General Multilayer Geometrically-Exact Beams/1-D Plates with Deformable Layer Thickness: Equations of Motion

Abstract

We formulate a theory of geometrically‐exact multilayer beams and one‐dimensional plates that account for the through‐the‐thickness deformation in each layer, in addition to shear deformation. The complete set of nonlinear equations of motion together with the appropriate boundary conditions are derived, and a linear constitutive law is postulated for the model. The number of layers is arbitrary and unlimited, with a reference layer arbitrarily chosen among the layers. The length and the thickness of each layer are also variable, making the modeling of multilayer structures with ply drop‐offs possible. The present theory reduces exactly to the case of multilayer structures without through‐the‐thickness deformation, and to the case of single‐layer structures. The formulation allows the description of large deformation and large overall motion in multilayer structures.

Analysis of Fly Fishing Rod Casting Dynamics

“…By doing this, we obtain a simple kinematic relationship between strain and displacements. As discussed in [16,19,22,23], the nonlinear beam axial strain, , shear strain, γ, and bending curvature, κ, can be expressed in terms of axial displacement u(x), transverse displacement, w(x), and rotation, displacement, θ, as follows for a straight beam:…”

“…The strain expressions are the same as those obtained by Antman [20], Simo and Vu-Quoc [16], and Vu-Quoc and Ebcioglu [22], in which the strains were derived in a vector form. The next step is to apply the finite element techniques to discretize the beam system.…”

The Thomsen model of inserts in sandwich composites: An evaluation

“…• Higher-order nonlinear single-layer theories that account for thickness change (see for example, [12,13,14,15,16]).…”