• Structural Engineering and Mechanics
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• 제10권2호
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• pp.111-123
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• 2000

An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.

• 대한기계학회논문집
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• 제6권2호
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• pp.176-182
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• 1982

이 논문에서는 평판의 배선형 해석에 대한 Berger의 방정식을 쉘좌표가 직교곡선좌표계로 표시 되는 Shallow 쉘에 대하여 일반화하여 운동방정식을 유도하였다. 해석의 예로서, 이 방정식을 사용하여 고정된 경계를 가진 원판과 Shallow 구쉘에 대한 배선형 진동문제를 해석하였으며, 정력학의 문제로서 원판이 동심원내에 균일하중을 받을때와 중심에 집중하중을 받을 때의 large deflection에 대하여 고찰하였고 나중문제에 대한 수치해를 구하였다.

• 한국공간구조학회논문집
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• 제4권4호
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution 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 complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Structural Engineering and Mechanics
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• 제3권1호
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• pp.25-34
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• 1995

General free vibration characteristics of cantilevered circular cylindrical tanks are analyzed using the integral equations technique with the cubic spline functions. For computations, the partial differential equations for thin shallow shells as given by Flugge's have been employed after the addition of the inertia forces. The application of the method is illustrated with a numerical examples of tanks which are free at the top edge and fixed at the bottom. The results obtained by this method have been compared with the available results and a good agreement was found.

• Steel and Composite Structures
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• 제20권5호
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• pp.1043-1066
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• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Structural Engineering and Mechanics
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• 제47권4호
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• pp.559-573
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• 2013

Geometrically non-linear axisymmetric bending of a shallow spherical shell with a clamped or a simply supported edge under axisymmetric load was investigated numerically. The partial load was introduced by the Heaviside step function, and the solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for three geometrical parameters. The accuracy of the algorithm was checked by comparing the central deflection, the radial membrane stress at the edge, or the transverse shear force with the solutions of plates and shells in the literature and good agreement was obtained. The main findings of the study can be outlined as follows: (i) If the shell is fully loaded the central deflection of a clamped shell is larger than that of a simply supported shell provided that the shell is not very shallow, (ii) if the shell is partially loaded the central deflection of the shell is sensitive to the parameters of thickness, depth, and partial loading but the influence of the boundary conditions is negligible.

• Advances in aircraft and spacecraft science
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• 제3권3호
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• pp.317-330
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• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

• Structural Engineering and Mechanics
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• 제19권5호
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• pp.535-550
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• 2005

The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.

• Structural Engineering and Mechanics
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• 제70권1호
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• pp.125-131
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• 2019

A nine node isoparametric plate bending element is used for bending analysis of laminated composite skew cylindrical shell panels. Both thick and thin shell panels are solved. Rotary inertia and shear deformation are incorporated by considering first order shear deformation theory. The analysis is performed considering shallow shell theory. Both shallow and moderately deep skew cylindrical shells are investigated. Skew cylindrical shell panels having different thickness ratios (h/a), radius to length ratios (R/a), ply angle orientations, number of layers, aspect ratio (b/a), boundary conditions and various loading (concentrated, uniformly distributed, linear varying and doubly sinusoidal varying) conditions are analysed. Various new results are presented.

• Structural Engineering and Mechanics
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• 제55권1호
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• pp.29-46
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies of a truncated shallow and deep conical shell with linearly varying thickness along the meridional direction free at its top edge and clamped at its bottom edge. 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 $u_r$, $u_{\theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Strain and kinetic energies of the truncated conical shell with variable thickness 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. The frequencies from the present 3-D method are compared with those from other 3-D finite element method and 2-D shell theories.