributions are determined enforcing the fulfillment of the equilibrium and heat conduction equation at selected points across the thickness. As shown by the comparison with exact solutions of benchmark test cases, the present model accurately predicts displacement, stress and temperature variations across the thickness from constitutive equations, even when thickness is extreme and the thermo-elastic properties of layers are distinctly different. Its basic advantage over existing models is a lower computational effort under the same accuracy.