Vibration analysis of orthotropic rectangular plates on elastic foundations

The vibration responses of orthotropic plates on nonlinear elastic foundations are numerically modeled using the differential quadrature method. The differential quadrature technique is utilized to transform partial differential equations into a discrete eigenvalue problem. Numerical results and those from literature closely correspond to each other. Numerical results demonstrate that elastically restrained stiffness, plate aspect ratio and foundation stiffness significantly impact the dynamic behavior of orthotropic plates.     

Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations

Thermo-mechanical buckling analysis of the orthotropic auxetic plates (with negative Poisson ratios) has not been performed so far, especially, in the hygrothermal environments. The complexity increases when the auxetic plate is fabricated from functionally graded orthotropic materials and surrounded by an elastic foundation. The aforementioned analyses are carried out in the present research, for the first time. The buckling loads may be uniaxial or biaxial ones. Moreover, temperature and moisture dependent material properties are considered. The pre-buckling effects are also considered in the paper. The high-order shear-deformation governing differential equations are solved based on a new differential quadrature method (DQM). The resulting solution may cover many practical simpler applications. A comprehensive parametric study is accomplished for a wide range of geometric and material properties parameters and various boundary conditions. Results reveal that the hygrothermal conditions lead to degradations in the material properties and buckling strengths, especially for higher gradation exponents, the elastic foundation may enhance the buckling behavior through monitoring the buckling pattern, the buckling load decreases as the orthotropy angle increases, and the auxeticity has reduced the buckling strength for the employed material and environmental information.     

Nonlinear transient response of orthotropic thin rectangular plates on elastic foundations

This paper presents geometrically nonlinear transient analysis of rectilinearly orthotropic thin rectangular plates resting on Winkler and Pasternak foundations for uniformly distributed step function and sinusoidal pulse loadings. The orthogonal point collocation method in the space domain and Newmark-β scheme in the time domain are employed. Immovable clamped and simply-supported plates are analysed. An approximate method is used to predict the maximum dynamic response to step loads from the results for static loads and is found to yield sufficiently accurate results.     

Stress intensity factors in finite orthotropic plates with a crack under mixed mode deformation

Mixed mode fracture problem is analyzed for the finite orthotropic plate where an inclined crack parallel to the fibre direction is centrally placed. Modified mapping collocation method with both uniform stress and uniform displacement boundary conditions is utilized to calculate stress intensity correction factors for glass/ epoxy and graphite/epoxy composites. Computed results are presented for selected combinations of crack length to width ratio L/W and plate aspect ratio H/W with various fibre orientations.     

A contour integral computation of stress intensity factors in the cracked orthotropic elastic plates

Stress intensity factors in the cracked orthotropic elastic plates are obtained numerically using a reciprocal work contour integral technique. The integral representation for calculating the intensities of elastic singular stresses at cracks, notches and corners can be extended to treat the rectilinearly anisotropic crack problems. An extension of the method can be done immediately with identification of the characteristic singular solutions and construction of the corresponding complementary elastic states. A centrally cracked tension plate with various degree of orthotropy is analyzed to assess accuracy of the computational procedures newly adopted. Two cracked orthotropic plates modelling bidirectional fiber-reinforced composites are treated: symmetric Mode I type of double edge crack tension plate and mixed mode type of cantilever plate with a single edge crack.     

Determination of elastic constants from measured natural frequencies of specially orthotropic cantilever plates

Abstract

The present paper examines the possibility of evaluating the elastic constants of specially orthotropic rectangular thin plates from the measured natural frequencies of cantilever plates. An expression is developed for orthotropic rectangular thin cantilever plates to determine natural frequencies, and its validity is demonstrated through finite element analysis as well as using published test results.     

Quasi-square holes with maximum failure strength in orthotropic plates

In orthotropic plates, such as fibre-reinforced composites containing openings, failure occurs not only because of stress concentration, but also as a result of combined stresses and anisotropic strengths. Using the Hencky-Von Mises distortion energy failure criterion, the quasi-square hole shapes yielding maximum failure strength have been determined.     

Closed-form analysis of the buckling loads of symmetrically laminated orthotropic plates considering elastic edge restraints

The initial buckling loads of symmetrically laminated rectangular orthotropic plates under uniaxial compression are determined in a closed-form analytical manner. The considered laminates are simply supported at all edges and furthermore subjected to elastic rotational restraints at the unloaded edges. The analysis approach which is based on the assumptions of Classical Laminate Plate Theory employs a representation for the transverse displacements consisting of a system of trigonometric functions in both inplane coordinate directions. Due to its simplicity, a closed-form solution for the critical buckling load is possible which is useful for preliminary design purposes. The presented approach is compared to closed-form analytical and numerical data available in the literature and is found to be in favorable agreement.     

On buckling of orthotropic compressed plates with circular holes

Buckling and post-buckling behaviour of square plates having central circular holes is analysed with the aid of the finite element method. Four different degrees of orthotropy pertinent to real materials are examined. Both uniaxial and biaxial compression are considered for various types of boundary conditions. Also, buckling of polar orthotropic annular plates is analysed for different boundary conditions and material properties. In the case of small holes a perturbation method is applied to both kinds of plates.     

Flexure of clamped semi-infinite orthotropic plates

Using the method of biorthogonal functions developed by Johnson and Little [8], solutions have been obtained for the flexure of semi-infinite orthotropic plates whose long edges are clamped and upon whose short edge (a) deflection and slope, or (b) deflection and moment, or (c) moment and shear force are prescribed. Some numerical results are presented when zero deflection and constant bending moment are prescribed on the short edge of the plate.     

Cruciform crack in an orthotropic elastic plane

The problems of determining the stress and displacement fields in an infinite orthotropic plane containing a cruciform crack 387-1, y=0 and 387-2, x=0 when (I) the shape of the crack is prescribed and (II) the cracks are opened by given normal pressures, are reduced to mixed boundary value problems for the quarter plane. Using integral transform techniques, a closed form solution is obtained for problem I, whereas the solution of problem II has been reduced to solving a Fredholm integral equation of second kind with non-singular kernel. Numerical calculation of the stress intensity factor and crack energy in the case of a linear loading function for various crack lengths are presented for problem II, using the values of material constants for a Boron-Epoxy composite.     

Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element

A high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees-of-freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.     

Axisymmetric postbuckling of orthotropic thick annular plates

Summary This study deals with the geometrically nonlinear postbuckling response of cylindrically orthotropic thick annular plates subjected to inplane radial compressive load at the outer edge. Clamped and simply supported plates with a free hole and a plugged hole have been considered. Governing differential equations are expressed in terms of transverse displacementw, shear rotation and stress function . Polynomial expansions are employed for these three field variables and the orthogonal point collocation method has been used to obtain the discretised equations. Buckling loads have been determined by solving a linear eigen-value problem using the method of inverse iterations. Postbuckling loads for different central deflections have been obtained by solving the nonlinear differential equations. The effect of thickness ratio, orthotropic parameter, annular ratio and the edge conditions has been investigated. The effect of shear deformation on the buckling loads increases with the orthotropic parameter and the thickness-to-radius ratio.Notations a, b, h Outer and inner radii and thickness of the plate - E ,E ,v ,v Young's moduli, Poisson's ratios - Orthotropic parameter:E /E _r - G _rz /E _r - u ^*,u ₀ ^* Radial displacement, radial displacement at mid plane - r, , z Cylindrical polar coordinates - , ^* Strains and stresses - w ^*,w ,w Transverse displacement, shear rotation and stress function - w, , Dimensionless deflection, shear rotation and stress function - N _r ,N ,Q _r Inplane stress resultants and transverse shear - M _r ,M Moment resultants - k ² Shear correction factor - , (r–b)/(a–b), b/(a–b) - a/h - _r ^b , ^m Radial bending stress, circumferential membrane stress - N, _i Number and radii of collocation points - Eigenvalue for buckling With 6 Figures