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Static-kinematic duality in beams, plates, shells and its central role in the finite element method

Static-kinematic duality in beams, plates, shells and its central role in the finite element method AbstractStatic and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual work principle. From the matrix operator formulation it clearly emerges the identity of the usual Finite Element Method definition of elastic stiffness matrix and the classical definition of Ritz-Galerkin matrix. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

Static-kinematic duality in beams, plates, shells and its central role in the finite element method

Curved and Layered Structures , Volume 4 (1): 14 – Jan 26, 2017

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Publisher
de Gruyter
Copyright
© 2017
eISSN
2353-7396
DOI
10.1515/cls-2017-0005
Publisher site
See Article on Publisher Site

Abstract

AbstractStatic and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual work principle. From the matrix operator formulation it clearly emerges the identity of the usual Finite Element Method definition of elastic stiffness matrix and the classical definition of Ritz-Galerkin matrix.

Journal

Curved and Layered Structuresde Gruyter

Published: Jan 26, 2017

References