On the Theory of Functionally Graded Moderately Thick Composite Shells

2013 ◽  
Vol 05 (03) ◽  
pp. 1350012
Author(s):  
P. H. Wen ◽  
Ferri Aliabadi
Keyword(s):  
Exact Solutions ◽  
Shell Theory ◽  
Middle Surface ◽  
Functionally Graded ◽  
Transform Domain ◽  
Governing Equations ◽  
The Laplace Transform ◽  
Benchmark Solutions ◽  
First Time ◽  
Shear Deformable

In this paper, exact solutions for double curved functionally graded shells subjected to static and dynamic distributed loads are presented for the first time. Shear deformable shell theory is used and the governing equations for the laminated and functionally graded shells with respect to the middle surface are presented in the Laplace transform domain. The exact solutions of the laminated and functionally graded shells should serve as benchmark solutions for numerical methods.

Thermoelastic Vibration of Shear Deformable Functionally Graded Curved Beams with Microstructural Defects

2018 ◽  
Vol 18 (11) ◽  
pp. 1850135 ◽  
Author(s):  
Mohammad Amir ◽  
Mohammad Talha
Keyword(s):  
Material Properties ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Opening Angle ◽  
Curved Beams ◽  
Microstructural Defects ◽  
Thermoelastic Vibration ◽  
Benchmark Solutions ◽  
Shear Deformable

In the present study, the thermoelastic vibration of shear deformable functionally graded material (FGM) curved beams with microstructural defects (porosity) has been analyzed by the finite element method. The formulation is based on the higher-order shear deformation theory. The material properties of FGM beams are allowed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Even and uneven distributions of porosities in the beam have been considered with temperature-dependent material properties. Comparison and convergence study has been performed to validate the present formulation. Parametric studies have been done to study the effect of different influencing parameters on the frequency of the FGM curved beam, i.e. porosity, temperature rise, volume fraction index and opening angle. Some new results are presented which can be used as benchmark solutions for future research.

Multiphysics of Multilayered and Functionally Graded Cylinders Under Prescribed Hygrothermomagnetoelectromechanical Loading

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
A. H. Akbarzadeh ◽  
D. Pasini
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Cross Section ◽  
Functionally Graded ◽  
Governing Equations ◽  
Multilayered Cylinder ◽  
Hollow Cylinders ◽  
Insight Into ◽  
Circular Disks ◽  
Long Cylinder

This paper examines the multiphysics of multilayered and functionally graded cylinders subjected to steady-state hygrothermomagnetoelectromechanical loading. The cylinder is assumed to be axisymmetric, infinitely long, and with either hollow or solid cross section that is, both polarized and magnetized radially. The multiphysics model is used to investigate the effect of moisture, temperature, magnetic, electric, and mechanical loadings. The influence of imperfectly bonded interfaces is also accounted for in the governing equations. Exact solutions of differential equations are obtained for each homogenous layer of the multilayered cylinder. The results are verified with those available in literature for a homogenous infinitely long cylinder and can also be applied to study the multiphysics of thin circular disks. Maps are presented for solid and hollow cylinders to visualize the effect of hygrothermomagnetoelectromechanical loading, heterogeneity of bonded layers, and imperfectly bonded interfaces. The plots offer insight into the behavior of heterogeneous magnetoelectroelastic media in a steady state hygrothermal field.

Axial Buckling and Dynamic Stability of Functionally Graded Microshells Based on the Modified Couple Stress Theory

2015 ◽  
Vol 15 (04) ◽  
pp. 1450070 ◽  
Author(s):  
Raheb Gholami ◽  
Reza Ansari ◽  
Abolfazl Darvizeh ◽  
Saeed Sahmani
Keyword(s):  
Dynamic Stability ◽  
Couple Stress ◽  
Shell Theory ◽  
Scale Parameter ◽  
Functionally Graded ◽  
Governing Equations ◽  
First Order ◽  
Axial Buckling ◽  
Aspect Ratios ◽  
Modified Couple Stress

A nonclassical first-order shear deformation shell model is developed to analyze the axial buckling and dynamic stability of microshells made of functionally graded materials (FGMs). For this purpose, the modified couple stress elasticity theory is implemented into the first-order shear deformation shell theory. Unlike the classical shell theory, the newly developed shell model contains an internal material length scale parameter to capture efficiently the size effect. By using the Hamilton's principle, the higher-order governing equations and boundary conditions are derived. Afterward, the Navier solution is utilized to predict the critical axial buckling loads of simply-supported functionally graded (FG) microshells. Moreover, the governing equations are written in the form of Mathieu–Hill equations and then Bolotin's method is employed to determine the instability regions. A parametric study is conducted to investigate the influences of static load factor, axial wave number, dimensionless length scale parameter, material property gradient index, length-to-radius and length-to-thickness aspect ratios on the axial buckling and dynamic stability responses of FGM microshells. It is revealed that size effect plays an important role in the value of critical axial buckling load and instability region of FGM microshells especially corresponding to those with lower aspect ratios.

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

2021 ◽  
pp. 095440622110211
Author(s):  
Nguyen Van Long ◽  
Van-Loi Nguyen ◽  
Minh-Tu Tran ◽  
Duc-Kien Thai
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Material Properties ◽  
Middle Surface ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Governing Equations ◽  
Fg Beam ◽  
Nonlinear Static

In this paper, an exact solution for nonlinear static behaviors of functionally graded (FG) beams with porosities resting on the elastic foundation is presented. The FG material properties with porosities are assumed to vary along the thickness of the beam, and two types of porosity distributions are considered. Actually, the geometrical middle surface of the FG beam selected in computations is very popular in the literature. By contrast, in this study, the physical neutral surface of the beam is utilized. Based on the Timoshenko beam theory, von Kármán nonlinear assumption, together with neutral surface concept, the nonlinear governing equations of the FG beam resting on the elastic foundation are derived. By using the physical neutral surface, the nonlinear governing equations have simple forms and can be solved directly. The exact solution for the problem with all immovable and moveable boundary conditions is conducted in detail. Some numerical investigations to show the effects of boundary conditions, material properties, length-to-thickness ratio, elastic foundation coefficients and several types of applied load on nonlinear static bending behaviors of the beam are given.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes

2021 ◽  
pp. 107754632110004
Author(s):  
Hassan Afshari ◽  
Hossein Amirabadi
Keyword(s):  
Carbon Nanotubes ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Conical Shells ◽  
First Order ◽  
Effective Mechanical Properties ◽  
Comprehensive Study

In this article, a comprehensive study is conducted on the free vibration analysis of rotating truncated conical shells reinforced with functionally graded agglomerated carbon nanotubes The shell is modeled based on the first-order shear deformation theory, and effective mechanical properties are calculated based on the Eshelby–Mori–Tanaka scheme along with the rule of mixture. By considering centrifugal and Coriolis accelerations and initial hoop tension, the set of governing equations is derived using Hamilton’s principle and is solved numerically using the differential quadrature method Convergence and accuracy of the presented model are confirmed and the effects of different parameters on the forward and backward frequencies of the rotating carbon nanotube-reinforced truncated conical shells are investigated.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

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