• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.758-769
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• 1986

A general analytical procedure is developed for evaluating the free vibration characteristics of orthotropic and laminated composite circular cylindrical shells. The solution is obtained through a direct solution procedure with axial mode displacements presented as simple Fourier series expressions. On the basis of the various thin shell theories most commonly used, the frequency equation is derived and is expressed in a unified form. The present analysis can deal with shells which are made of an arbitrary number of bonded layers each with a different thickness and different elastic orthotropic properties, and have classical boundary conditions of any kind. Several examples are shown with the consideration of the effects of fiber orientations and boundary conditions as well as different shell geometries and material properties. To verify the validity and accuracy of this analysis, the results are compared with the experimental and analytical results of other workers. Agreement among the various results is found to be fairly good.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.82-88
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• 2007

Thermal Buckling and free vibration analyses of multi-layered composite conical shells based on a layerwise displacement theory are performed. The Donnell's displacement-strain relationships of conical shell structure are applied. The natural frequencies are compared with the ones existing in the previous literature for laminated conical shells with several cone semi-vertex angles. Moreover, the thermal buckling behaviors of the laminated conical shell are investigated to consider the effect of the semi-vertex angle, subtended angle, and radius to thickness ratio on the structural stability.

• Journal of KSNVE
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• v.6 no.4
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• pp.457-467
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• 1996

The analytical solutions for the free vibration and buckling of cross -ply laminated composite cylindrical shell with the orthogonal stiffeners, i. e., axial stiffeners(stringers) and circumferential stiffeners(rings), are presented using the energy method. The stiffeners are assumed to be an integral part of the shell and have been directly included in analysis(it's called discrete stiffener theory). The effect of the parameters such as the stacking sequences, the shell thickness, the shell length-to-radius ratio are studied. By comparison with the previously published analytical results for the stiffened cylindrical shells, it is shown that natural frequencies can be determined with adequate accuracy.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.69-72
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Journal of the Korean Society of Safety
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• v.31 no.6
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• pp.6-11
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• 2016

CFRP composite laminates are widely used as structural materials for airplanes, automobile and aerospace vehicles because of their high strength and stiffness. This study aims to examine an effect of curvature on the penetration fracture characteristic of an orthotropic composite laminated shell. For the purpose, we manufactured orthotropic CFRP shell specimen with different curvatures, and conducted a penetration test using an air-gun. Those specimens were prepared to varied curvature radius(${\infty}$, 200mm, 150mm and 100mm)and were stacked to $[O^{\circ}{_3}/90^{\circ}{_3}]_s$. When the specimen is subjected to transverse impact by a steel sphere(${\Phi}10$), the velocity of steel sphere was measured both before and after impact by determining the time for it to pass two ball-screen sensors located a known distance apart. As the curvature increases, the absorption energy and the critical penetration energy increased linearly because the resistance to the bending moment. Patterns of cracks caused by the penetration of CFRP laminated shells included fiber breakage, lamina fracture, matrix crack interlaminar crack and intralaminar crack.

• 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.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1445-1463
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• 2016

The effects of moisture and temperature on buckling of laminated composite cylindrical shell panels are investigated both numerically and experimentally. A quadratic isoparametric eight-noded shell element is used in the present analysis. First order shear deformation theory is used in the present finite element formulation for buckling analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for parametric study on the buckling of shell panels under hygrothermal field. Benchmark results on the critical loads of hygrothermally treated woven fiber glass/epoxy laminated composite cylindrical shell panels are obtained experimentally by using universal testing machine INSTRON 8862. The effects of curvature, lamination sequences, number of layers and aspect ratios on buckling of laminated composite cylindrical curved panels subjected to hygrothermal loading are considered. The results are presented showing the reduction in buckling load of laminated composite shells with the increase in temperature and moisture concentrations.

• Steel and Composite Structures
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• v.25 no.3
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• pp.337-346
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• 2017

Sandwich shells made of composite materials are the main focus on recent literature parallel to the requirements of industry. They are commonly chosen for the modern engineering applications which require moderate strength to weight ratio without dependence on conventional manufacturing techniques. The investigations on hyperbolic paraboloidal formed sandwich composite shells are limited in the literature contrary to shells that have a number of studies, consisting of doubly curved surfaces, arbitrary boundaries and laminations. Because of the lack of contributive data in the literature, the aim of this study is to present the effects of curvature on hyperbolic paraboloidal formed, layered sandwich composite surfaces that have arbitrary boundary conditions. Analytical solution methodology for the analyses of stresses and deformations is based on Third Order Shear Deformation Theory (TSDT). Double Fourier series, which are specialized for boundary discontinuity, are used to solve highly coupled linear partial differential equations. Numerical solutions showing the effects of shell geometry are presented to provide benchmark results.

• Steel and Composite Structures
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• v.52 no.5
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• pp.595-608
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• 2024

This study presents a static analysis of thin shallow cylindrical and spherical panels, as well as plates (which are a special case of shells), under Levy-type mixed boundary conditions and various loading conditions. The study utilizes the boundary discontinuous double Fourier series method, where displacements are expressed as trigonometric functions, to analyze the system of partial differential equations. The panels are subjected to a simply supported type 3 (SS3) boundary condition on two opposite edges, while the remaining two edges are subjected to clamped type 3 (C3) boundary conditions. The study presents comprehensive tabular and graphical results that demonstrate the effects of curvature on the deflections and moments of thin shallow shells made from symmetric and antisymmetric cross-ply laminated composites, as well as isotropic steel materials. The proposed model is validated through comparison with existing literature, and the convergence characteristics are demonstrated. The changing trends of displacements and moments are explained in detail by investigating the effect of various parameters, such as stacking lamination, material types, curvature, and loading conditions.