Dynamic Formulation for Geometrically Exact Sandwich Beams and One-Dimensional Plates

Abstract

A new theory of sandwich beams/one-dimensional plates is presented with finite rotations and shear allowed in each layer. The layers, variable in number from one to three, need not have the same thickness and the same length, thus allowing for ply drop-off. Restricting to planar deformation, the cross section has a motion identical to that of a multibody system that consists of rigid links connected by hinges. Large deformation and large overall motion are accommodated, with the beam dynamics referred directly to an inertial frame. An important approximated theory is developed from the general nonlinear equations. The classical linear theory is recovered by consistent linearization.

Nonlinear dynamics of elastic rods using the Cosserat theory: Modelling and simulation

“…Alternatively, the moving frame can be described by the rotation group SO(3) as the formulations in Vu-Quoc (1988, 1991), Vu-Quoc and Deng (1995) and Vu-Quoc and Ebcioglu (1995). The three successive rotations starts by rotating the basis {e 1 , e 2 , e 3 } an angle w(s, t) about the axis aligned with the director e 2 as shown in Fig.…”

“…For the three-dimensional problem, we refer to Vu-Quoc (1988, 1991) for a geometrically exact rod model incorporating shear and torsion-warping deformation. Further studies on the dynamic formulation of sandwich beams have been presented in Vu-Quoc and Deng (1995) and Vu-Quoc and Ebcioglu (1995) based on the geometrically-exact description of the kinematics of deformation. Moreover, Esmailzadeh and Jalili (1998) investigated the parametric response of cantilever Timoshenko beams with lumped mass, but restricted themselves to consideration of nonlinear inertia terms.…”

A co-rotational formulation for 3D beam element using vectorial rotational variables

“…Updated Lagrangian formulation (Bathe and Bolourchi 1979, Cardona and Geradin 1988, Chen and Blandford 1991, Misra et al 2000, Teh and Clarke 1999 and co-rotational formulation (Battini and Pacoste 2002, Crisfield 1990, Crisfield and Moita 1996, Hsiao et al 1987, Hsiao and Lin 2000a, Teh and Clarke 1998, certainly, there also exist some mixed type formulations of them (Jiang and Chernuka 1994, Hsiao and Lin 2000b, Lin and Hsiao 2001. In addition, Simo and Vu-Quoc developed a class of geometrically-exact beam formulation, this formulation demonstrates its computational efficiency in large displacement analyses of frame structures and benefit in solving dynamic problems of flexible beam or beams system subject to large overall motions (Simo and VuQuoc 1986a,b, 1988, Vu-Quoc and Deng 1995, Vu-Quoc and Ebcioglu 1995, 1996, Vu-Quoc and Simo 1987. For convenience, these formulations can also be classified into two groups: formulations with asymmetric element tangent stiffness matrices and formulations with symmetric element tangent stiffness matrices.…”

“…For convenience, these formulations can also be classified into two groups: formulations with asymmetric element tangent stiffness matrices and formulations with symmetric element tangent stiffness matrices. Due to the non-commutativity of spatial rotations, most co-rotational formulations belong to the first group, and the geometrically-exact beam formulation proposed by Simo and Vu-Quoc also falls into this category (Simo and Vu-Quoc 1986a,b, 1988, Vu-Quoc and Deng 1995, Vu-Quoc and Ebcioglu 1995, 1996, Vu-Quoc and Simo 1987. For an asymmetric tangent stiffness matrix, more storage is occupied so as to store all its components.…”

Analysis of Fly Fishing Rod Casting Dynamics

“…Because most modern fly rods are fabricated by the graphite-epoxy composite materials, the geometrically-exact composite beam models can be used to capture the dynamic behavior of fish rods [12,13]. In addition, the fly rods are hollow and tapered beam structures.…”