Smart control of functionally graded sandwich plates by incorporating Murakami zig-zag function

2022 ◽  
pp. 107754632110564
Author(s):  
Nuruzzama M Khan ◽  
R Suresh Kumar
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Composite Layer ◽  
Orientation Angle ◽  
Element Model ◽  
Functionally Graded ◽  
Piezoelectric Composite ◽  
Sandwich Plates ◽  
Material System

This study is aimed at incorporating the zig-zag effect by Murakami zig-zag function in the development of a finite element model for active constraining layer damping treatment of functionally graded sandwich plates. The present sandwich construction consists of functionally graded facings distanced by a ceramic core. The substrate functionally graded plate is subjected to active constraining layer damping treatment, which in itself is a two-layered material system comprised of a viscoelastic layer and a 1–3 piezoelectric composite layer. The deformation kinematics of the functionally graded sandwich plate active constraining layer damping system is shaped using Murakami zig-zag function , and the finite element model is obtained by the virtual work principle. A standard feedback control system has been implemented, and a MATLAB subroutine has been developed to present the open- and closed-loop responses. Substrate plates with functionally graded configurations 1-1-1, 1-2-1, and 2-1-2 are considered to evaluate the effect of active constraining layer damping on damping the frequency responses of these plates. Investigation on damping performance has been carried out, bearing in mind the change in power-law index with top and bottom ceramic-/metal-rich surfaces. Also, the effect of variation in fiber orientation angle (obliquely reinforced) of the piezoelectric composite material on the active constraining layer damping performance has been examined thoroughly.

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded

scholarly journals Piezoelectric Beam Finite Element Model and Its Reduction and Control

2021 ◽  
Vol 71 (1) ◽  
pp. 87-106
Author(s):  
Kutiš Vladimír ◽  
Paulech Juraj ◽  
Gálik Gálik ◽  
Murín Justín
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
State Space ◽  
State Space Model ◽  
Element Model ◽  
Functionally Graded ◽  
Fem Model ◽  
Space Model ◽  
Piezoelectric Beam ◽  
Reduced State

Abstract The paper deals with the development of the finite element method (FEM) model of piezoelectric beam elements, where the piezoelectric layers are located on the outer surfaces of the beam core, which is made of functionally graded material. The created FEM model of piezoelectric beam structure is reduced using the modal truncation method, which is one of model order reduction (MOR) method. The results obtain from reduced state-space model are compared with results obtain from finite element model. MOR state-space model is also used in the design of the linear quadratic regulator (LQR). Created reduced state-space model with feedback with the LQR controller is analysed and compared with the results from FEM model.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

scholarly journals STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL

2020 ◽  
Vol 57 (6A) ◽  
pp. 77
Author(s):  
Nguyen Van Chinh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Classical Boundary ◽  
Bending Behavior

In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

Material parameter identification in functionally graded structures using isoparametric graded finite element model

2016 ◽  
Vol 23 (6) ◽  
pp. 685-698 ◽  
Author(s):  
Lixin Huang ◽  
Ming Yang ◽  
Xiaojun Zhou ◽  
Qi Yao ◽  
Lin Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Parameter Identification ◽  
Material Parameter ◽  
Element Model ◽  
Functionally Graded ◽  
Identification Algorithm ◽  
Material Parameter Identification ◽  
Measured Displacement ◽  
Graded Structures

AbstractAn identification algorithm based on an isoparametric graded finite element model is developed to identify the material parameters of the plane structure of functionally graded materials (FGMs). The material parameter identification problem is formulated as the problem of minimizing the objective function, which is defined as a square sum of differences between measured displacement and calculated displacement by the isoparametric graded finite element approach. The minimization problem is solved by using the Levenberg-Marquardt method, in which the sensitivity calculation is based on the differentiation of the governing equations of the isoparametric graded finite element model. The validity of this algorithm is illustrated by some numerical experiments. The numerical results reveal that the proposed algorithm not only has high accuracy and stable convergence, but is also robust to the effects of measured displacement noise.

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