Journal ArticleDOI
Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates
R D Mindlin,R D Mindlin +1 more
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This article is published in Journal of Applied Mechanics-transactions of The Asme.The article was published on 1951-03-01. It has received 4554 citations till now. The article focuses on the topics: Elasticity (economics) & Rotary inertia.read more
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The dynamic stiffness matrix of two-dimensional elements: application to Kirchhoff's plate continuous elements
TL;DR: In this article, a procedure for building the dynamic stiffness matrix of two-dimensional elements with free edge boundary conditions is described, and a Kirchhoff rectangular plate element is constructed from this solution.
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Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory
TL;DR: In this paper, a variationally consistent exponential shear deformation theory for the bi-directional bending and free vibration analysis of thick plates is presented. But the theory does not require shear correction factor.
Journal ArticleDOI
An advanced theory of moderately thick plate vibrations
TL;DR: In this paper, a simple formula for natural frequencies of a simply supported plate is derived, and a characteristic equation is also obtained for a plate with simply supported two opposite edges for different aspect ratios and relative thickness, and very good agreement is achieved.
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Vibration Analysis of Discontinuous Mindlin Plates by Differential Quadrature Element Method
F.-L. Liu,K.M. Liew +1 more
TL;DR: In this paper, a new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in which the complex plate domain is decomposed into small simple continuous subdomains (elements).
Journal ArticleDOI
A new rectangular finite element based on the strain approach for plate bending
Lamine Belounar,Mohamed Guenfoud +1 more
TL;DR: In this article, a new four nodes rectangular finite element for the linear analysis of plate bending with transverse shear effect was developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Journal ArticleDOI
LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars
TL;DR: In this article, the correction for shear of the differential equation for transverse vibrations of prismatic bars is discussed, where the correction is based on the correction of the transverse vibration of a prismatic bar.
Journal ArticleDOI
X. On the transverse vibrations of bars of uniform cross-section
TL;DR: In this article, the transverse vibrations of bars of uniform cross-section were studied and the authors proposed a method to measure the transversal vibrations of a bar of uniform shape.
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Über die Berücksichtigung der Schubverzerrung in ebenen Platten
TL;DR: Ausgehend von einem kinematischen Schema wird eine Methode entwickelt, welche es moglich macht, den Anschlus der technischen Festigkeitslehre an die mathematische Elastizitatstheorie zu bewerkstelligen.