• Steel and Composite Structures
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• v.51 no.4
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• pp.391-406
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• 2024

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.283-290
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• 2001

Various laminates consisting of thin, unidirectional layers may be achieved by laying up laminae in different reinforcement directions and stacking sequences. Thus, the behavior of nonhomogeneous, anisotropic laminated structures is quite different from that of isotropic ones. The anisotropic laminated shell theory derived here, that includes the effect of transverse shear deformations, can give higher accuracy than thin shell theories. In this paper, by using closed-form solutions for shallow shells having simple supported boundary, extensive numerical study for anisotropic laminated shells were made to investigate the stacking sequence effects for various shells, and to show comparisons to the results between this paper and the existing literature.

• Structural Engineering and Mechanics
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• v.10 no.2
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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.

• Advances in nano research
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• v.17 no.2
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• pp.95-107
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• 2024

In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.2
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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.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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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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• v.3 no.1
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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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• v.20 no.5
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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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• v.47 no.4
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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 nano research
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• v.17 no.1
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• pp.1-8
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• 2024

In this paper, stability analysis of sandwich toroidal shell segments (TSSs) with carbon nanotube (CNT)-reinforced face sheets featuring various types of auxetic cores, surrounded by elastic foundations under radial pressure is presented. Two distinct types of auxetic structures are considered for the core, including re-entrant auxetic structure and graphene origami (GOri)-enabled auxetic structure. The nonlinear stability equilibrium equations of the longitudinally shallow shells are formulated using the von Karman shell theory, in conjunction with Stein and McElman approximation while considering Winkler-Pasternak's elastic foundation to simulate the interaction between the shell and elastic foundation. The Galerkin method is employed to derive the nonlinear stability responses of the shells. The numerical investigations show the influences of various types of auxetic-core layers, CNT-reinforced face sheets, as well as elastic foundation on the stability of sandwich shells.