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R-function method and variational method for the bending problem of functionally graded plates with fixed supports and complex shapes. [PDF]

Sci Rep
Su K, Li S.
europepmc   +1 more source

Bending Solutions of Sectorial Thick Plates Based on Reissner Plate Theory

Mechanics Based Design of Structures and Machines, 2005
This paper is concerned with the bending of sectorial and annular sectorial thick plates with the radial edges simply supported. The Reissner plate theory has been adopted to cater for the effect of transverse shear deformation. In solving the aforementioned plate problems, we derive the relationships between the bending solutions of the Reissner plate
Wang, C.M., Nazmul, I.M., Matsumoto, T., Wang, Q.   +3 more
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Dynamic Bergan–Wang theory for thick plates

Mathematics and Mechanics of Complex Systems, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Askes, Harm, Wallace, Alexandra R.
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Generalized Theory for Bending of Thick Plates

Transactions of the Canadian Society for Mechanical Engineering, 1990
Several refined theories of plates have been developed in the recent decade. All such theories have attempted to incorporate the effects of transverse shear stresses and transverse normal stress and strain which become important as the ratio of the plate thickness to characteristic length (h/L) increases.
Ammar K. Muhammad, Mohammad H. Baluch, Abul K. Azad   +2 more
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The refined theory of piezoelectric thick plates

2009 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA 2009), 2009
Based on linear piezoelasticity theory, without requirement of any ad hoc assumptions concerning the deformation or the stress state, various two-dimensional equations have been deduced systematically and directly from the three-dimensional theory of thick rectangular plates by using the general solution of transversely isotropic piezoelasticity and ...
null Yang Gao, null Bao-sheng Zhao, null Si-peng Xu   +2 more
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An advanced theory of moderately thick plate vibrations [PDF]

Journal of Sound and Vibration, 2013
In thick plate vibration theory, the governing equations are stated with a system of three partial differential equations of motion with total deflection, which consists of bending deflection and shear contribution, and angles of rotation as fundamental variables.
Tomić, Marko, Senjanović, Ivo, Vladimir, Nikola   +2 more
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Refined Theory for Thick Composite Plates

Journal of Engineering Mechanics, 1988
A refined theory for the bending of composite plates is developed, based on an assumed variation of the shear stresses through the thickness. The influence of transverse normal strain, transverse normal stress, and shear deformation is accounted for in the formulation. The development yields a bending‐extension coupling, yielding a tenth‐order boundary
George Z. Voyiadjis, Mohammed H. Baluch
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A Refined Theory of Anisotropic Thick Plates

1990
For the deformation of anisotropic plates with arbitrary thickness, a refined theory is proposed to derive approximate equations with any desired accuracy, and general two-dimensional equations in the n-th order approximation are presented. The approximate equations presented are solved for a graphite/epoxy composite plate subjected to a sinusoidally ...
Satoru IGARASHI, Katsuhisa SHIBUKAWA
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On the Elastodynamic Theory of Thick Circular Plates

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1980
AbstractConsidering elastodynamic deformation of circular plates, this paper presents a generalization of the method of initial functions in cylindrical coordinates. The governing equations of the theory are derived from the three dimensional elastodynamic equations. The method is applied to the free vibration of the clamped circular plate.
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Theory for plates of medium thickness

Journal of Applied Mathematics and Mechanics, 1962
Abstract A theory of elastic Isotropic plates of constant thickness is constructed without assumptions about the nature of the deformations of the transverse linear elements. The stresses σ xx , σ xy , σ yy are expanded in a series of Legendre polynomials P k ( 2z h ) .
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