The vibration of mindlin plates
01 May 1999-pp 200-246
About: The article was published on 1999-05-01. It has received 11 citations till now.
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TL;DR: In this paper, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated.
Abstract: Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown fields (Analysis). IGA can be based on a variety of CAD descriptions, the most widely used today being non-uniform rational B-splines (NURBS). In this article, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated. The method employs NURBS basis functions to both represent the geometry (exactly) and the unknown field variables. One of the main advantages of the present method is directly inherited from IGA, that is to easily increase the approximation order. To avoid using a shear correction factor, a third-order shear deformation theory (TSDT) is introduced. It requires C1-continuity of generalized displacements and the NURBS basis functions are well sui...
138 citations
Cites methods from "The vibration of mindlin plates"
...[73], finite element method by Hinton [74] and exact solutions in [75]....
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TL;DR: In this paper, the Lagrange's delta sequence kernel (DSC-LK) was used for vibration analysis and the results of the LK were compared with both those in the literature and newly computed GDQ results.
119 citations
TL;DR: In this paper, a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels is presented.
Abstract: The present article illustrates a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels. The theoretical framework relates to the dynamic analysis of shell structures by using a general displacement field based on the Carrera Unified Formulation (CUF), including the stretching effect for each layer. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order layer-wise formulation is to propose a kinematic assumption, with an arbitrary number of degrees of freedom. The main aim of this work is to determine the explicit fundamental operators that can be used for the layer-wise (LW) approach. These fundamental operators are obtained for the first time by the author and are related to motion equations of doubly-curved shells described in an orthogonal curvilinear co-ordinate system. The free vibration shell and...
87 citations
25 Mar 2014
TL;DR: In this article, a new technique for solving the static analysis of arbitrarily shaped composite plates by using Strong Formulation Finite Element Method (SFEM) is presented, which is an extension of the classic Generalized Differential Quadrature (GDQ) procedure.
Abstract: This paper provides a new technique for solving the static analysis of arbitrarily shaped composite plates by using Strong Formulation Finite Element Method (SFEM). Several papers in literature by the authors have presented the proposed technique as an extension of the classic Generalized Differential Quadrature (GDQ) procedure. The present methodology joins the high accuracy of the strong formulation with the versatility of the well-known Finite Element Method (FEM). The continuity conditions among the elements is carried out by the compatibility or continuity conditions. The mapping technique is used to transform both the governing differential equations and the compatibility conditions between two adjacent sub-domains into the regular master element in the computational space. The numerical implementation of the global algebraic system obtained by the technique at issue is easy and straightforward. The main novelty of this paper is the application of the stress and strain recovery once the displacement parameters are evaluated. Computer investigations concerning a large number of composite plates have been carried out. SFEM results are compared with those presented in literature and a perfect agreement is observed.
64 citations
TL;DR: In this paper, the stress and strain recovery procedure applied for solving doubly-curved structures with variable radii of curvature has been considered using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the inplane displacement parameters are defined independently from the ones through the shell thickness.
Abstract: The stress and strain recovery procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of...
59 citations
References
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4,554 citations
296 citations
TL;DR: In this paper, a solution for the free vibration eigenvalues of Mindlin plates resting on uniform lateral elastic edge support was obtained for the rotational stiffness of the Mindlin plate.
39 citations
TL;DR: In this paper, the Rayleigh-Ritz superposition method was used to obtain accurate solutions for the natural frequencies and mode shapes of the completely free Mindlin plate, and the computed eigenvalues were tabulated for a number of plate aspect and thickness ratios.
35 citations
TL;DR: In this article, the free flexural vibration of clamped rectangular Mindlin plates was analyzed using the method of superposition and it was shown that the rotatory inertia does not significantly affect plate flexural vibrations.
Abstract: The method of superposition is further developed to analyze free flexural vibration of clamped rectangular Mindlin plates. Comparison of results given by Mindlin’s theory of plates with those previously obtained by Reissner’s theory has shown that the rotatory inertia does not significantly affect plate flexural vibration. Accurate eigenvalues are presented for a number of values of plate aspect ratio along with two representative values of thickness ratio.
10 citations