Restatement of first-order shear-deformation theory for laminated plates

A restatement of the first-order shear-deformation theory of plates is offered and verified numerically by exact 3-D elasticity results. Based on a more appropriate physical assumption, the restated theory innovatively interprets its variables and applies elasticity equations in a more pertinent manner. It assumes physically that only in some average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after deformation. Hence the in-plane displacement is still approximated, in an average sense, as linear and the transverse deflection as constant through the plate thickness. The associated nominal-uniform transverse shear strain directly derived from these displacement held assumptions is identified as the weighted-average transverse shear strain through the plate thickness with the corresponding transverse shear stress as the weighting function, while the actual transverse shear strain is permitted to vary through the thickness and satisfies the constitutive law with its stress counterpart. Likewise, the average rotation of the line is identified as its weighted-average value, instead of the one evaluated from a linear regression of the inplane displacement with the least-square method. Examination of bending energy and transverse shear energy supports this interpretation. In addition, an effective transverse shear stiffness parameter is identified and proven appropriate. This restated first-order, shear-deformation theory yields accurate local as well as global response predictions without employing a shear-correction factor. Copyright (C) 1996 Elsevier Science Ltd.