Refined theory of orthotropic plates subject to tangential surface loads

Abstract

The existence of two correction coefficients traditionally introduced to account for the effect of the distribution of tangential stresses over the thickness of a plate is discussed. The virtual-work principle is used to generalize the expressions for the coefficients to the case of arbitrary loading. These expressions and hypotheses for displacements help to derive equations for orthotropic rectangular plates subject to tangential surface loads. These equations account for the effect of the distribution of tangential stresses over the thickness of the plate. Numerical examples are given. The results obtained are compared with those produced by other theories Keywords: orthotropic rectangular plate, correction coefficient, distribution of tangential stresses over plate thickness, virtual-work principle, tangential surface loadsIntroduction. The shear theories of plates based on hypotheses for displacements use correction coefficients K x and K y to account for the effect of the distribution of the tangential stresses t xz and t yz over the thickness of the plate [6, 14, etc.]. Contrastingly, the theories based on hypotheses for t xz and t yz [2,8] are constructed making direct use of the distribution of these stresses, which makes the correction coefficients unnecessary.This paper discusses the existence of K x and K y . The virtual-work principle is used to generalize the expressions for K x and K y to the case of arbitrary loading. These expressions and hypotheses for displacements are used to derive equations for orthotropic rectangular plates subject to tangential surface loading. These equations account for the effect of the distribution of t xz and t yz . Numerical examples are given. The results are compared with those produced by other theories [2,4,8,[15][16][17][18].