The Effect of Porosity on Elastic Stability of Toroidal Shell Segments Made of Saturated Porous Functionally Graded Materials

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hadi Babaei ◽  
Mohsen Jabbari ◽  
M. Reza Eslami
Keyword(s):  
Elastic Stability ◽  
Functionally Graded ◽  
Toroidal Shell ◽  
Geometrical Parameters ◽  
Equilibrium Equations ◽  
Closed Form Solutions ◽  
Porous Shell ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability

Abstract This research deals with the stability analysis of shallow segments of the toroidal shell made of saturated porous functionally graded (FG) material. The nonhomogeneous material properties of porous shell are assumed to be functionally graded as a function of the thickness and porosity parameters. The porous toroidal shell segments with positive and negative Gaussian curvatures and nonuniform distributed porosity are considered. The nonlinear equilibrium equations of the porous shell are derived via the total potential energy of the system. The governing equations are obtained on the basis of classical thin shell theory and the assumptions of Biot's poroelasticity theory. The equations are a set of the coupled partial differential equations. The analytical method including the Airy stress function is used to solve the stability equations of porous shell under mechanical loads in three cases. Porous toroidal shell segments subjected to lateral pressure, axial compression, and hydrostatic pressure loads are analytically analyzed. Closed-form solutions are expressed for the elastic buckling behavior of the convex and concave porous toroidal shell segments. The effects of porosity distribution and geometrical parameters of the shell on the critical buckling loads of porous toroidal shell segments are studied.

Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytropes with indices $n>1$

2021 ◽  
Vol 8 (3) ◽  
pp. 474-485
Author(s):  
M. V. Vavrukh ◽  
◽  
D. V. Dzikovskyi ◽  
Keyword(s):  
Integral Form ◽  
Axial Rotation ◽  
Geometrical Parameters ◽  
Surface Form ◽  
Equilibrium Equations ◽  
Method Of Integral Equations ◽  
Mass Moment ◽  
Self Consistent ◽  
Nonlinear Equilibrium ◽  
Mass Moment Of Inertia

A new method for finding solutions of the nonlinear equilibrium equations for rotational polytropes was proposed, which is based on a self-consistent description of internal region and periphery using the integral form of equations. Dependencies of geometrical parameters, surface form, mass, moment of inertia and integration constants on angular velocity were calculated for indices $n=2.5$ and $n=3$.

Closed Form Solutions for the Problem of Statical Behavior of Nano/Micromirrors Under the Effect of Capillary Force and Van Der Waals Force

2011 ◽  
Author(s):  
Ali Darvishian ◽  
Hamid Moeenfard ◽  
Hasan Zohoor ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Capillary Force ◽  
Rotation Angle ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Combined Effect ◽  
Geometrical Parameters ◽  
Closed Form Solutions ◽  
The Stability ◽  
Vdw Force ◽  
Stability Limits

The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW toque applied to the mirror. Finally analytical tool Homotopy Perturbation Mehtod (HPM) is utilized for prediction of the nano/micromirror behaviour under combined capillary and vdW force. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system.

scholarly journals Elastic Stability Analysis of a Two-Layered Functionally Graded Cylindrical Shell under Axial Compression with the use of Energy Approach

2009 ◽  
Vol 18 (6) ◽  
pp. 096369350901800 ◽  
Author(s):  
H. Sepiani ◽  
A. Rastgoo ◽  
M. Ahmadi ◽  
A.Ghorbanpour Arani ◽  
K. Sepanloo
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Axial Compression ◽  
Elastic Layer ◽  
Elastic Stability ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Minimum Potential

This paper investigates the elastic axisymmetric buckling of a thin, simply supported functionally graded (FG) cylindrical shell embedded with an elastic layer under axial compression. The analysis is based on energy method and simplified nonlinear strain-displacement relations for axial compression. Material properties of functionally graded cylindrical shell are considered graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Using minimum potential energy together with Euler equations, equilibrium equations are obtained. Consequently, stability equation of functionally graded cylindrical shell with an elastic layer is acquired by means of minimum potential energy theory and Trefftz criteria. Another analysis is made using the equivalent properties of FG material. Numerical results for stainless steel-ceramic cylindrical shell and aluminum layer are obtained and critical load curves are analyzed for a cylindrical shell with an elastic layer. A comparison is made to the results in the literature. The results show that the elastic stability of functionally graded cylindrical shell with an elastic layer is dependent on the material composition and FGM index factor, and the shell geometry parameters and it is concluded that the application of an elastic layer increases elastic stability and significantly reduces the weight of cylindrical shells.

Dynamic Response of Functionally Graded Circular Cylindrical Shells

2008 ◽  
Vol 47-50 ◽  
pp. 608-611 ◽  
Author(s):  
Seyyed Mohammad Reza Khalili ◽  
K. Malekzadeh ◽  
A. Davar
Keyword(s):  
Dynamic Response ◽  
Power Law ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Superposition Method ◽  
Equilibrium Equations ◽  
Mode Superposition Method ◽  
Impulse Load

In this paper the response of circular cylindrical shell made of Functionally Graded Material (FGM) subjected to lateral impulse load was investigated. The effective material properties are assumed to vary continuously along the thickness direction according to a volume fraction power law distribution. First order shear deformation theory (FSDT) and Love's first approximation theory were utilized in the equilibrium equations. The boundary condition was considered to be simply supported. Displacement components are product of functions of position and time. Equilibrium equations for free and forced vibrations were solved using the Galerkin method. The impulse load in the form of time varying uniform pressure was applied onto a small rectangular area of the shell surface. The function of time for displacement components is obtained using the results of free vibration and convolution integral. Finally time response of displacement components is derived using mode superposition method. The influence of material composition (power law exponent), geometrical parameters (length to radius and radius to thickness ratios) and load parameters (position and size of the area of the applied load and peak pressure value for different pulse type) on the dynamic response was investigated.

Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load

2016 ◽  
Vol 837 ◽  
pp. 52-57
Author(s):  
Martin Psotny
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Buckling And Postbuckling Of An Imperfect Plate Subjected To The Shear Load

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Shear Load ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of an imperfect plate subjected to the shear load is presented. To solve this problem, a specialized computer program based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6827-6850 ◽  
Author(s):  
Ahmed Y Ali ◽  
Hamad M Hasan
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Nonlinear Dynamic ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Toroidal Shell ◽  
Geometrical Parameters ◽  
Nonlinear Dynamic Stability

This study investigates the nonlinear dynamic buckling of the exponentially functionally graded orthotropic toroidal shell segments under constant loading rates under the shear deformation theory with the damping influence. The properties of the shell material are assumed to be graded according to the exponential distribution function through the shell thickness direction. The shear deformation theory with von Karman nonlinearity, Stein and McElman assumption, initial imperfection, and damping effect are adopted to create the theoretical formulations. Nonlinear dynamic stability equation is solved using Galerkin's procedure and the fourth-order Runge–Kutta technique. The dynamic buckling loads are evaluated by using Budiansky–Roth criterion. Moreover, different parameter influences such as geometrical parameters, velocity, imperfections, damping ratios, and nonhomogeneous parameters on the dynamic buckling are examined in detail. The obtained results are validated with the previous publications and the good agreements are shown.

scholarly journals Nonlinear Analysis of Buckling & Postbuckling

2014 ◽  
Vol 14 (1) ◽  
pp. 75-80
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Iteration Algorithm ◽  
Nonlinear Finite Element Method ◽  
Buckling Mode ◽  
Initial Imperfections ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.

Thermal Postbuckling of Imperfect Circular Functionally Graded Material Plates: Examination of Voigt, Mori–Tanaka, and Self-Consistent Schemes

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Y. Kiani ◽  
M. R. Eslami
Keyword(s):  
Functionally Graded Material ◽  
Initial Imperfection ◽  
Functionally Graded ◽  
Circular Plates ◽  
Equilibrium Equations ◽  
Simply Supported ◽  
Self Consistent ◽  
Nonlinear Equilibrium ◽  
Graded Material ◽  
Thermal Postbuckling

Thermal postbuckling of solid circular plates made of a through-the-thickness functionally graded material (FGM) is analyzed in this paper. Initial imperfection of the plate is also taken into account. Each thermomechanical property of the plate is assumed to be a function of the temperature and thickness coordinate. Equivalent properties of the FGM media are obtained based on three different homogenization schemes, namely, Voigt rule, Mori–Tanaka scheme, and self-consistent estimate. Temperature profile is assumed to be through-the-thickness direction only. The solution of the heat conduction equation is obtained using an iterative central finite difference scheme. Various types of thermal loadings, such as uniform temperature rise, temperature specified at surfaces, and heat flux, are considered. Nonlinear equilibrium equations of the plate are obtained by means of the conventional Ritz method. Solution of the resulting nonlinear equilibrium equations and temperature distribution are obtained simultaneously at each step of heating. It is shown that response of a perfect clamped FGM plate is of the bifurcation type of buckling with stable postbuckling equilibrium branch, whereas imperfect clamped and perfect/imperfect simply supported FGM plates do not reveal the bifurcation type of instability through the nonuniform heating process. Furthermore, amplitude of initial imperfection is an important factor on the equilibrium path of FGM circular plates, especially for simply supported ones.

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