• Steel and Composite Structures
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• v.33 no.2
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• pp.245-259
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• 2019

The present study aims to investigate the ultimate strength and geometric nonlinear behavior of composite plates containing initial imperfection subjected to combined end-shortening strain and lateral pressure loading by using a semi-analytical method. In this study, the first order shear deformation plate theory is considered with the assumption of large deflections. Regarding in-plane boundary conditions, two adjacent edges of the laminates are completely held while the two others can move straightly. The formulations are based on the concept of the principle of minimum potential energy and Newton-Raphson technique is employed to solve the nonlinear set of algebraic equations. In addition, Hashin failure criteria are selected to predict the failures. Further, two distinct models are assumed to reduce the mechanical properties of the failure location, complete ply degradation model, and ply region degradation model. Degrading the material properties is assumed to be instantaneous. Finally, laminates having a wide range of thicknesses and initial geometric imperfections with different intensities of pressure load are analyzed and discuss how the ultimate strength of the plates changes.

• Steel and Composite Structures
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• v.45 no.6
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• pp.831-837
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• 2022

Numerical investigation on dynamic characteristics of sandwich plates under periodic and thermal loads has been presented by assuming that the plate has three layers which are a foam core and two skins. The foam core made of Aluminum has porosities with uniform and graded dispersions. The sandwich plate has been supposed to be affected by periodical compressive loads. Also, temperature variation causes uniform thermal load. The formulation has been established based upon a higher-order plate theory and Ritz method has been used to solve the equations of motion. The stability boundaries have also been obtained performing Bolotin's method. It will be indicated that stability boundaries of the sandwich plate depend on periodical load parameters, porosities, skin thickness and temperature.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.56-65
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• 1996

Recently, with development of mechanics of materials, as pursuing the high speed of the ships, there has been an increasing demand on the composite construction which satisfies high strength and low weight at the same time. A sandwich element is a type of composite construction, which is composed of thin, strong, stiff and relatively high density faces and a thick, light, and weaker core material. As the second moment is increased by faces separated from the neutral axis farther, a sandwich element is most effective light structural form. In this study, Rayleigh-Ritz Energy Method is adopted, which can analyze sandwich plate relatively simply and exactly. Stresses and buckling loads are analyzed exactly, when uniform lateral pressure load, inplane compression and inplane shear are acting at the sandwich plate. Including a wrinkling stress, this study can be applied to the initial design and minimum weight design of sandwich plates.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.140-148
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• 1992

The free vibration problem of symmetrically laminated composite rectangular plates is formulated based on anisotropic thick plate theory including the effects of shear deformation and rotary inertia. Considering the difficulty of obtaining closed-form solutions, Rayleigh-Ritz analysis using polynomials having the property of Timoshenko beam functions as trial functions is adopted. The boundary conditions elastically restrained against rotation are accomodated as well as classical boundary conditions. From the results of numerical studies, the validity of the present method is verified. And it is also found that the adoption of thick plate theory for the vibration analysis of laminated composite plates is essential because of the relatively large shear deformation effect, and that the convergence of the Rayleigh quotient to the stationary value is less rapid in anisotropic composite plates than that in the orthotropic ones due to more complicated mode shapes of the former.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.603-619
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• 2018

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.4
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• pp.419-429
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• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.115-136
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• 2014

In this study, an extended Kantorovich method, employing multi-term displacement functions, is applied to analyze the vibration problem of symmetrically laminated plates with arbitrary boundary conditions. The vibration behaviors of laminated plates are determined based on the variational principle of total energy minimization and the iterative Kantorovich method. The out-of-plane displacement is represented in the form of a series of a sum of products of functions in x and y directions. With a known function in the x or y directions, the formulation for the variation of total potential energy is transformed to a set of governing equations and a set of boundary conditions. The equations and boundary conditions are then numerically solved for the natural frequency and vibration mode shape. The solutions are verified with available solutions from the literature and solutions from the Ritz and finite element analysis. In most cases, the natural frequencies compare very well with the reference solutions. The vibration mode shapes are also very well modeled using the multi-term assumed displacement function in the terms of a power series. With the method used in this study, it is possible to solve the angle-ply plate problem, where the Kantorovich method with single-term displacement function is ineffective.

• Journal of the Earthquake Engineering Society of Korea
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• v.16 no.3
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• pp.1-12
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• 2012

In this study, an analysis method for the earthquake response of an offshore wind turbine model is developed, considering the effects of the fluid-structure-soil interaction. The turbine is modeled as a tower with a lumped mass at the top of it. The tower is idealized as a tubular cantilever founded on flexible seabed. Substructure and Rayleigh-Ritz methods are used to derive the governing equation of a coupled structure-fluid-soil system incorporating interactions between the tower and sea water and between the foundation and the flexible seabed. The sea water is assumed to be a compressible but non-viscous ideal fluid. The impedance functions of a rigid footing in water-saturated soil strata are obtained from the Thin-Layer Method (TLM) and combined with the superstructure model. The developed method is applied to the earthquake response analysis of an offshore wind turbine model. The method is verified by comparing the results with reference solutions. The effects of several factors, such as the flexibility of the tower, the depth of the sea water, and the stiffness of the soil, are examined and discussed. The relative significance of the fluid-structure interaction over the soil-structure interaction is evaluated and vice versa.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.119-129
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• 2004

A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.141-154
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• 1993

In this paper, a method to calculate the ultimate compressive strength of welded one-sided stiffened plates simply supported along all edges is proposed. At first initial imperfections such as distortions and residual stresses due to welding are predicted by using simplified methods. Then, the collapse modes of the stiffened plate are assumed and collapse loads for each mode are calculated. Among these loads, the lowest value is selected as the ultimate strength of the plate. Collapse modes are assumed as follows ; (1) Overall buckling of the stiffened plate$\rightarrow$Overall collapse due to stiffener bending (2) Local buckling of the plate part$\rightarrow$Local collapse of the plate part$\rightarrow$Overall collapse due to stiffener yielding (3) Local buckling of the plate part$\rightarrow$Overall collapse due to stiffener berthing (4) Local buckling of the plate part$\rightarrow$Local collapse of the plate part$\rightarrow$Overall collapse due to stiffener tripping. The elastic large deflection analysis based on the Rayleigh-Ritz method is carried out, and plastic analysis assuming hinge lines is also carried out. Collapse load is defined as the cross point of the two analysis curves. This method enables the utimate strength to be calculated with small computing time and a good accuracy. Using the present method, characteristics of the stiffener including torsional rigidity, bending and tripping can also be clarified.