Closed-form solution and analysis of the plate twist test in sandwich and laminated composites

Abstract

A new anticlastic bending solution for the deflection and rotations of laminated composite plates and sandwich panels applicable to plates under torsion or bending with opposite curvatures is developed using first-order shear deformation theory and the theorem of minimum potential energy. The novelty of the proposed solution relies on being algebraic, taking into account the overhang, employing variable shear correction factors and twisting moment (Mxy), and considering the influence of the twist (D66), bending (D11,D12,D22) and shear stiffnesses (A44,A55). A finite element model is also developed for comparison. Both approaches are validated with compliance measurements previously reported, observing good agreement (less than 10% difference with respect to experiments) for most orthotropic and isotropic plates. Because Mxy is the main driving-load of anticlastic bending, its distribution is analyzed on several plates. According to finite element modeling, Mxy attains a quarter of the applied load (P/4) within the mid-plane of a glass/epoxy 0/906s laminated composite, but it has a parabolic behavior for sandwich panels with compliant cores. Good match is obtained between compliance predictions by the first-order shear deformation theory and the finite element model for square laminate plates with aspect ratios between (8.4<width/thickness<101) and square sandwich panels with (3.9<width/thickness<59) and shear modulus ratios (from 1 to 1800) between core and face sheets.