• 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.

• Advanced Composite Materials
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• v.18 no.1
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• pp.21-42
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• 2009

The vibration characteristics of post-buckled laminated composite doubly curved shells are investigated. The finite element method is used for the analysis of post-buckling and free vibration of post-buckled laminated shells. The geometric non-linear finite element model includes the general non-linear terms in the strain-displacement relationships. The shell geometry used in the present formulation is derived using an orthogonal curvilinear coordinate system. Based on the principle of virtual work the non-linear finite element equations are derived. Arc-length method is implemented to capture the load-displacement equilibrium curve. The vibration characteristics of post-buckled shell are performed using tangent stiffness obtained from the converged deflection. The code is first validated and then employed to generate numerical results. Parametric studies are performed to analyze the snapping and vibration characteristics. The relationship between loads and fundamental frequencies and between loads and the corresponding displacements are determined for various parameters such as thickness ratio and shallowness.

• Steel and Composite Structures
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• v.28 no.3
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• pp.389-401
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• 2018

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

• 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.

• 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.