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A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free... The first goal of this work is to present a literature review regarding the use of several sets of admissible functions in the Ritz method. The papers reviewed deal mainly with the analysis of buckling and free vibration of isotropic and anisotropic beams and plates. Theoretically, in order to obtain a correct solution, the set of admissible functions must not violate the essential or geometric boundary conditions and should also be linearly independent and complete. However, in practice, some of the sets of functions proposed in the literature present a bad numerical behavior, namely in terms of convergence, computational time and stability. Thus, a second goal of the present work is to compare the performance of several sets of functions in terms of these three features. To achieve this objective, the free vibration analysis of a fully clamped rectangular plate is carried out using six different sets of functions, along with the study of the convergence of natural frequencies and mode shapes, the computational time and the numerical stability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Computational Methods in Engineering Springer Journals

A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

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Publisher
Springer Journals
Copyright
Copyright © 2017 by CIMNE, Barcelona, Spain
Subject
Engineering; Mathematical and Computational Engineering
ISSN
1134-3060
eISSN
1886-1784
DOI
10.1007/s11831-017-9214-7
Publisher site
See Article on Publisher Site

Abstract

The first goal of this work is to present a literature review regarding the use of several sets of admissible functions in the Ritz method. The papers reviewed deal mainly with the analysis of buckling and free vibration of isotropic and anisotropic beams and plates. Theoretically, in order to obtain a correct solution, the set of admissible functions must not violate the essential or geometric boundary conditions and should also be linearly independent and complete. However, in practice, some of the sets of functions proposed in the literature present a bad numerical behavior, namely in terms of convergence, computational time and stability. Thus, a second goal of the present work is to compare the performance of several sets of functions in terms of these three features. To achieve this objective, the free vibration analysis of a fully clamped rectangular plate is carried out using six different sets of functions, along with the study of the convergence of natural frequencies and mode shapes, the computational time and the numerical stability.

Journal

Archives of Computational Methods in EngineeringSpringer Journals

Published: Mar 24, 2017

References