Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates
01 Nov 1970-International Journal of Solids and Structures (Elsevier B.V.)-Vol. 6, Iss: 11, pp 1463-1481
TL;DR: In this article, a unified exact analysis for the statics and dynamics of a class of thick laminates is presented, which leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems.
About: This article is published in International Journal of Solids and Structures.The article was published on 1970-11-01. It has received 770 citations till now. The article focuses on the topics: Plate theory & Vibration of plates.
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TL;DR: In this paper, a new standard plate theory, which accounts for cosine shear stress distribution and free boundary conditions for shear stresses upon the top and bottom surfaces of the plate, is presented.
932 citations
TL;DR: In this paper, a higher-order shear deformation theory of plates accounting for the von Karman strain was presented, which contains the same dependent unknowns as in the Hencky-Mindlin type first-order deformation theories and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
695 citations
TL;DR: A review of the reported studies in the area of thermo-elastic and vibration analyses of functionally graded (FG) plates with an emphasis on the recent works published since 1998 is presented in this paper.
695 citations
TL;DR: In this article, a higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia.
629 citations
TL;DR: In this paper, exact solutions for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings are derived.
Abstract: Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.
584 citations
References
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Book•
01 Jan 1959
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Abstract: CONTENTS: BENDING OF LONG RECTANGULAR PLATES TO A CYLINDRICAL SURFACE PURE BENDING OF PLATES SYMMETRICAL BENDING OF CIRCULAR PLATES SMALL DEFLECTIONS OF LATERALLY LOADED PLATES SIMPLY SUPPORTED RECTANGULAR PLATES RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS CONTINUOUS RECTANGULAR PLATES PLATES ON ELASTIC FOUNDATION PLATES OF VARIOUS SHAPES SPECIAL AND APPROXIMATE METHODS IN THEORY OF PLATES BENDING OF ANISTROPIC PLATES BENDING OF PLATES UNDER THE COMBINED ACTION OF LATERAL LOADS AND FORCES IN THE MIDDLE PLANE OF THE PLATE LARGE DEFLECTIONS OF PLATES DEFORMATION OF SHELLS WITHOUT BENDING GENERAL THEORY OF CYLINDRICAL SHELLS SHELLS HAVING THE FORM OF A SURFACE OF REVOLUTION AND LOADED SYMMETRICALLY WITH RESPECT TO THEIR AXIS.
10,200 citations
4,554 citations
2,971 citations
Book•
01 Jan 1969
TL;DR: In this article, elementary differential equations and boundary value problems are studied in the context of boundary value problem, where boundary value is defined as a function of the boundary value of the elementary differential equation.
Abstract: Elementary differential equations and boundary value problems , Elementary differential equations and boundary value problems , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
1,575 citations
TL;DR: In this paper, a two-dimensional linear theory of motions of heterogeneous plates is deduced from the three-dimensional theory of elasticity, which is specialized to cases of symmetrically laminated aeolotropic, orthotropic and isotropic plates.
710 citations