• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.87-103
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• 2015

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake's length and thickness on the critical buckling load.

• Coupled systems mechanics
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• v.11 no.4
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• pp.357-371
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• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.23-35
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• 2019

In this study we derive the governing equations of a functionally graded piezoelectric disk, subjected to thermo-electro-mechanical loads. First order shear deformation theory is used for description of displacement field. Principles of minimum potential energy is used to derive governing equations in terms of components of the displacement field and the electric potential. The governing equations are derived for a disk with variable thickness. The numerical results are presented in terms of important parameters of the problem such as profile of variable thickness, in-homogeneous index and other related parameters.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.343-353
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• 2020

Based on the Precise Transfer Matrix Method (PTMM), the dynamic model is constructed to observe the vibration behaviour of cylindrical shells with variable thickness by solving a set of first-order differential equations. The free vibration of stiffened cylindrical shells with variable thickness can be obtained to compare with the exact solution and FEM results. The reliability of the present method of free vibration is well proved. Furthermore, the effect of thickness on the vibration responses of the cylindrical shell is also discussed. The acoustic response of immersed cylindrical shells is analyzed by a Pluralized Wave Superposition Method (PWSM). The sound pressure coefficient can be gained by collocating points along the meridian line to satisfy the Neumann boundary condition. The mode convergence analysis of the cylindrical shell is carried out to guarantee calculation precision. Also, the reliability of the present method on sound radiation is verified by comparing with experimental results and numerical results.

• Smart Structures and Systems
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• v.18 no.4
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• pp.755-786
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• 2016

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

• Journal of the Korean Society of Safety
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• v.6 no.4
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• pp.45-52
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• 1991

The purpose of a fatigue crack arrest desing is to prvent a fatigue fracture of machine and structure resulted from unstable crack growth. In all cases of load transfer to second elements such as stringers, doublers or flangers, crack arrest is possible; arrest occuring when the fatigue crack reaches the second element. In the present work, the possibility of crack arrest and the design criterion of fatigue crack arrest in the variable thickness plates are examined numericaiiy by using fatigue crack arrest thresthod $\Delta$K$_{th}$of SA-508 reactor vessel steel and stress intensity factor which was obtained in the previous work as a result of 3-dimensional finite element analysis for CT type variable thickness plates having discontinuous interface.e.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.749-765
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• 2008

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love's first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1433-1438
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• 1991

본 연구에서는 팔렛을 갖는 유한폭 변후판재 내의 모드 Ⅰ균열에 대하여 3차 원 유한요소법으로 응력확대계수를 수치해석하였다.

• Structural Engineering and Mechanics
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• v.40 no.6
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• Korean Journal of Optics and Photonics
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• v.12 no.6
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• pp.472-478
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• 2001

We determined the optical constants and thickness of organic electroluminescence thin films using variable angle spectroscopic ellipsometry. Using the measured transmittance spectra and the spectroscopic ellipsomeoy data of the organic films on glass substrates in the optically transparent region, we determined the effective thickness and the refractive indices of organic thin films. Then by applying a numerical inversion method to variable angle spectro-ellipsometry data, we determined the complex refractive index at each wavelength including the optically absorbing region, as well as the thickness and surface micro-roughness of the organic thin films. The calculated transmittance spectra showed a tight agreement with the measured ones, confining the validity of the present model analysis.