Local/global stiffness matrix formulation for composite materials and structures

Abstract

An efficient algorithm is outlined for solving boundary-value problems involving laminated composite materials and structures that require satisfaction of both continuity of tractions and displacements along common interfaces. The method is based on the systematic construction of a global stiffness matrix for the entire laminated structure in terms of local stiffness matrices of the individual layers. The local stiffness matrix relates the traction components at the upper and lower (or inner and outer) surface of a given layer to the corresponding displacements. The assembly of local stiffness matrices into a global stiffness matrix is carried out by enforcing continuity conditions along the interfaces which, in effect, leads to reformulation of the problem in terms of interfacial displacements as the basic unknown variables. This, in turn, results in the elimination of certain redundant continuity conditions and thus reduction in the number of simultaneous algebraic equations that need to be solved. An additional advantage of the local/global stiffness matrix formulation is the ease with which certain mixed boundary-value problems can be reduced to singular integral equations of the Fredholm type for the determination of unknown quantities such as the contact pressure in the case of contact problems and the crack-opening displacement in the case of interfacial crack problems.