Approach to Three-Dimensional Analysis of Finite Three-Layered Composite Plates with a Through Crack

The paper presents an analytical approach to evaluation of the stresses, strains and displacements in a composite symmetrically laminated three-layered plate with a through crack. The plate is subjected to tensile and shearing loads (Modes I and II). In-plane stresses, strains and displacements are represented by the products of terms that depend on the in-plane coordinates and a polynomial including powers of the thickness coordinate. The in-plane terms are specified as real functions using the previous two-dimensional solution. The coefficients at the powers of the thickness coordinate can be obtained using the principle of virtual work or equilibrium of forces in a number of cross sections. If is shown, that if the latter method of the evaluation of the coefficients is used, transverse normal and shearing stresses can be found by direct integration of the three-dimensional equilibrium equations, i.e. these equations are satisfied exactly. The approach discussed in the paper can be extended to laminates with an arbitrary number of generally orthotropic layers. The solution for the case of a plate with several parallel cracks can be obtained by superposition of solutions obtained for a single crack.