Buckling Analysis of Multilayered Functionally Graded Composite Cylindrical Shells

In this paper, the buckling analysis of a multilayered composite cylindrical shell which volume fraction of its fiber varies according to power law in longitudinal direction, due to applied compressive axial load is studied. Rule of mixture model and reverse of that are employed to represent elastic properties of this fiber reinforced functionally graded composite. Strain displacement relations employed are based on Reissner-Naghdi-Berry’s shell theory. The displacement finite element model of the equilibrium equations is derived by employing weak form formulation. The Lagrangian shape function for in-plane displacements and Hermitian shape function for displacement in normal direction to the surface of mid-plane are used. Then, finite element code is written in MATLAB based on stated method to obtain the critical axial buckling load. Numerical results show that despite having the same layout and average volume fraction of fibers, the critical axial buckling load of functionally graded composite cylindrical shell is more than that of traditional composite in which the volume fraction of its fiber is constant throughout the shell.

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Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell

Thin-Walled Structures ◽

10.1016/j.tws.2009.08.003 ◽

2010 ◽

Vol 48 (1) ◽

pp. 25-32 ◽

Cited By ~ 34

Author(s):

T. Rahman ◽

E.L. Jansen

Keyword(s):

Finite Element ◽

Cylindrical Shell ◽

Buckling Analysis ◽

Composite Cylindrical Shell ◽

Coupled Mode ◽

Post Buckling

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Buckling Analysis of Circular FGM Plate Having Variable Thickness Under Uniform Compression by Finite Element Method

Volume 4b: Design for Manufacturing and the Life Cycle Conference ◽

10.1115/detc2005-84019 ◽

2005 ◽

Author(s):

Abazar Shamekhi ◽

Mohammad H. Naei

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Variable Thickness ◽

Buckling Analysis ◽

Functionally Graded ◽

Buckling Load ◽

Thin Plates ◽

Thickness Variation ◽

Simply Supported ◽

Element Method

This study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

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Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x16651154 ◽

2016 ◽

Vol 28 (2) ◽

pp. 272-289 ◽

Cited By ~ 1

Author(s):

Mohammadreza Saviz

Keyword(s):

Finite Element ◽

Cylindrical Shell ◽

Functionally Graded Material ◽

Volume Fraction ◽

Virtual Work ◽

Electrical Potential ◽

Axial Direction ◽

Functionally Graded ◽

Radial Coordinate ◽

Graded Material

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

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BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SKEW PLATES: AN EFFICIENT FINITE ELEMENT APPROACH

International Journal of Applied Mechanics ◽

10.1142/s1758825113500415 ◽

2013 ◽

Vol 05 (04) ◽

pp. 1350041 ◽

Cited By ~ 18

Author(s):

M.N.A. GULSHAN TAJ ◽

ANUPAM CHAKRABARTI

Keyword(s):

Finite Element ◽

Volume Fraction ◽

Shear Deformation Theory ◽

Buckling Analysis ◽

Functionally Graded ◽

Element Formulation ◽

Skew Angle ◽

Buckling Behavior ◽

Metal Plates ◽

Graded Material

In the present study, an attempt has been made to present the Co finite element formulation based on third order shear deformation theory for buckling analysis of functionally graded material skew plate under thermo-mechanical environment. Here, prime emphasis has been given to study the influence of skew angle on the buckling behavior of functionally graded plate. Two dissimilar homogenization schemes, namely Mori–Tanaka scheme and Voigt rule of mixture are employed to sketch their influence for the interpretation of data. Temperature-dependent material properties of the constituents of the plate are considered to perform thermal analysis. Numerical examples are solved using different mixture of ceramic and metal plates to generate the new results and relative imperative conclusions are highlighted. The roles played by the different factors like loading condition, volume fraction index, skew angle, boundary condition, aspect ratio, thickness ratio and homogenization schemes on buckling behavior of the FGM skew plates are presented in the form of tables and figures.

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Buckling of Functionally-Graded Beams with Partially Delaminated Piezoelectric Layers

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455414501041 ◽

2016 ◽

Vol 16 (03) ◽

pp. 1450104 ◽

Cited By ~ 7

Author(s):

Mohammad Ebrahim Torki ◽

Junuthula N. Reddy

Keyword(s):

Finite Element ◽

Volume Fraction ◽

Equations Of Motion ◽

Functionally Graded ◽

Design Tool ◽

Buckling Load ◽

Validity Of Results ◽

Critical Buckling Load ◽

Piezoelectric Layers ◽

Coordinate Origin

The critical buckling load of a functionally-graded simply-supported beam with partially delaminated piezoelectric layers is discussed. The governing equations of motion are derived using two different, i.e. Euler–Bernoulli and Timoshenko beam theories, and the buckling load was evaluated from the exact solution to the corresponding eigenvalue equation. The equations were simplified to some extent by shifting the coordinate origin such that there is zero bending-extension coupling. Effects induced by the delaminated length, asymmetry, piezoelectric thickness, voltage, and the functionally graded materials (FGMs) volume fraction are evaluated. The validity of results and the invoked assumptions were successfully verified with existing results and finite element calculations. There is some difference between the analytical buckling load and that calculated with the finite element method (FEM), proven small in amount but predictable in terms of the piezoelectric thickness. Further, a general formula is derived to evaluate the dimensionless critical buckling load with the parameters obtained from regression analysis of the solution that can be utilized for all cases where the materials are not far different in their mechanical properties. The results can be utilized as benchmark design tool.

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Buckling Analysis of Variable Stiffness Composite Cylindrical Shells Based on Hermite Curves

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.805.191 ◽

2019 ◽

Vol 805 ◽

pp. 191-197

Author(s):

Chun Bo Nian ◽

Xiao Ping Wang ◽

Jing Yu Pei

Keyword(s):

Cylindrical Shell ◽

Cylindrical Shells ◽

Initial Point ◽

Variable Stiffness ◽

Tangential Direction ◽

Buckling Analysis ◽

Buckling Load ◽

Practical Significance ◽

Composite Cylindrical Shell ◽

End Point

Based on the Hermite curve, the buckling behavior of a variable stiffness composite cylindrical shell is investigated. Firstly, the cylindrical shell is unfolded into a plane, and the Hermite curve is taken as the basic reference path on the plane and the variation of the fiber orientation is obtained. Then, the finite element analysis pre-processing program of the variable stiffness composite cylindrical shell is written by Python to develop ABAQUS interactive interface. Finally, the GUI plug-in is developed successfully, the buckling analysis of the constant stiffness and variable stiffness cylindrical shells is carried out and the effect of buckling load on the initial tangential direction q1, the initial point tangential magnitude L1, the end point tangential direction q2, the end point tangential magnitude L2 is preliminarily explored. It is found that the buckling load of the variable stiffness cylindrical shell is improved greatly. The secondary development of ABAQUS by Python is used to realize the automatic modeling and calculation analysis of the variable stiffness cylindrical shell parts, which provides research ideas and processes for practical engineering research, and has certain practical significance.

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Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes636 ◽

2007 ◽

Vol 221 (11) ◽

pp. 1241-1247 ◽

Cited By ~ 23

Author(s):

M H Naei ◽

A Masoumi ◽

A Shamekhi

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Functionally Graded Material ◽

Variable Thickness ◽

Buckling Analysis ◽

Functionally Graded ◽

Buckling Load ◽

Simply Supported ◽

Graded Material ◽

Element Method

The current study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander's non-linear strain-displacement relation for thin plates. The finite-element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson's ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

Download Full-text