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. Bas ed on a more appropriate physical assumption, the restated theory inno vatively interprets its variables and applies elasticity equations in a more pertinent manner. It assumes physically that only in some avera ge sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after defo rmation. Hence the in-plane displacement is still approximated, in an average sense, as linear and the transverse deflection as constant thr ough the plate thickness. The associated nominal-uniform transverse sh ear strain directly derived from these displacement held assumptions i s identified as the weighted-average transverse shear strain through t he plate thickness with the corresponding transverse shear stress as t he weighting function, while the actual transverse shear strain is per mitted to vary through the thickness and satisfies the constitutive la w with its stress counterpart. Likewise, the average rotation of the l ine is identified as its weighted-average value, instead of the one ev aluated from a linear regression of the inplane displacement with the least-square method. Examination of bending energy and transverse shea r energy supports this interpretation. In addition, an effective trans verse shear stiffness parameter is identified and proven appropriate. This restated first-order, shear-deformation theory yields accurate lo cal as well as global response predictions without employing a shear-c orrection factor. Copyright (C) 1996 Elsevier Science Ltd.