• 복합신소재구조학회 논문집
• /
• 제3권2호
• /
• pp.1-10
• /
• 2012

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. 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-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the anisotropic composite material. 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. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

• Structural Engineering and Mechanics
• /
• 제74권2호
• /
• pp.227-241
• /
• 2020

The bi-axial and shear buckling behavior of laminated hypar shells having rhombic planforms are studied for various boundary conditions using the present mathematical model. In the present mathematical model, the variation of transverse shear stresses is represented by a second-order function across the thickness and the cross curvature effect in hypar shells is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic second-order distribution of transverse shear strains across the thickness of the shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine nodes curved isoparametric element is used. So far, there exists no solution for the bi-axial and shear buckling problem of laminated composite rhombic (skew) hypar shells. As no result is available for the present problem, the present model is compared with suitable published results (experimental, FEM, analytical and 3D elasticity) and then it is extended to analyze bi-axial and shear buckling of laminated composite rhombic hypar shells. A C⁰ finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc. It is seen that the dimensionless buckling load of rhombic hypar increases with an increase in c/a ratio (curvature). Between symmetric and anti-symmetric laminations, the symmetric laminates have a relatively higher value of dimensionless buckling load. The dimensionless buckling load of the hypar shell increases with an increase in skew angle.

• Computers and Concrete
• /
• 제26권2호
• /
• pp.185-201
• /
• 2020

This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

• 한국강구조학회 논문집
• /
• 제14권4호
• /
• pp.519-527
• /
• 2002

쉘 구조물은 지붕 구조물, 굴뚝 구조물, 압력구조물, 선박구조물, 항공구조물 등에 널리 사용되는 구조물이다. 본 논문은 전단변형 효과를 고려한 비등방성 복합성층 원뿔형 쉘의 자유진동에 관하여 연구하였다. 복합재료는 2개 또는 이상의 재료들로 구성되어 구조적인 효율성을 증진시키도록 구성된 재료이다. 이러한 복합재료로 구성된 구조물의 거동은 매우 복잡하기 때문에 해석해를 구하기가 거의 불가능하다. 따라서 본 연구에서는 이러한 복합재료로 구성된 원뿔형 쉘의 자유진동을 해결하는데 유한차분법을 사용하였다. 중심각, 정점각 및 다른 기하학적 파라미터의 진동에 대한 효과를 연구하였고, 진동모드 형상을 예시함으로서 진동모드에 관한 물리적 및 공학적인 이해를 증진시키고자 하였다.

• 전산구조공학
• /
• 제6권1호
• /
• pp.117-125
• /
• 1993

일반적으로 복합재료 적층원통관의 강도와 강성은 세장모수, coupling 강성모수, 섬유배향각, 적층방법, 그리고 적층수 등의 변동성에 매우 민감하게 변화한다. 본 논문에서는 복합재료 적층원통관의 합리적인 신뢰성해석을 수행할 수 있는 강도 및 좌굴한계상태함수를 제안하고, 전술한 인자들이 GFRP(Glass Fiber Reinforced Plastic) 적층원통관의 강도 및 좌굴신뢰성에 미치는 영향을 고찰하였다. 이들은 복합재료 적층원통관의 강도 및 좌굴신뢰성에 매우 다양하고 복합적인 영향을 미치기 때문에 최적설계기법이나 설계규준의 개발등을 통하여 설계관련 인자들을 설계에 합리적으로 반영하므로서 실무에서 균형설계(Balanced Design)를 위한 일관성 있는 안전도/신뢰도의 확보가 가능하다고 사료된다.

• Steel and Composite Structures
• /
• 제6권4호
• /
• pp.353-366
• /
• 2006

The discrete singular convolution (DSC) algorithm for determining the frequencies of the free vibration of single isotropic and orthotropic laminated conical shells is developed by using a numerical solution of the governing differential equations of motion based on Love's first approximation thin shell theory. By applying the discrete singular convolution method, the free vibration equations of motion of the composite laminated conical shell are transformed to a set of algebraic equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The obtained results are in excellent agreement with those in the literature.

• 대한토목학회논문집
• /
• 제31권6A호
• /
• pp.409-415
• /
• 2011

Angle-Ply 적층쉘의 진동특성에 관한 최적화해석을 위해 1차전단변형이론에 의한 Ritz Method를 이용하여 이론적으로 해석하고, 수치해석에 의해 고유진동수와 진동모드를 해석하여 적층수, 쉘의 지지조건, 적층순서에 미치는 영향을 정량적으로 검토하여 적층복합원통쉘의 기본고유진동수의 최적화를 위한 최적인 적층구성에 미치는 영향을 명확히 규명하고자 한다.

• 한국강구조학회 논문집
• /
• 제11권2호통권39호
• /
• pp.117-129
• /
• 1999

본 연구의 목적은 복합재료의 이점을 증명하고, 비등방성 대칭 적층 원통형 쉘의 거동을 분석하는 것으로서, 비등방성 대칭 적층 원통형 쉘을 해석하기 위해서 전진차분법, 중앙차분법, 후진차분법으로 구성되어 있는 유한차분법을 적용하였다. 본 연구에서는 처짐과 모멘트를 자유도로 고려하였으며, 이는 모멘트 계산시 발생할 수 있는 오차를 줄일 수 있는 장점을 가지고 있다. 또한 4변이 모두 단순지지된 경계조건을 고려하였다. 수치해석 결과, 유한차분법에 의한 본 연구의 프로그램이 비등방성 대칭 적층 원통형 쉘의 해석에 적합함을 알 수 있으며, 효과적인 보강섬유의 배치 방법을 제시하였다.

• Structural Engineering and Mechanics
• /
• 제81권6호
• /
• pp.769-780
• /
• 2022

This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.

• Structural Engineering and Mechanics
• /
• 제58권1호
• /
• pp.59-91
• /
• 2016

Laminated composite shells are commonly used in various engineering applications including aerospace and marine structures. In this paper, using semi-analytical finite strip method, the buckling behavior of laminated composite deep as well as thick shells of revolution under follower forces which remain normal to the shell is investigated. The stiffness caused by pressure is calculated for the follower forces subjected to external fibers in thick shells. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness-shear flexibility. Displacements and rotations in the middle surface of shell are approximated by combining polynomial functions in the meridional direction as well as truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of loads direction will be derived for each strip of the shell. Assembling of these matrices results in global load stiffness matrix which may be un-symmetric. Upon forming linear elastic stiffness matrix called constitutive stiffness matrix, geometric stiffness matrix and load stiffness matrix, the required elements for the second step analysis which is an eigenvalue problem are provided. In this study, different parameter effects are investigated including shell geometry, material properties, and different boundary conditions. Afterwards, the outcomes are compared with other researches. By considering the results of this article, it can be concluded that the deformation-dependent pressure assumption can entail to decrease the calculated buckling load in shells. This characteristic is studied for different examples.