Journal ArticleDOI
Reduction scheme for some structural eigenvalue problems by a variational theorem
TLDR
In this paper, an accurate reduction scheme for structural eigenvalue problems is deduced from a variational theorem in which the displacement, velocity and/or momentum fields are taken to be independent.Abstract:
An accurate reduction scheme for structural eigenvalue problems is deduced from a variational theorem in which the displacement, velocity and/or momentum fields are taken to be independent.read more
Citations
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Journal ArticleDOI
A reduction scheme for problems of structural dynamics
TL;DR: In this paper, a method for reducing the size of finite element systems in dynamics is presented based upon a variational theorem in which it is admissible to describe the inertial properties of structures by way of independent displacement, velocity and momentum fields.
Journal ArticleDOI
Practical Reduction of Structural Eigenproblems
TL;DR: In this article, a modified Guyan reduction method was proposed to reduce the error in the calculation of the eigenvectors of the system and which does not require matrix inversions whatsoever.
Journal ArticleDOI
Imposition of time-dependent boundary conditions in FEM formulations for elastodynamics: critical assessment of penalty-type methods
TL;DR: In this article, a variationally consistent incorporation of time dependent boundary conditions is proposed to avoid ad hoc procedures and is applicable to both linear as well as nonlinear problems, and it is shown that well known and broadly implemented modelling techniques such as large mass and large spring methods arise as limiting cases of the penalty formulation.
Journal ArticleDOI
The finite element method in problems of nonlinear optics
TL;DR: In this article, the authors investigated the applicability of the finite element method to the problem of thermal self-action in a nonlinear medium and presented a general approach to the cretion of conservative computation schemes based on varitional principles.
Journal ArticleDOI
Performance of reduction methods for fluid–structure and acoustic eigenvalue problems
TL;DR: In this article, a methodology is presented for measuring the effectiveness of a finite element approach when compared with a reference finite element method with respect to accuracy and computation, which is applied to the Hughes reduction method for structural eigenvalue problems.
References
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Journal ArticleDOI
Reduction of stiffness and mass matrices
TL;DR: In this article, the authors proposed a method for reducing the size of the stiffness matrix by eliminating coordinates at which no forces are applied, based on the procedure used in Ref. 1 for stiffness matrix reduction.
The Finite Element Method in Structural and Continuum Mechanics
O. C. Zienkiewicz,Y.K. Cheung +1 more
TL;DR: In this paper, a mathematical reference record was created on 2004-09-07, modified on 2016-08-08, and used for modelisation of mathematical reference records for the Mathematique Reference Record.
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The numerical solution of eigenvalue problems in which the eigenvalue problems in which the eigenvalue parameter appears nonlinearly, with an application to differential equations
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