• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.783-797
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• 2016

Exact solutions for stresses, strains, and displacements of a perforated rectangular plate by an arbitrarily located circular hole subjected to both linearly varying in-plane normal stresses on the two opposite edges and in-plane shear stresses are investigated using the Airy stress function. The hoop stress occurring at the edge of the non-central circular hole are computed and plotted. Stress concentration factors (the maximum non-dimensional hoop stresses) depending on the location and size of the non-central circular hole and the loading condition are tabularized.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.99-111
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• 2004

An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.325-342
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• 2020

The current study is focused on the evaluation of the ultimate strength of stiffened panels found in ship hull structures that are subjected to combined uniaxial thrust, in-plane and out-of-plane bending moments. This loading condition, which is in general ignored when performing buckling checks, applies to representative control geometries (stiffener with attached plating) as a consequence of the linearly varying normal stresses along the ship's depth induced by the hull-girder vertical bending moment. The problem is generalized by introducing a non-uniform thrust described by a displacement ratio and rotation angle and by introducing the slenderness ratios, within the practical range of interest. The formed design space is explored through methods sourcing from Design of Experiments and by applying non-linear finite element procedures. Surrogate empirical models have been constructed through regression analysis and Response Surface Methods. An additional empirical model is provided to the literature for predicting the ultimate strength under uniaxial thrust. The numerical experimentation has shown that is a significant influence on the ultimate strength of stiffened panels as the thrust non-uniformity increases.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.65-76
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• 2017

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

• Journal of Korean Association for Spatial Structures
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• v.6 no.4 s.22
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• pp.81-92
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• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.