On the Dynamic Response of Imperfection Sensitive Higher Order Functionally Graded Plates with Random System Parameters

2019 ◽  
Vol 11 (03) ◽  
pp. 1950025 ◽  
Author(s):  
Mohammed Shakir ◽  
Mohammad Talha
Keyword(s):  
Volume Fraction ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Power Law Distribution ◽  
Random System ◽  
System Parameters

This paper presents the influence of various random system parameters on dynamics response of imperfection sensitive higher order shear deformable functionally graded material (FGM) plates. Young’s moduli, Poisson’s ratio and volume fraction index are considered as random system parameters. The material properties of the FGM plates are assumed to vary along the thickness direction using simple power-law distribution in terms of the volume fraction of the constituents. The plate kinematics is based on Reddy’s higher order shear deformation theory. Finite element method (FEM) is employed in conjunction with first-order perturbation technique (FOPT) and Newmark integration scheme to explore the influence of different system parameters, like volume fraction indices, aspect ratio, material uncertainties, and imperfection amplitude on the dynamic responses of the FGM plates.

Influence of Material Stochasticity on Buckling Characteristics of Initially Imperfect Higher-Order Shear Deformable Gradient Plates

2020 ◽  
pp. 2150004
Author(s):  
Mohammed Shakir ◽  
Mohammad Talha
Keyword(s):  
Material Properties ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Power Law Distribution ◽  
Geometric Imperfection ◽  
Governing Differential Equation ◽  
And Performance ◽  
Shear Deformable

This paper demonstrates the influence of material stochasticity on buckling characteristics of higher-order shear deformable gradient plates with initial geometric imperfections. The gradient plates are assessed by smooth variation in the volume fraction of the constituents (i.e. ceramic and metal) as power-law distribution function in the thickness direction. The effective material properties are achieved by means of the Voigt model. Plate kinematic based on Reddy’s higher-order shear deformation theory (HSDT) associated with initial geometric imperfection in the transverse direction is employed. The governing differential equation is produced using a variational approach. The mean and standard deviation of the critical buckling load are evaluated using finite element method and a mean-centered first-order perturbation technique in order to highlight the variation in buckling response. Numerical results are compared both in deterministic and probabilistic frameworks along with convergence in support of efficacy and performance of the proposed model. Based on the results, it can be concluded that the combined influence of geometric imperfection and uncertain material properties prominently affect the buckling response of the gradient plates.

scholarly journals Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Francesco Tornabene ◽  
Alessandro Ceruti
Keyword(s):  
Dynamic Optimization ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Search Space ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Static Deflection ◽  
Power Law Distribution ◽  
Graded Material ◽  
Doubly Curved

This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure.

Influence of Material Uncertainty on Vibration Characteristics of Higher-Order Cracked Functionally Gradient Plates Using XFEM

2021 ◽  
Vol 13 (05) ◽  
Author(s):  
Ahmed Raza ◽  
Mohammad Talha ◽  
Himanshu Pathak
Keyword(s):  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Partition Of Unity ◽  
Higher Order ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Level Set Function

In this study, the influence of material uncertainty on the vibration characteristics of the cracked functionally graded materials (FGM) plates is investigated. Extended stochastic finite element formulation is implemented to model the cracked FGM plate with material uncertainty using higher-order shear deformation theory (HSDT). The level set function is employed to track the crack in the FGM domain. The concept of partition of unity technique is implemented to enrich the primary variable with additional functions. The gradation of the material properties along the thickness direction is done using the power-law distribution. The first-order perturbation technique (FOPT) is incorporated in the methodology for stochastic vibration analysis. The convergence and validation study has been performed to verify the efficacy and accuracy of the formulation. Numerical results are obtained to show the effects of various influential parameters like crack length, gradient index, thickness ratio, and boundary condition on the covariance of the square of natural frequencies. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of cracked FGM plates with material randomness.

Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory

2018 ◽  
Vol 10 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Power Law Distribution ◽  
Skew Angle

This paper deals with the free vibration of a skew functionally graded material (FGM) plate in the thermal environment. A higher-order shear deformation theory (HOSDT) is employed to develop a finite element model of the plate. The material properties are assumed to be temperature-dependent and are graded along the thickness direction as per simple power law distribution in terms of volume fraction of metal and ceramic constituent phases. The model is based on an eight-noded isoparametric element with seven degrees of freedom (DOFs) per node. The general displacement equation provides C[Formula: see text] continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. The governing equations are derived using the Hamilton’s principle. The obtained results are compared with the published results to determine the accuracy of the method. The effects of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies are investigated.

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

Free Vibration Responses of Functionally Graded Spherical Shell Panels Using Finite Element Method

2013 ◽  
Author(s):  
Vishesh Ranjan Kar ◽  
Subrata Kumar Panda
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Spherical Shell ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Vibration Responses ◽  
Support Conditions

Free vibration responses of functionally graded spherical shell panels are investigated in the present article. A general mathematical model is developed based on higher order shear deformation theory mid-plane kinematics. The effective material properties are graded in the thickness direction according to a power-law distribution and it varies continuously from metal (bottom surface) to ceramic (top surface). The model is discretized using a nine noded quadrilateral Lagrangian element. A convergence test has been done with different mesh refinement and compared with the available published results. In addition to that the present study includes an ANSYS model check with the developed mathematical model to show the efficacy. New results are computed for different parameters such as volume fraction, thickness ratio, curvature ratio and support conditions which indicates the effect of parametric study on non-dimensional frequency parameters.

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.

scholarly journals Nonlinear Dynamics of Imperfect FGM Conical Panel

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Yan Niu ◽  
Yuxin Hao ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Shaowu Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Engineering Application ◽  
Shear Deformation Theory ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

Structures composed of functionally graded materials (FGM) can satisfy many rigorous requisitions in engineering application. In this paper, the nonlinear dynamics of a simply supported FGM conical panel with different forms of initial imperfections are investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers of the imperfection, amplitudes of the imperfection, and damping on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories, phase portraits, and Poincare maps are obtained to show the dynamic responses of the system.

Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload

2015 ◽  
Vol 230 (1) ◽  
pp. 102-119 ◽  
Author(s):  
Frederico Martins Alves da Silva ◽  
Roger Otávio Pires Montes ◽  
Paulo Batista Gonçalves ◽  
Zenón José Guzmán Nuñez Del Prado
Keyword(s):  
Cylindrical Shell ◽  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Time Dependent ◽  
Nonlinear Frequency ◽  
Power Law Distribution

In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequency–amplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.

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