Exact elasticity solution for buckling of composite laminates

An exact elasticity solution is presented for the buckling of a simply-supported orthotropic plate whose behavior is referred to as cylindrical bending. The general class of problems involving the geometric configuration of any number of orthotropic layers bonded together and subjected to an inplane compressive load is also analyzed by making use of the uniform prebuckling stress assumption which is equivalent to the membrane assumption used in plate theories. The closed-form expressions for the displacements and stresses are derived and the nonlinear eigenvalue equations are presented which are used to solve for critical loads. The results obtained from the exact solution are compared with the critical loads furnished by the classical laminate theory, the first order and the refined third order shear deformation theory. The solution provides a means of accurate assessment of existing two-dimensional plate theories.