Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 2: Numerical results and discussions

2015 ◽  
Vol 37 (4) ◽  
pp. 251-262
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Buckling Load ◽  
Geometrical Parameters ◽  
Thermal Loads ◽  
First Order ◽  
Elastic Foundations ◽  
Buckling Behavior ◽  
Post Buckling

Based on the first-order shear deformation plate theory (FSDT), the smeared stiffeners technique and Galerkin method, the analytical expressions to determine the static critical buckling load and analyze the post-buckling load-deflection curves of FGM plates reinforced by FGM stiffeners resting on elastic foundations and subjected to in-plane compressive loads or thermal loads are established in part 1. In this part, we will use them to study the effects of temperature, stiffener, volume fraction index, geometrical parameters, elastic foundations on the buckling and post-buckling behavior of plates. In addition, the results in comparisons between the classical plate theory (CPT) and the first order shear deformation theory (FSDT) also are carried out and shown that the buckling and post-buckling behavior of more thick plate should be studied by FSDT.

scholarly journals Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 1: Governing equations establishment

2015 ◽  
Vol 37 (3) ◽  
pp. 187-204
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Buckling Load ◽  
Thermal Loads ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling ◽  
Analysis Of Stability

In this paper, the buckling and post-buckling behaviors of eccentrically  stiffened functionally graded material (ES-FGM) plates on elastic  foundations subjected to in-plane compressive loads or thermal loads are  investigated by an analytical solution. The novelty of this work is that FGM  plates are reinforced by FGM stiffeners and the temperature, stiffener,  foundation are considered. The first-order shear deformation  plate theory is used. The thermal elements of plate and stiffeners in  fundamental equations are introduced. Theoretical formulations based on the  smeared stiffeners technique and the first-order shear deformation plate  theory, are derived. The analytical expressions to determine the static  critical buckling load and post-buckling load-deflection curves are  obtained.

Initial Post-buckling Behavior of Thick Rings Under Uniform External Hydrostatic Pressure

1995 ◽  
Vol 62 (2) ◽  
pp. 338-345 ◽  
Author(s):  
Lei Fu ◽  
A. M. Waas
Keyword(s):  
Hydrostatic Pressure ◽  
Shear Deformation ◽  
Buckling Load ◽  
Deformation Analysis ◽  
Two Dimensional ◽  
Composite Ring ◽  
Buckling Behavior ◽  
Buckling Stability ◽  
Post Buckling ◽  
Beam Type

The initial post-buckling behavior of thick rings under external uniform hydrostatic pressure is investigated. In the analysis, no assumptions are placed upon the relative magnitudes of the elongations and rotations, and the ring is assumed to be elastic and extensional. The importance of including certain nonlinear terms in the initial post-buckling stability analysis and the effects of nonzero shearing strains on the buckling load and the initial post-buckling stability are examined. It is shown that the classical Kirchhoff assumptions, when employed for a ring lead to nonvanishing through thickness strains, εzz and εzθ, with the latter being proportional to the through thickness coordinate z. An approximate first order shear deformation analysis and a two-dimensional elasticity analysis (without beam-type kinematical assumptions) of the initial post-buckling behavior of thick rings are presented and the thickness effects on the buckling load and the initial post-buckling behavior are examined. The formulation for the composite ring was reduced to that of an isotropic ring and the results thus obtained were compared with published one-dimensional results in the literature. It is found from both the shear deformation and the two-dimensional analysis that the initial post-buckling behavior of the isotropic ring and the composite rings studied are stable. The influence of thickness on the degree of stability in the immediate post-buckling response is characterized.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

2013 ◽  
Vol 5 (1) ◽  
pp. 90-112 ◽  
Author(s):  
S. Jafari Mehrabadi ◽  
B. Sobhaniaragh ◽  
V. Pourdonya
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Effective Material Properties

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

1988 ◽  
Vol 55 (3) ◽  
pp. 611-617 ◽  
Author(s):  
R. Schmidt ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Plate Theory ◽  
Small Strain ◽  
Present Theory ◽  
Shell Structures ◽  
Governing Equations ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Principle Of Virtual Displacements

A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Ka´rma´n type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates

2016 ◽  
Vol 32 (5) ◽  
pp. 539-554 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
A. Shahabodini
Keyword(s):  
Size Effect ◽  
Nonlinear Equations ◽  
Forced Vibration ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Continuation Method ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Governing Equations ◽  
First Order

AbstractIn this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

Buckling and Post Buckling Behavior of a Transversely Stiffened Ship Hull Model

1964 ◽  
Vol 8 (04) ◽  
pp. 7-21
Author(s):  
H.G. Schultz
Keyword(s):  
Reasonable Agreement ◽  
Ship Hull ◽  
Buckling Load ◽  
Experimental Results ◽  
Postbuckling Behavior ◽  
Pure Bending ◽  
Box Girder ◽  
Buckling Behavior ◽  
Theoretical Investigations ◽  
Post Buckling

In the paper presented the behavior of a transversely formed box-girder model subjected to pure bending is discussed, where the deck plating of the model is loaded above the buckling load. The experimental results obtained are in reasonable agreement with theoretical investigations and show the influence of fabrication initiated plate deflections on the buckling and postbuckling behavior of the deck plating clearly. A method is suggested for determining the buckling load of plates having large initial deformations.

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