The Room-Temperature Shapes of Four-Layer Unsymmetric Cross-Ply Laminates

Abstract

A previous approximate theory for predicting the room-temperature shapes of unsymmetric laminates is examined in light of the assumptions regarding the inplane strains. The previous theory, which was a geometrically nonlinear extension of classical lamination theory, was felt to be restrictive and this paper develops a new theory in which these restrictions are relaxed. It is shown that despite the previous concern, there is little difference between the previous theory and this theory. This paper presents numerical results for the inplane residual strains of unsymmetric laminates which have cooled from curing into a cylindrical room-temperature shape. It is shown that the residual strains are compressive and practically independent of spatial loca tion on the laminate. In another facet of the paper, the room-temperature shapes of all four-layer unsymmetric cross-ply laminates are predicted. There are only four unique stacking arrangements for this category of laminates and it is shown that their room-temperature shapes are a strong function of their size and their stacking arrangement. Depending on these parameters, the room-temperature shape of a four-layer cross-ply unsymmetric laminate can be a unique saddle shape, a unique cylindrical shape, or a cylindrical shape that can be snapped through to another cylindrical shape.