• Journal of the Society of Disaster Information
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• v.11 no.4
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• pp.527-533
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• 2015

A simplified method for the calculation of dynamic characteristics of initially stressed antisymmetric cross-ply laminated shells is presented in this paper using the natural frequencies under unloading state. The equation of motion of laminated shell with two opposite edges simply supported is investigated on the basis of Rayleigh-Ritz method and Mindlin shell theory with effect of the curvature term. The relationships of the non-dimensional natural frequencies with initial stresses the coeffcients of critical buckling and the boundaries of te dynamic principal instability region can be characterized by the non-dimensional natureal frequencies under unloading state. Numerical examples are presented t verify the simplified equations and to illustrate potential applications of the analysis.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.3
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• pp.24-34
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• 2010

This paper analyzed the partial differential equations of laminated composite shells of revolution by using the finite difference method. The proof that numerical results are reasonable and accurate is obtained through converge ratio analysis and commercial program LUSAS for the structural analysis. The purpose of this study is to examine closely the engineering advantages and to analyze the structural behaviors of the anisotropic shells of revolution. Thus, the relevant reinforcement and most suitable arrangement of fiber to produce the highest strength are proposed through the numerical results according to a variety of parameter study. Namely, the distribution of displacements and stress resultants are analyzed according to the change of meridian's curvature, the ratio of height-width of shell, subtended angle, fiber angle, and so on. Using these distribution, the most suitable shell may be proposed to produce the highest strength. Also, the configuration of the entire laminated composite conical shells is analysed, and a variety of the design criterion of circular conical shell are proposed and studied in engineering view points.

• Steel and Composite Structures
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• v.39 no.3
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• pp.291-306
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• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.691-700
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• 1998

Based on Von Karman-Donnell kinematic assumptions for laminated shells, the nonlinear vibration behaviour of antisymmetrically or asymmetrically laminated cross-ply circular cylindrical shells with clamped and simply-supported ends are studied by a multi-mode approach. A equation is formulated and satisfies the associated compatibility equation and all boundary conditions. The displacement function is assumed to take the form of the lowest linear vibration mode and to satisfy continuity of the circumferential displacement. The nonlinear vibration equation is derived by the Galerkin's method. And nonlinear frequency is obtained by using the harmonic balance method as a function of lamination parameters, material constants, aspect ratio and amplitude of vibration. The effect of initial imperfection is also included. Results of the non-linear vibration are presented for different amplitudes of initial imperfection and four sets of boundary conditions. Present results are compared well with existing analysis results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.3
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• pp.279-293
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• 2004

The analysis of linear static and free vibration problems of isotropic and laminated composite plates and shells is performed by the improved 9-node shell element with the new strain displacement relationship. In that relationship, the effect of new additional terms between the bending strain and displacement has been investigated in the warping problem. Natural co ordinate based strains, stresses and constitutive equations are used. The assumed natural strain method is used to alleviate both membrane and shear locking behavior from the element. The Lanczos method is employed in the calculation of the eigenvalues of laminated composite structures and the Gauss integration rule is adopted to evaluate the mass matrix. The numerical examples are compared with the analytical solutions to validate the current formulation and the results presented could be useful for the understanding of the behaviour of laminates under free vibration conditions.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.2
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• pp.164-171
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• 2005

This study aims to examine an effect of stacking sequence and curvature on the penetration characteristic of a composite laminated shell. For the purpose, we manufactured specimens with different stacking sequences and curvatures, and conducted a penetration test using an air-gun. To examine an influence according to stacking sequence, as flat plate and curvature specimen had more plies, their critical penetration energy was higher, Critical penetration energies of specimen A and C with less interfaces somewhat higher than those of B and D with more interfaces. The reason that with less interfaces, critical penetration energy was higher is pre-impact bending stiffness of composite laminated shell with less interfaces was lower than that of laminated shell with more interfaces, but bending stiffness after impact was higher. And it is because interface, the weakest part of the composite laminated shell, was influenced by transverse impact. As curvature increases, critical penetration energy increases linearly. It is because as curvature increases, resistance to in-plane deformation as well as bending deformation increases, which need higher critical penetration energy. Patterns of cracks caused by penetration of composite laminated shells include interlaminar crack, intralaminar crack, and laminar fracture. A 0$^{\circ}$ply laminar had a matrix crack, a 90$^{\circ}$ply laminar had intralaminar crack and laminar fracture, and interface between 0$^{\circ}$and 90$^{\circ}$laminar had a interlaminar crack. We examined crack length and delamination area through a penetration test. For the specimen A and C with 2 interface, the longest circumferential direction crack length and largest delamination area were observed on the first interface from the impact point. For the specimen B and D with 4 interface, the longest crack length and largest delamination area were observed on the third interface from the impact point.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.843-846
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• 1994

The bucking and postbuckling behavior of composite laminated long cylinders under lateral pressure are investigated by the nonlinear finite element method. A long cylinder of 3-D shell problem is modelled as 2-D plane strain problem for analysis. And for the finite element analysis, eight nodes quadratic element is utilized. Arc-length method is adopted for the iteration and load-increment along postbuckling equilibrium path. The composite laminated cylinders in study are composed of cross-plied uniaxially reinforced shells. As a prsult, buckling load and postbuckling behavior are discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.119-125
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• 1997

The finite element analysis of plate and shell structures has been one of the major research interests for many years because of the technological importance of such structures. Quite often these structures are constructed by laminated composites. This is due to the high specific stiffness and strength of composite structures. The main objective of this paper is to extend the use of an improved degenerated shell element to the large displacement analysis of plates and shells with laminated composites. The total Lagrangian approach has been chosen for the definition of the deformation and the solution to the nonlinear equilibrium equations is obtained by the Newton-Raphson method.

• Advances in concrete construction
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• v.14 no.5
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• pp.309-315
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• 2022

This paper depicts the diagram of cylindrical shells as an essential idea. It centers around an outline of exploration and use of cylindrical shell in expansive current circumstance. In view of investigation of the current and prospect of model as a piece of present exploration work, a straightforward contextual analysis is examined with Love's shell theory based on Galerkin's method. The cylindrical shells are attached from one end of the cylindrical shells. The frequencies of ring support shells are investigated against the half axial wave mode. The frequencies increase on increasing the half axial wave mode. Also, the frequencies are downsized with ring supports. The software MATLAB is preferred to others because in this software computing coding is very easy to do. Just single command 'eig' furnishes shell frequencies and mode shapes by calculating eigenvalues and eigenvectors respectively. The shell vibration frequencies for cylindrical shells are compared with those results found in the open literature.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.497-516
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• 1998

A relatively simple two-dimensional multilayered shell model is presented for predicting both global quantities and stress distributions across the thickness of multilayered thick shells, that is based on a third-order zig-zag approach. As for any zig-zag model, the layerwise kinematics is accounted for, with the stress continuity conditions at interfaces met a priori. Moreover, the shell model satisfies the zero transverse shear stress conditions at the upper and lower free surfaces of the shell, irrespective of the lay-up. By changing the parameters in the displacement model, some higher order shell models are obtained as particular cases. Although it potentially has a wide range of validity, application is limited to cylindrical shell panels in cylindrical bending, a lot of solutions of two-dimensional models based on rather different simplyfying assumptions and the exact three-dimensional elasticity solution being available for comparisons for this benchmark problem. The numerical investigation performed by the present shell model and by the shell models derived from it illustrates the effects of transverse shear modeling and the range of applicability of the simplyfying assumptions introduced. The implications of retaining only selected terms depending on the radius-to-thickness ratio are focused by comparing the present solutions to the exact one and to other two-dimensional solutions in literature based on rather different simplyfying assumptions.