APPROXIMATE ANALYSIS OF THE BENDING AND VIBRATION OF LAMINATES

Transverse shear effects are important for the bending and vibration of laminated plates.When a laminate is in bending,it is assumed in this paper that the transverse displacement is constant through the plate thickness,and the in-plane displacements vary linearly through each layer,i.e.,they are piecewise linear through the plate thickness.The tatter means that the transverse shear strains within each layer area assumed to be different each other.There are two methods to relate the transverse shear strains within each layer;(1)Demand the continuity of two shear stress components at all interfaces,It is equivalent to that tra nsverse shear stresses are constant respectively through the plate thickness.(2)Assume that transverse shear stresses vary parabolically through the plate thickness.There two metliods correspond with two models of the displacements of the laminates called Piecewise (1)and Piecewise (2) schemes respectively in this paper.According to these two schemes,the governing equations for the bending of a specially orthotropic laminate under a lateral load are obtained on the basis of the principle of minimum potential energy.