Thermo-Mechanical Buckling Analysis of Functionally Graded Skew Laminated Plates with Initial Geometric Imperfections

2018 ◽  
Vol 10 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Sanjay Singh Tomar ◽  
Mohammad Talha
Keyword(s):  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Geometric Imperfections ◽  
Efficiency And Effectiveness ◽  
Governing Differential Equation ◽  
Parametric Studies ◽  
Mechanical Buckling ◽  
Initial Geometric Imperfections ◽  
Continuous Displacement

The aim of the present study is to investigate thermo-mechanical buckling response of skew functionally graded laminated plates (FGLP) with initial geometric imperfections. The formulation has been performed using Reddy’s higher order shear deformation theory (HSDT) with the [Formula: see text] continuous displacement field. A nine-noded isoparametric element has been employed to discretize the domain of the plate. Variational principle has been used to derive the governing differential equation of the problem. Several examples with various comparison and parametric studies have been shown to prove the efficiency and effectiveness of the present formulation. The numerical results have been highlighted with different system parameters and boundary conditions.

scholarly journals Mechanical Buckling Analysis of Saturated Porous Functionally Graded Elliptical Plates Subjected to In-Plane Force Resting on Two Parameters Elastic Foundation Based on HSDT

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mohammad Hossein Sharifan ◽  
Mohsen Jabbari
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Potential Energy Function ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Mechanical Buckling ◽  
Two Parameters

Abstract In this paper, mechanical buckling analysis of a functionally graded (FG) elliptical plate, which is made up of saturated porous materials and is resting on two parameters elastic foundation, is investigated. The plate is subjected to in-plane force and mechanical properties of the plate assumed to be varied through the thickness of it according to three different functions, which are called porosity distributions. Since it is assumed that the plate to be thick, the higher order shear deformation theory (HSDT) is employed to analyze the plate. Using the total potential energy function and using the Ritz method, the critical buckling load of the plate is obtained and the results are verified with the simpler states in the literature. The effect of different parameters, such as different models of porosity distribution, porosity variations, pores compressibility variations, boundary conditions, and aspect ratio of the plate, is considered and has been discussed in details. It is seen that increasing the porosity coefficient decreases the stiffness of the plate and consequently the critical buckling load will be reduced. Also, by increasing the pores' compressibility, the critical buckling load will be increased. Adding the elastic foundation to the structure will increase the critical buckling load. The results of this study can be used to design more efficient structures in the future.

Imperfection sensitivity in the vibration behavior of functionally graded arches by considering microstructural defects

2018 ◽  
Vol 233 (8) ◽  
pp. 2763-2777 ◽  
Author(s):  
Mohammad Amir ◽  
Mohammad Talha
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Imperfection Sensitivity ◽  
Vibration Behavior ◽  
Microstructural Defects ◽  
Geometrical Imperfections ◽  
Parametric Studies ◽  
Benchmark Solutions

In this paper, imperfection sensitivity in the vibration behavior of functionally graded arches with microstructural defects (porosity) has been studied. The temperature-dependent material properties of functionally graded arches are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on the Reddy’s higher order shear deformation theory using finite element method. Convergence and comparison studies have been performed to describe the efficacy of the present formulation. The obtained results have been compared with the limited available literature. The parametric studies have been performed to study the influence of the temperature rise, volume fraction index, and porosity index on the frequency response of the functionally graded arches. The effect of various modes of initial geometrical imperfections has also been examined. The obtained numerical results can be used as benchmark solutions for future researches in this field of study.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

Numerical simulation of the thermomechanical buckling analysis of bidirectional porous functionally graded plate using collocation meshfree method

2021 ◽  
pp. 146442072110585
Author(s):  
Rahul Kumar ◽  
Achchhe Lal ◽  
Bhrigu Nath Singh ◽  
Jeeoot Singh
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plate ◽  
Aspect Ratios ◽  
Radial Basis ◽  
Mechanical Buckling

This paper presents some new and valuable numerical results for the thermo-mechanical buckling analysis of bidirectional porous functionally graded plates with uniform and non-uniform temperature rise. The strong form formulation is implemented for thermo-mechanical buckling in the framework of higher-order shear deformation theory. The material property with four schemes of porosity distribution of bidirectional porous functionally graded plate is taken by a modified power law. The governing differential equations are accomplished utilizing the principle of virtual works. The multi-quadric radial basis function is implemented for discretizing the governing differential equations. The multi-quadric radial basis function Euclidean norm is modified to analyze the square as well as rectangular plates without changing the shape parameters. Convergence and validation studies are performed to show the accuracy, effectiveness, and consistency of the present meshfree collocation method. The influence of different porosity distributions, span to thickness ratios, aspect ratios, grading index, temperature raise, boundary conditions, and porosity index on thermomechanical buckling load is evaluated. Some novel results for the bidirectional porous functionally graded plate are also enumerated that can be utilized as benchmark results for future reference.

Thermal Post-Buckling of Laminated Plates Comprising Functionally Graded Materials With Temperature-Dependent Properties

2004 ◽  
Vol 71 (6) ◽  
pp. 839-850 ◽  
Author(s):  
K. M. Liew ◽  
J. Yang ◽  
S. Kitipornchai
Keyword(s):  
Functionally Graded Materials ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Post Buckling ◽  
Temperature Dependent Properties

This paper presents thermal buckling and post-buckling analyses for moderately thick laminated rectangular plates that contain functionally graded materials (FGMs) and subjected to a uniform temperature change. The theoretical formulation employs the first-order shear deformation theory and accounts for the effect of temperature-dependent thermoelastic properties of the constituent materials and initial geometric imperfection. The principle of minimum total potential energy, the differential quadrature method, and iterative algorithms are used to obtain critical buckling temperatures and the post-buckling temperature-deflection curves. The results are presented for both symmetrically and unsymmetrically laminated plates with ceramic/metal functionally graded layers, showing the effects of temperature-dependent properties, layup scheme, material composition, initial imperfection, geometric parameters, and boundary conditions on buckling temperature and thermal post-buckling behavior.

scholarly journals Natural Frequency Analysis of Functionally Graded Orthotropic Cross-Ply Plates Based on the Finite Element Method

2019 ◽  
Vol 24 (2) ◽  
pp. 52 ◽  
Author(s):  
Michele Bacciocchi ◽  
Angelo Tarantino
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Mode Shapes ◽  
Thickness Direction ◽  
Thick Plates ◽  
Natural Frequency Analysis

This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is the modelling of the reinforcing fibers of the orthotropic layers assuming a non-uniform distribution in the thickness direction. The Halpin–Tsai approach is employed to define the overall mechanical properties of the composite layers starting from the features of the two constituents (fiber and epoxy resin). Several functions are introduced to describe the dependency on the thickness coordinate of their volume fraction. The analyses are carried out in the theoretical framework provided by the first-order shear deformation theory (FSDT) for laminated thick plates. Nevertheless, the same approach is used to deal with the vibration analysis of thin plates, neglecting the shear stiffness of the structure. This objective is achieved by properly choosing the value of the shear correction factor, without any modification in the formulation. The results prove that the dynamic response of thin and thick plates, in terms of natural frequencies and mode shapes, is affected by the non-uniform placement of the fibers along the thickness direction.

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