• Journal of the Korea institute for structural maintenance and inspection
• /
• v.8 no.2
• /
• pp.147-158
• /
• 2004

For stiffened plates composed of composite materials, many researchers have used a finite element method which connected isoparametric plate elements and beam elements. However, the finite element method is difficult to reflect local behavior of stiffener because beam elements are transferred stiffness for nodal point of plate elements, especially the application is limited in case of laminated composite structures. In this paper, for analysis of laminated composite stiffened plates, 3D shell elements for stiffener and plate are employed. Reissner-Mindlin's first order shear deformation theory is considered in this study. But when thickness will be thin, isoparamatric plate bending element based on the theory of Reissner-Mindlin is generated by transverse shear locking. To eliminate the shear locking and virtual zero energy mode, the substitute shear strain field is used. A deflection distribution is investigated for simple supported rectangular and skew stiffened laminated composite plates with arbitrary orientation stiffener as not only variation of slenderness and aspect ratio of the plate but also variation of skew angle of skew stiffened plates.

• Structural Engineering and Mechanics
• /
• v.14 no.3
• /
• pp.245-262
• /
• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• Steel and Composite Structures
• /
• v.34 no.4
• /
• pp.615-623
• /
• 2020

In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.

• Smart Structures and Systems
• /
• v.9 no.6
• /
• pp.505-534
• /
• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• Structural Engineering and Mechanics
• /
• v.17 no.6
• /
• pp.789-817
• /
• 2004

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called "delta-point" technique.

• Journal of Korean Society of Steel Construction
• /
• v.11 no.4 s.41
• /
• pp.373-384
• /
• 1999

The shell structures with composite materials have the advantages in strength, corrosion resistance, and weight reduction. The objective of this study is to analyze anisotropic composite circular cylindrical shells with shear deformation theory. In applying numerical methods to solve differential equations of anisotropic shells, this paper use finite difference method. The accuracy of the numerical method can be improved by taking higher order of interval ${\Delta}$ to reduce error. This study compares the results of finite difference method with the results of ANSYS based on finite element method. Several numerical examples show the advantages of the stiffness increasement when the composite materials aroused. Therefore, it is expected that results of this study give various guides for change of the subtended angles, load cases, boundary conditions, and side-to-thickness ratio.

• Steel and Composite Structures
• /
• v.52 no.5
• /
• pp.515-524
• /
• 2024

The principal goal of the present study is to examine the aeroelastic analysis of cylindrical laminated shells with curvilinear fibers. To attain this objective, the equations of motion are firstly extracted according to the first-order shear deformation theory (FSDT). The linear piston theory is then implemented to estimate aerodynamic loads for various airflow angles over the cylindrical shell area, providing the aeroelastic equations. The well-known isogeometric analysis based on the NURBS basis functions is subsequently developed to discretize the aeroelastic equations of the considered problem. Finally, by writing the resultant equations in the standard form of an eigenvalue problem, the panel flutter analysis of a cylindrical variable stiffness composite laminated (VSCL) shell will be carried out. The comparison and validation of achieved results with the results of references mentioned in the literature are made to demonstrate the accurateness of the present formulation. Also, the influence of various parameters, including the airflow angle, fiber path orientation, radius of curvature, and converting symmetric lay-up to unsymmetrical lay-up on the flutter threshold is studied.

• Wind and Structures
• /
• v.25 no.2
• /
• pp.131-156
• /
• 2017

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin-Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton's principle is utilized for deriving the motion equations where the size effects are considered based on Eringen's nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

• Steel and Composite Structures
• /
• v.50 no.2
• /
• pp.149-158
• /
• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Structural Engineering and Mechanics
• /
• v.91 no.5
• /
• pp.503-516
• /
• 2024

The present research examines the primary resonance (PR) behaviors of oblique stiffened multilayer functionally graded (OSMFG) shallow shells featuring an FG porous (FGP) core under an external excitation. The research considers two distinct types of FGP cores: one characterized by uniform porosity distribution (UPD) and the other by non-uniform porosity distribution (NPD) along the thickness direction. Furthermore, the study explores two types of shallow shells: one with external oblique stiffeners and one with internal oblique stiffeners, which might have angles that are similar or different from each other. Using the stress function alongside the first-order shear deformation theory (FSDT), the research establishes a nonlinear model for OSMFG shallow shells. The strain-displacement relationships are obtained utilizing FSDT and von-Kármán's geometric assumptions. The Galerkin approach is utilized to discretize the nonlinear governing equations, allowing for the analysis of stiffeners at varied angles. To validate the obtained results, a comparison is made not only with the findings of previous research but also with the response of PR obtained theoretically with the method of multiple scales, using the P-T method. Renowned for its superior accuracy and reliability, the P-T method is deemed an apt selection within this framework. Additionally, the study investigates how differences in material characteristics and stiffener angles affect the system's PR behaviors. The results of this study can be used as standards by engineers and researchers working in this area, and they can offer important information for the design and evaluation of the shell systems under consideration.