A discussion on simple third-order theories and elasticity approaches for flexure of laminated plates

Abstract

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.