A Layer-Wise Laminate Theory Rationally Deduced From the Three-Dimenstonal Elasticity

Abstract

A layer-wise theory of laminated plates, which accounts for piecewise constant shear strain in the thickness, is derived from the three-dimensional elasticity theory by imposing suitable constraints on the strain and stress fields. At this aim, the functional of the three-dimensional elasticity is modified according to the Lagrange multipliers theory. In fact, a nonstandard application of the Lagrange theory is presented, because of the simultaneous presence of constraints on dual spaces. The imposed constraints make reactive strain and stress fields arise. Thus, it is necessary to distinguish between elastic and total strain and stress fields. The difference between them is emphasized in a numerical application.