• Steel and Composite Structures
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• 제23권1호
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• pp.1-16
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• 2017

This paper is presented to solve the buckling problem of functionally graded truncated conical shells subjected to displacement-dependent pressure which remains normal to the shell middle surface throughout the deformation process by the semi-analytical finite strip method. Material properties are assumed to be temperature dependent, and varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness shear flexibility with Sanders-type of kinematic nonlinearity. The element linear and geometric stiffness matrices are obtained using virtual work expression for functionally graded materials. The load stiffness also called pressure stiffness matrix which accounts for variation of load direction is derived for each strip and after assembling, global load stiffness matrix of the shell which may be un-symmetric is formed. The un-symmetric parts which are due to load non-uniformity and unconstrained boundaries have been separated. A detailed parametric study is carried out to quantify the effects of power-law index of functional graded material and shell geometry variations on the difference between follower and non-follower lateral buckling pressures. The results indicate that considering pressure stiffness which arises from follower action of pressure causes considerable reduction in estimating buckling pressure.

• Structural Engineering and Mechanics
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• 제55권4호
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• pp.785-799
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

• Steel and Composite Structures
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• 제43권5호
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• pp.603-623
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• 2022

This article is dedicated to predict the natural frequencies of joined conical shell structures made of Functionally Graded Material (FGM). The structure includes two conical segments. The equivalent material properties are found by using the rule of mixture based on Voigt model. In addition, three well-known patterns are employed for distribution of material properties throughout the thickness of the structure. The main objective of the present research is to propose a novel exponential pattern and obtain the related equivalent material properties. Furthermore, the Donnell type shell theory is used to obtain the governing equations of motion. Note that these equations are obtained by employing First-order Shear Deformation Theory (FSDT). In order to discretize the governing system of differential equations, well-known and efficient semi-analytical scheme, namely Generalized Differential Quadrature Method (GDQM), is utilized. Different boundary conditions are considered for various types of single and joined conical shell structures. Moreover, an applicable modification is considered for the continuity conditions at intersection position. In the first step, the proposed formulation is verified by solving some well-known benchmark problems. Besides, some new numerical examples are analyzed to show the accuracy and high capability of the suggested technique. Additionally, several geometric and material parameters are studied numerically.

• Structural Engineering and Mechanics
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• 제55권1호
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• pp.29-46
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies of a truncated shallow and deep conical shell with linearly varying thickness along the meridional direction free at its top edge and clamped at its bottom edge. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Strain and kinetic energies of the truncated conical shell with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated. The frequencies from the present 3-D method are compared with those from other 3-D finite element method and 2-D shell theories.

• 동력기계공학회지
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• 제19권5호
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• pp.52-59
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• 2015

This paper is presented for the free vibration of a conical shell with annular plates or circular plate using the transfer of influence coefficient. The governing equations of vibration of a conical shell, including annular plate, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-annular plates. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of finite element method, transfer matrix method and ANSYS. The conclusion show that the present method can accurately obtain natural vibration characteristics of the conical shell with annular or circle end plates.

• 대한조선학회지
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• 제21권2호
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• pp.19-27
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• 1984

An extension of the finite element method to the stability analysis of shells of revolution under static axisymmetric loading is presented in this paper. A systematic procedure for the formulation of the problem is based upon the principle of virtual work. This procedure results in an eigenvalue problem. For solution, the shell of revolution is discretized into a series of conical frusta. The buckling mode in the circumferential direction is assumed, this assumption makes the problem economical for the computing time. The present method is applied to a number of shells of revolution, under axial compression or lateral pressure, and comparision are made with other theoretical results. The results show good agreement each other. The effects of aspect ratio, boundary conditions and buckling modes on the buckling strength of shells of revolution are studied. Also the optimum shape of cylindrical shell under uniform axial compression is obtained from the view point of structural stability.

• 복합신소재구조학회 논문집
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• 제1권3호
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• pp.24-34
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• 2010

본 논문은 전단변형효과를 고려한 복합신소재 적층 쉘을 해석하기 위하여, 일반 쉘의 지배방정식을 유도하고, 이 방정식을 풀기 위하여 수치해석 기법중 하나인 유한차분법을 수행하였다. 유한차분법을 미분방정식을 지배방정식으로 가지는 구조물 해석시 간편하게 사용될 수 있고, 오차의 범위를 선택적으로 정할수 있는 장점이 있다. 수치해석 결과의 타당성을 검증하기 위하여 수렴도 분석과 범용 구조해석 프로그램인 LUSAS의 해석결과와 비교하였다. 본 논문의 목적은 전단변형 효과를 고려한 일반 쉘의 거동 특징 및 분석, 복합재료로 구성되었을 경우 정확한 거동을 분석하고, 쉘 구조물이 보다 높은 강성을 가질 수 있도록 하는 적절한 화이버의 보강방안과 다양한 조건 변화를 통해서 최적의 쉘 구조물을 제시하는 것이다. 쉘의 곡률의 변화에 따른 거동과 합응력의 변화를 분석하고, 쉘의 높이-너비 비와 화이버 보강각도 변화에 따른 처짐 및 합응력의 변화를 비교, 분석하여 보다 유리한 쉘 구조물을 제시하였다. 또한 다양한 하중을 가하여 쉘의 형상 변화를 비교 분석함으로서 비등방성 재료로 이루어진 일반 쉘의 거동에 대하여 분석하였다.

• Structural Engineering and Mechanics
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• 제90권6호
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• pp.601-610
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• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.129-136
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• 2023

In this paper, dynamic buckling of truncated conical shell made of carbon nanotubes (CNTs) composite is studied. In aerospace industries, this category of structures is utilized extensively due to wide range of engineering applications. To calculate the effective material properties of the nanocomposite, The Mori-Tanaka model is applied. Also, the motion equations are derived with the assistance of the first order shear deformation theory (FSDT), Hamilton's principle and energy method. Besides, In order to solve motion equations and analyze dynamic instability region (DIR) of the structure, mixed model of differential quadrature method (DQM) and Bolotin's method is used. Moreover, investigation of the different parameters effects such as geometrical parameters and volume fraction of CNTs on the analysis of the DIR of the structure is done. In accordance with the obtained results, the DIR will occur at higher frequencies by increasing the volume fraction of CNTs.

• Steel and Composite Structures
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• 제35권2호
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• pp.249-260
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• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.