Total Lagrangian formulation for the large displacement analysis of rectangular plates

Abstract

In this paper, a method for the non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co-ordinate system using the assumptions of the classical theories of plates. Non-linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time-invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two-parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non-linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non-linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.

An immersed boundary method for fluid–structure interaction with compressible multiphase flows

“…Several finite element formulations have been proposed for the large displacement and deformation analysis of flexible multi-body systems [18,42], including the floating frame of reference method, the incremental finite element method, the large rotation vector method and the absolute nodal coordinate formulation (ANCF). Previous studies show that the performance and efficiency of multi-body simulation codes depend largely on the coordinates selection [43,44,45,46]. ANCF proposed by Shabana et al [44,45] which employs a set of finite element coordinates defined in the global coordinate has a superiority in handling large structure deformation and rotation.…”

Aeroelastic Analysis of Rotor Blades Using Three Dimensional Flexible Multibody Dynamic Analysis

“…Experimental studies such as the Princeton beam test [Dowell and Traybar (1975)] have been conducted to investigate the response of beams made of isotropic material experiencing large deformation. The experiments conducted by Dugundji (1990a and1990b), on the other hand, dealt with composite beams exhibiting various types of coupling due to different ply layup. The nonlinear capabilities of the present method are therefore validated against the experimental results obtained by Minguet and Dugundji (1990a).…”

On Dynamic Stiffening of Flexible Bodies Having High Angular Velocity*

“…To develop a consistent linearized theory, it is helpful to initially express the velocity of P in terms up to the second order in the displacements of P relative to 'PI P 1 (5) Finally, by substituting from Eqs. 3 and 5 into Eq.…”