• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.181-197
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• 2024

A numerical method is presented in this paper, for buckling analysis of thin arbitrary stiffened composite cylindrical shells under axial compression. The stiffeners can be placed inside and outside of the shell. The shell and stiffeners are operated as discrete elements, and their interactions are taking place through the compatibility conditions along their intersecting lines. The governing equations of motion are obtained based on Koiter's theory and solved by utilizing the principle of the minimum potential energy. Then, the buckling load coefficient and the critical buckling load are computed by solving characteristic equations. In this formulation, the elastic and geometric stiffness matrices of a single curved strip of the shell and stiffeners can be located anywhere within the shell element and in any direction are provided. Moreover, five stiffened composite shell specimens are made and tested under axial compression loading. The reliability of the presented method is validated by comparing its numerical results with those of commercial software, experiments, and other published numerical results. In addition, by using the ANSYS code, a 3-D finite element model that takes the exact geometric arrangement and the properties of the stiffeners and the shell into consideration is built. Finally, the effects of Poisson's ratio, shell length-to-radius ratio, shell thickness, cross-sectional area, angle, eccentricity, torsional stiffness, numbers and geometric configuration of stiffeners on the buckling of stiffened composite shells with various end conditions are computed. The results gained can be used as a meaningful benchmark for researchers to validate their analytical and numerical methods.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.3
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• pp.332-348
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• 2012

The present study deals with the parametric resonance behaviour of laminated composite curved shell panels in a hygrothermal environment using Bolotin's approach. A simple laminated model is developed using first order shear deformation theory (FSDT) for the vibration and dynamic stability analysis of laminated composite shells subjected to hygrothermal conditions. A computer program based on the finite element method (FEM) in a MATLAB environment is developed to perform all necessary computations. Quantitative results are presented to show the effects of curvature, ply-orientations, degree of orthotropy and geometry of laminates on the parametric instability of composite curved shell panels for different temperature and moisture concentrations. The excitation frequencies of laminated composite panels decrease with the increase of temperature and moisture due to reduction of stiffness for all laminates.

• Advances in materials Research
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• v.5 no.4
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• pp.205-221
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• 2016

In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt's micromechanical model through the power-law distribution with and without temperature dependent properties. The mathematical model is developed using the higher-order shear deformation theory in conjunction with Green-Lagrange type nonlinear strain to consider large geometrical distortion under thermal load. The efficacy of the proposed model has been checked and the effects of various geometrical and material parameters on the buckling load are analysed in details.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.925-932
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• 1997

Two shear-flexible curved axisymmetric shell elements with two nodes, LCCS(linear curvature and constant strain) and CCCS(constant curvature and constant strain) are designed based on the assumed meridional strain fields and shallow shell geometry. At the element level, meridional curvature, membrane strain and shear strain fields are assumed by using polynomials and the displacement fields are obtained by integrating the assumed strain fields along the shallowly curved meridian. The formulated elements have high order displacement fields consistent with the strain field. Several test problems are given to demonstrate the performance of the two elements. Analysis results obtained reveal that the elements are very accurate in the displacement and the stress predictions.

• Smart Structures and Systems
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• v.25 no.4
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• pp.471-486
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• 2020

Stability analysis of three-layered piezoelectric doubly curved nano shell with accounting size dependency is performed in this paper based on first order shear deformation theory and curvilinear coordinate system relations. The elastic core is integrated with sensor and actuator layers subjected to applied electric potentials. The principle of virtual work is employed for derivation of governing equations of stability. The critical electrical and mechanical buckling loads are evaluated in terms of important parameters of the problem such as size-dependent parameter, two principle angle of doubly curved shell and two parameters of Pasternak's foundation. One can conclude that mechanical buckling loads are decreased with increase of nonlocal parameter while the electrical buckling loads are increased.

• Journal of Ocean Engineering and Technology
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• v.24 no.5
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• pp.88-93
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• 2010

Many pipes that are arranged longitudinally in ships have loops at intervals to prevent the failure of the pipes as they absorb large portions of the axial load caused by the bending of the hull girder and/or thermal loads when the pipes are carrying very hot fluids. Since the loops are curved at corners, an efficient method for conducting the structural analyses of these curved portions is required. In this paper, a pipe loop was analyzed by an analytical method and by the finite-element method in four different ways, i.e., based on straight-beam elements, curved-beam elements, 2-D shell elements, and 3-D solid elements. The results of the five analyses were compared to check the validity of the current curved-beam theory. The paper includes some suggestions on how to analyze the pipe loops efficiently.

• Geomechanics and Engineering
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• v.35 no.1
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• pp.81-93
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• 2023

Due to the unclear mechanism of the influence of temperature on the resonance problem of doubly curved shells, this article aims to explore this issue. When the ambient temperature rises, the composite structure will expand. If the thermal effects are considered, the resonance response will become more complex. In the design of structure, thermal effect is inevitable. Therefore, it is of significance to study the resonant behavior of doubly curved shell structures in thermal environment. In view of this, this paper extends the previous work (She and Ding 2023) to the case of the nonlinear principal resonance behavior of graphene platelet reinforced metal foams (GPLRMFs) doubly curved shells in thermal environment. The effect of uniform temperature field is taken into consideration in the constitutive equation, and the nonlinear motion control equation considering temperature effect is derived. The modified Lindstedt Poincare (MLP) method is used to obtain the resonance response of doubly curved shells. Finally, we study the effects of temperature changes, shell types, material parameters, initial geometric imperfection and prestress on the forced vibration behaviors. It can be found that, as the temperature goes up, the resonance position can be advanced.

• Steel and Composite Structures
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• v.18 no.4
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• pp.889-907
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• 2015

This paper aims to present an alternative analytical method for transient vibration analysis of doubly-curved laminated shells subjected to dynamic loads. In the method proposed, the governing differential equations of laminated shell are derived using the dynamic version of the principle of virtual displacements. The governing equations of first order shear deformation laminated shell are obtained by Navier solution procedure. Time-dependent equations are transformed to the Laplace domain and then Laplace parameter dependent equations are solved numerically. The results obtained in the Laplace domain are transformed to the time domain with the help of modified Durbin's numerical inverse Laplace transform method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Also effects of number of laminates, different material properties and shell geometries are discussed. The numerical results have proved that the presented procedure is a highly accurate and efficient solution method.

• Steel and Composite Structures
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• v.48 no.3
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• pp.263-273
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• 2023

This paper investigates dynamic characteristics of a graphene nanoplatelets reinforced composite (GNPRC) sandwich doubly curved shell based on the first-order shear deformation theory (FSDT) and Hamilton's principle. The sandwich doubly curved shell is fabricated from a core made of honeycomb materials sandwiched by composite GNPs reinforced face-sheets. Effective materials properties of composite face-sheets are assumed to vary based on Halpin-Tsai micromechanical models and rule of mixture. Furthermore, the material properties of honeycomb core are estimated using Gibson's formula. The fundamental frequencies of the shell are computed with changes of main geometrical and material properties such as amount and distribution type of graphene nanoplatelets, side length ratio, thickness to length ratio of and side length ratio of honeycomb. The Navier's technique is presented to obtain responses. Accuracy and trueness of the present model and analytical solution is confirmed through comparison of the results with available results in literature. It is concluded that an increase in thickness to length ratio yields a softer core with lower natural frequencies. Furthermore, increase in height to length ratio leads to significant decrease in natural frequencies.

• Steel and Composite Structures
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• v.15 no.4
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• pp.379-397
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• 2013

Conoidal shells are doubly curved stiff surfaces which are easy to cast and fabricate due to their singly ruled property. Application of laminated composites in fabrication of conoidal shells reduces gravity forces and mass induced forces compared to the isotropic constructions due to the high strength to weight ratio of the material. These light weight shells are preferred in the industry to cover large column free open spaces. To ensure design reliability under service conditions, detailed knowledge about different behavioral aspects of conoidal shell is necessary. Hence, in this paper, static bending, free and forced vibration responses of composite conoidal shells are studied. Lagrange's equation of motion is used in conjunction with Hamilton's principle to derive governing equations of the shell. A finite element code using eight noded curved quadratic isoparametric elements is developed to get the solutions. Uniformly distributed load for static bending analysis and three different load time histories for solution of forced vibration problems are considered. Eight different stacking sequences of graphite-epoxy composite and two different boundary conditions are taken up in the present study. The study shows that relative performances of different shell combinations in terms of static behaviour cannot provide an idea about how they will relatively behave under dynamic loads and also the fact that the points of occurrence of maximum static and dynamic displacement may not be same on a shell surface.