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Total Lagrangian formulation for the large displacement analysis of rectangular plates
Author(s) -
Chang Bilin,
Shabana A. A.
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620290107
Subject(s) - rigid body , translation (biology) , displacement (psychology) , rotation (mathematics) , displacement field , finite element method , invariant (physics) , deformation (meteorology) , classical mechanics , mathematical analysis , equations of motion , mathematics , linear elasticity , geometry , physics , psychology , biochemistry , chemistry , messenger rna , meteorology , mathematical physics , psychotherapist , gene , thermodynamics
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.