MULTILAYER BEAMS - A GEOMETRICALLY EXACT FORMULATION

We review and extend our recent work on a new theory of multilayer str uctures, with particular emphasis on sandwich beams/1-D plates. Both t he formulation of the equations of motion in the general dynamic case and the computational formulation of the resulting nonlinear equations of equilibrium in the static case based on a Galerkin projection are presented. Finite rotations of the layer cross sections are allowed, w ith shear deformation accounted for in each layer. There is no restric tion on the layer thickness; the number of layers can vary between one and three. The deformed profile of a beam cross section is continuous , piecewise linear, with a motion in 2-D space identical to that of a planar multibody system that consists of three rigid links connected b y hinges. With the dynamics of this multi (rigid/flexible) body being referred directly to an inertial frame, the equations of motion are de rived via the balance of (1) the rate of kinetic energy and the power of resultant contact (internal) forces/couples, and (2) the power of a ssigned (external) forces/couples. The present formulation offers a ge neral method for analyzing the dynamic response of flexible multilayer structures undergoing large deformation and large overall motion. Wit h the layers not required to have equal length, the formulation permit s the analysis of an important class of multilayer structures with ply drop-off. For sandwich structures, an approximated theory with infini tesimal relative outer-layer rotations superimposed onto finite core-l ayer rotation is deduced from the general nonlinear equations in a con sistent manner. The classical linear theory of sandwich beams/1-D plat es is recovered upon a consistent linearization. Using finite element basis functions in the Galerkin projection, we provide extensive numer ical examples to verify the theoretical formulation and to illustrate its versatility.