A MODEL OF A LINEAR VISCOELASTIC ANISOTROPIC PLATE, CONSIDERING AN ARBITRARY INHOMOGENEITY OF THE MATERIAL

Abstract

The paper derives a model of an arbitrary inhomogeneous, anisotropic thin plate with linear viscoelastic components under a slowly varying in time loading; the components of a plate are also supposed anisotropic. The displacements of an inhomogeneous plate are developed following the integral formula approach of composite mechanics, by establishing an interrelation between Laplace transformants of displacement fields of the inhomogeneous plate and a homogeneous one with the corresponding type of anisotropy, so-called concomitant. The interrelation comes from an integral formula approximation by the structural functions technique; in this paper, the first-order approximation of the integral formula is considered. A system of partial differential equations for the first-order structural functions is adjusted for the case of linear viscoelastic components, both in the Laplace and time domain. For a concomitant body, Timoshenko plate equations are generalized onto the anisotropic case. An explicit form of displacements and strains of an inhomogeneous plate is obtained. An example−an instantly applied bending of a simply supported plate, composed of isotropic, asymmetrically laid layers−is considered.