Asymptotic Homogenization Models for Smart Composite Plates with Rapidly Varying Thickness: Part I-Theory

2004 ◽  
Vol 2 (1) ◽  
pp. 16 ◽  
Author(s):  
A. L. Kalamkarov ◽  
A. V. Georgiades
Keyword(s):  
Composite Plates ◽  
Smart Composite ◽  
Asymptotic Homogenization ◽  
Varying Thickness

scholarly journals Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part I – Model Development

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
D. A. Hadjiloizi ◽  
A.L. Kalamkarov ◽  
Ch. Metti ◽  
A. V. Georgiades
Keyword(s):  
Effective Properties ◽  
Practical Importance ◽  
Electric Displacement ◽  
Micromechanical Model ◽  
Composite Plates ◽  
Thin Elastic Plate ◽  
Smart Composite ◽  
Uniform Thickness ◽  
Asymptotic Homogenization ◽  
Static Approximation

AbstractA comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly-varying thickness is developed in the present paper. A rigorous three-dimensional formulation is used as the basis of multiscale asymptotic homogenization. The asymptotic homogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of a set of differential equations and associated boundary conditions. These systems of equations are called unit cell problems and their solution yields such coefficients as the effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and others. Among these coefficients, the so-called product coefficients are also determined which are present in the behavior of the macroscopic composite as a result of the interactions and strain transfer between the various phases but can be absent from the constitutive behavior of some individual phases of the composite material. The model is comprehensive enough to allow calculation of such local fields as mechanical stress, electric displacement and magnetic induction. In part II of this work, the theory is illustrated by means of examples pertaining to thin laminated magnetoelectric plates of uniform thickness and wafer-type smart composite plates with piezoelectric and piezomagnetic constituents. The practical importance of the model lies in the fact that it can be successfully employed to tailor the effective properties of a smart composite plate to the requirements of a particular engineering application by changing certain geometric or material parameters. The results of the model constitute an important refinement over previously established work. Finally, it is shown that in the limiting case of a thin elastic plate of uniform thickness the derived model converges to the familiar classical plate model.

Micromechanics of Smart Composite Plates with Periodically Embedded Actuators and Rapidly Varying Thickness

2006 ◽  
Vol 19 (3) ◽  
pp. 251-276 ◽  
Author(s):  
A. L. Kalamkarov ◽  
A. V. Georgiades ◽  
K. Challagulla ◽  
G. C. Saha
Keyword(s):  
Composite Plates ◽  
Smart Composite ◽  
Varying Thickness

Electric Potential Recovery in Smart Composite Plates

2020 ◽  
Vol 2 (2-3) ◽  
pp. 161-168
Author(s):  
Yong-Min Jeong ◽  
Jun-Sik Kim
Keyword(s):  
Electric Potential ◽  
Composite Plates ◽  
Smart Composite

scholarly journals MULTI-MODAL VIBRATION CONTROL OF SMART COMPOSITE PLATES

1999 ◽  
Vol 48 (6Appendix) ◽  
pp. 122-127 ◽  
Author(s):  
Jae-Hung HAN ◽  
Junji TANI ◽  
In LEE
Keyword(s):  
Vibration Control ◽  
Composite Plates ◽  
Smart Composite ◽  
Modal Vibration

Analytical modeling of laminated composite plates integrated with piezoelectric layer using Trigonometric Zigzag theory

2020 ◽  
Vol 54 (29) ◽  
pp. 4691-4708
Author(s):  
Aniket Chanda ◽  
Rosalin Sahoo
Keyword(s):  
Transverse Shear ◽  
Piezoelectric Layer ◽  
Composite Plate ◽  
Laminated Composite ◽  
Composite Plates ◽  
Solution Technique ◽  
Shear Stresses ◽  
Smart Composite ◽  
Laminated Composite Plate ◽  
Zigzag Theory

The analytical solution for static analysis of laminated composite plate integrated with piezoelectric fiber reinforced composite actuator is obtained using a recently developed Trigonometric Zigzag theory. The kinematic field consists of five independent field variables accommodating non-linear variation of transverse shear strains through the thickness of the laminated composite plate. The principle of minimum potential energy is adopted to derive the governing equations of equilibrium. Navier’s solution technique is employed to convert the system of coupled partial differential equations into a system of algebraic equations. The electric potential is assumed to vary linearly through the thickness of the piezoelectric layer. The analytical formulation also does not include voltage as an additional primary variable. The response in the form of deflection and stresses are obtained for smart composite plates subjected to electro-mechanical loads and compared with the elasticity solutions and available results reported by other researchers in the existing literature. The transverse shear stresses are accurately determined by an efficient post-processing technique of integrating the equilibrium equations of elasticity. Parametric studies on actuation in the response of the smart composite plate are also presented graphically in order to have a clear understanding of the static behavior.

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