A parametric study for thick plates resting on elastic foundation with variable soil depth

The soil depth is generally considered to be constant for the analysis of plates resting on elastic foundation in the literature. However, it is most reasonable to have a variable subsoil depth as the plate dimensions get larger. In present study, linearly varying subsoil depth is considered as well as constant, linear and quadratic variation of modulus of elasticity with subsoil depth. Also, a parametric study is performed to demonstrate the behavior of thick plates on elastic foundations with variable soil depth. Modified Vlasov Model is used for the analysis of the plate foundation system, and 8-noded Mindlin plate element incorporating shear strain throughout plate thickness is used for the finite element model. Numerical examples are obtained from the literature to compare results and to show the influence of variable soil stratum depth on the behavior of plates. Displacements, bending moments, and shear forces are presented in tabular and graphical formats. As far as results are compared, it can be concluded that variable soil depth significantly affects the variation of the displacements and therefore the internal forces of the plate while keeping it constant ends up with unrealistic results.     

Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method

Free vibration analysis of moderately thick rectangular FG plates on elastic foundation with various combinations of simply supported and clamped boundary conditions are studied. Winkler model is considered to describe the reaction of elastic foundation on the plate. Governing equations of motion are obtained based on the Mindlin plate theory. A semi-analytical solution is presented for the governing equations using the extended Kantorovich method together with infinite power series solution. Results are compared and validated with available results in the literature. Effects of elastic foundation, boundary conditions, material, and geometrical parameters on natural frequencies of the FG plates are investigated.     

Large deflection analysis of the moderately thick general theta ply laminated plates on nonlinear elastic foundation with various boundary conditions

This paper presents a powerful method i.e. the kinetic Dynamic Relaxation for analyzing general theta ply laminated plates, resting on nonlinear elastic foundation with different boundary conditions. Comprehensive comparison and parametric studies prove accuracy and efficiency of the proposed approach with interesting specifications such as fully vector calculations, independency to configuration, situation and angle of plies so that general theta ply laminated plate with simultaneous coupling between membrane, bending and shear strains could be analyzed as simple as analyzing of symmetric cross ply plate. Moreover, the proposed technique could simply satisfy complicated boundary conditions such as free and movable edges.     

Elastic stability of inhomogeneous thin plates on an elastic foundation

We study the elastic stability of infinite inhomogeneous thin plates on an elastic foundation under in-plane compression. The elastic stiffness constants depend on the coordinate variable in the thickness direction of the plate. The elastic foundation is represented as a Winkler-type model characterized by linear and nonlinear spring constants. First we derive the Föppl–von Kármán equations by taking variations of the elastic strain energy. Next we develop the linear stability analysis of the plate under uniform in-plane compression and explicitly derive the critical loads and wave numbers for particular three cases. The effects of the material inhomogeneity, material orthotropy and loading orthotropy on the critical states are examined independently. Finally, we perform a weakly nonlinear analysis of the plate at the onset of the buckling instability. With the multiple scales method, the amplitude equations for the unstable modes that provide insight into the mode type and its amplitude are derived and then the effect of the material inhomogeneity on buckling modes are evaluated qualitatively.     

Buckling and post-buckling of annular plates on an elastic foundation

On the basis of von Kárman equations,the axisymmetric buckling and post-bucklingof annular plates on anelastic foundation is(?)tematically discussed byusing shootingmethods.     

Large deflection analysis of plates on elastic foundation by the boundary element method

A boundary element method is developed for the large deflection analysis of thin elastic plates resting on elastic foundation. The subgrade reaction may depend linearly (Winkler-type) or nonlinearly on the deflection as well as on the point coordinates (nonhomogeneous subgrade). Moderately large deflections are examined as described by the von Karman equations. The plate may have arbitrary shape and its boundary may be subjected to any type of boundary condition. The proposed method uses the fundamental solution of the linear plate theory and treats the nonlinearities as well as the subgrade reaction as unknown domain forces. Numerical results are presented to illustrate the method and demonstrate its effectiveness and accuracy.     

Static analysis of rectangular thick plates resting on two-parameter elastic boundary strips

In this paper, the Generalized Differential Quadrature (GDQ) method is used to obtain bending solution of moderately thick rectangular plates. The plate is resting on two-parameter elastic (Pasternak) foundation or strips with a finite width. Various combinations of clamped, simply supported and free boundary conditions are considered. According to the first-order shear deformation theory, the governing equations of the problem consist of three second-order partial differential equations (PDEs) in terms of displacement and rotations of the plate. The governing equations and solution domain is discretized based on the GDQ method. It is demonstrated that the method converges rapidly while providing accurate results with relatively small number of grid points. Accuracy of the results is examined using available data in the literature for Pasternak foundation. Furthermore, due to lack of data for Pasternak strips, all predictions are verified by finite element analysis which can be used as benchmark in future studies.     

Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations

The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functionally graded(FG) layer and a graphene platelet(GPL) reinforced porous layer, respectively. Henceforth, the combined layers will be referred to as a two-dimensional(2D) FG/GPL plate. Two types of porosity and three graphene dispersion patterns, each of which is distributed through the p...     

Large amplitude free vibrations of irregular plates placed on an elastic foundation

A unified method for determining the lowest natural frequency of large amplitude free vibrations of thin elastic plates of any shape and placed on elastic foundation is given. The conformal mapping technique is introduced and Galerkin's method is used to calculate approximate values of the lowest natural frequency. Time periods for circular, square and cornered plates placed on elastic foundation have been determined for simply supported and clamped edge boundary conditions. Practical values have also been determined experimentally. The results are presented in the form of graphs and they are compared with other known results.     

Nonlinear axisymmetric static and transient analysis of orthotropic thick annular plates

Summary This paper deals with the geometrically nonlinear axisymmetric static and transient response of moderately thick cylindrically orthotropic circular plates subjected to uniformly distributed and ring loads. Immovable clamped and simply supported annular plates with and without a rigid plug subjected to static and step function loads have been considered. Shear deformation and rotary inertia have been included. Orthogonal point collocation method and Newmark- scheme have been employed to solve the differential equations expressed in terms of transverse displacement , shear rotation and stress function . The effect of transverse shear has been investigated for isotropic and orthotropic plates. A simple approximate method has also been used to predict the maximum dynamic response to step loads from the results for static loads.

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Nichtlineare, axialsymmetrische, statische und dynamische Analyse orthotroper, dicker Kreisringplatten

Übersicht Es wird das geometrisch nichtlineare, axialsymmetrische Verhalten orthotroper Kreisring-platten unter gleichmäßig bzw. ringförmig verteilten Lasten untersucht. Eingespannte und gelenkig gelagerte Platten mit oder ohne starrem Pfropfen unter statischer oder dynamischer Belastung werden behandelt, wobei Schubdeformation und Drehträgheit berücksichtigt werden. Eine Kollokationsmethode und das Newmarksche -Schema werden angewendet, um die Differentialgleichungen für die Durchbiegung , die Verdrehung und die Spannungsfunktion zu lösen.

     

Resonant effects of local loads on circular sandwich plates on an elastic foundation

The axisymmetric forced vibrations of a circular sandwich plate on an elastic foundation are studied. The plate is subjected to axisymmetric surface and mechanical loads with frequency equal to one of the natural frequencies of the plate. The foundation reaction is described by the Winkler model. To describe the kinematics of an asymmetric sandwich, the hypothesis of broken normal is used. The core is assumed to be light. The analytical solution of the problem is obtained and numerical results are analyzed     

NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

IntroductionThe moderate thickness plates on elastic foundation are a kind of important structure instructural engineering. The mechanic characters of the plates on elastic foundation withdifferent boundary conditions have been received considerable atten…     

非均匀Winkler弹性地基上变厚度矩形板自由振动的DTM求解

针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法（DTM）,研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。     

Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach

This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.     

Postbuckling analysis of columns resting on an elastic foundation

The postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed. This is established by employing an approximate analytic technique leading to very reliable results in the vicinity of the critical state. It was found that the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections. Moreover, a simple but readily analyzed mechanical model is proposed to simulate the salient features of buckling mechanism of the column on elastic foundation with those of the model. The simplicity, reliability and efficiency of the proposed analysis as well as the successful modeling of the buckling mechanism of the column by that of a single mode mechanical model are illustrated with the aid of numerical examples.     

Nonlinear vibration of generally laminated anisotropic thick plates

Summary Nonlinear equations of motion of generally laminated anisotropic plates are derived by use of Hamilton's principle. The effects of transverse shear and rotatory inertia are included in the analysis. The equations of motion so obtained readily reduce to those obtained in a recent nonlinear theory of anisotropic plates including transverse shear and rotatory inertia and to the dynamic von Kármán equations of plates. Based on the Galarkin procedure and principle of harmonic balance approximate solutions to the governing equations of generally laminated rectangular plates are formulated for various boundary conditions. Including the effects of transverse shear and rotatory inertia numerical results for the ratio of nonlinear frequency to linear frequency of symmetric angle-ply and cross-ply laminates, unsymmetric angle-ply and cross-ply laminates and an arbitrarily laminated plate are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, thickness-to-span ratio and aspect ratio. Present results are also compared with the existing data.

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Nichtlineare Schwingungen von anisotropen, dicken Verbundplatten

übersicht Die nichtlinearen Bewegungsgleichungen anisotroper, dicker Verbundplatten werden mit Hilfe des Prinzips von Hamilton hergeleitet. Dabei werden die Einflüsse der Schubspannungen und der Drehträgheit berücksichtigt. Mit dem Verfahren von Galerkin und der Methode der harmonischen Balance werden Näherungslösungen für Rechteckplatten bei verschiedenen Randbedingungen gewonnen. Numerische Ergebnisse für verschiedene Materialparameter sind graphisch dargestellt und werden mit bereits bekannten Ergebnissen verglichen.

     

Nonlinear equations of elastic deformation of plates

A method for constructing nonlinear equations of elastic deformation of plates with boundary conditions for stresses and displacements at the face surfaces in an arbitrary coordinate system is proposed. The initial three–dimensional problem of the nonlinear theory of elasticity is reduced to a one–parameter sequence of two–dimensional problems by approximating the unknown functions by truncated series in Legendre polynomials. The same unknowns are approximated by different truncated series. In each approximation, a linearized system of equations whose differential order does not depend on the boundary conditions at the face surfaces which can be formulated in terms of stresses or displacements is obtained.     

Nonlinear bending analysis of FGM rectangular plates with various supported boundaries resting on two-parameter elastic foundations

In this paper, model of the FGM plates resting on two-parameter elastic foundations is put forward by using on physical neutral surface and high-order shear deformation theory. Material properties are assumed to be temperature dependent and vary along the thickness, while Poisson’s ratio depends weakly on temperature change and position and is assumed to be a constant. It is worth noting that physical neutral surface will be changed with temperature. The character of physical neutral surface higher-order shear deformation plate theory is that the displacements have special forms, stretching-bending couplings are eliminated in constitutive equations, and governing equations have the simple and similar forms as homogeneous isotropic plates. The validity of physical neutral surface higher-order shear deformation plate theory can be confirmed by comparing with related researchers’ results. Nonlinear bending approximate solutions of FGM rectangular plates with six cases of boundary conditions are given out using Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions, and volume fraction index are discussed in detail.