ON A CONSISTENT FIRST-ORDER SHEAR-DEFORMATION THEORY FOR LAMINATED PLATES

This paper systematically states the consistent first-order shear-defo rmation theory for laminated plates recently proposed by Qi and Knight . It assumes that only in an average sense does a straight line origin ally normal to the midplane remain straight and rotate relative to the normal of the midplane, and in a local sense a slight displacement pe rturbation around the average rotated line is also permitted after def ormation. Since the curved line is very shallow, the present theory st ill approximates linear in-plane and constant transverse displacements through the thickness just as Reissner and Mindlin's first-order shea r-deformation theory does. Reissner and Mindlin's theory leads to unif orm transverse shear strain distributions by employing pointwise strai n-displacement relationships, and satisfies the transverse shear const itutive relationships only in an average corrected form. In contrast, Qi and Knight's theory accounts for variable transverse shear strain d istributions by enforcing pointwise constitutive relationships, and re lates transverse shear strains to kinematic unknowns only in a weighte d-average form. Through-the-thickness transverse shear strains are thu s consistent with the stress counterparts and their transverse-shear-s tress-weighted-average values are just the nominal-uniform transverse shear strains which correspond to the average rotations. The new theor y combines the advantages of several prevailing 2D laminated plate the ories while overcoming their drawbacks. Numerical results far the cyli ndrical bending problem of orthotropic laminated plates exhibit excell ent agreement between Qi and Knight's theory and Pagano's 3D exact ela sticity results. (C) 1997 Elsevier Science Limited.