K.M. Liew

ACTIVE CONTROL OF FGM PLATES WITH INTEGRATED PIEZOELECTRIC SENSORS AND ACTUATORS

Abstract In this paper, a finite element formulation based on the classical laminated plate theory is presented for the shape and vibration control of the functionally graded material (FGM) plates with integrated piezoelectric sensors and actuators. The properties of the FGM plates are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant velocity feedback control algorithm is used for the active control of the dynamic response of the FGM plate through closed loop control. The static and dynamic responses are presented in both tabular and graphical forms for an FGM plate of aluminum oxide/Ti–6A1–4V material composition. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of FGM plates are examined.

Society and civilization: An optimization algorithm based on the simulation of social behavior

The ability to mutually interact is a fundamental social behavior in all human and insect societies. Social interactions enable individuals to adapt and improve faster than biological evolution based on genetic inheritance alone. This is the driving concept behind the optimization algorithm introduced in this paper that makes use of the intra and intersociety interactions within a formal society and the civilization model to solve single objective constrained optimization problems. A society corresponds to a cluster of points in the parametric space while a civilization is a set of all such societies. Every society has its set of better performing individuals (leaders) that help others to improve through information exchange. This results in the migration of a point toward a better performing point, analogous to an intensified local search. Leaders improve only through an intersociety information exchange that results in the migration of a leader from a society to another. This helps the better performing societies to expand and flourish.

A Swarm Metaphor for Multiobjective Design Optimization

This paper presents a new optimization algorithm to solve multiobjective design optimization problems based on behavioral concepts similar to that of a real swarm. The individuals of a swarm update their flying direction through communication with their neighboring leaders with an aim to collectively attain a common goal. The success of the swarm is attributed to three fundamental processes: identification of a set of leaders, selection of a leader for information acquisition, and finally a meaningful information transfer scheme. The proposed algorithm mimics the above behavioral processes of a real swarm. The algorithm employs a multilevel sieve to generate a set of leaders, a probabilistic crowding radius-based strategy for leader selection and a simple generational operator for information transfer. Two test problems, one with a discontinuous Pareto front and the other with a multi-modal Pareto front is solved to illustrate the capabilities of the algorithm in handling mathematically complex problems. Three well-studied engineering design optimization problems (unconstrained and constrained problems with continuous and discrete variables) are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. The results clearly indicate that the swarm algorithm is capable of generating an extended Pareto front, consisting of well spread Pareto points with significantly fewer function evaluations when compared to the nondominated sorting genetic algorithm (NSGA).

EQUILIBRIUM CONFIGURATION AND CONTINUUM ELASTIC PROPERTIES OF FINITE SIZED GRAPHENE

This paper presents a continuum mechanics approach to modelling the elastic deformation of finite graphene sheets based on Brenners potential. The potential energy of the graphene sheet is minimized for determining the equilibrium configuration. The four edges of the initially rectangular graphene sheet become curved at the equilibrium configuration. The curving of the sides is attributed to smaller coordination number for the atoms at the edges compared to that of the interior atoms. Considering two graphene models, with only two or all four edges constrained to be straight, the continuum Youngs moduli of graphene are computed applying the Cauchy–Born rule. The computed elastic constants of the graphene sheet are found to conform to orthotropic material behaviour. The computed constants differ considerably depending on whether a minimized or unminimized configuration is used for computation.

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.

ANALYSIS OF THE THERMAL STRESS BEHAVIOUR OF FUNCTIONALLY GRADED HOLLOW CIRCULAR CYLINDERS

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoelasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work.

Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading

Abstract In this paper, a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented. A profile for the volume fraction is assumed and a normal-mode expansion of the equations of motion yields a system of Mathieu–Hill equations the stability of which is analyzed by the Bolotin’s method. The present study examines the effects of the volume fraction of the material constituents and their distribution on the parametric response, in particular the positions and sizes of the instability regions.

Mechanical design and optimization of capacitive micromachined switch

Abstract Design and optimization of a shunt capacitive micromachined switch is presented. The micromachined switch consists of a thin metal membrane called the “bridge” suspended over a center conductor, and fixed at both ends to the ground conductors of a coplanar waveguide (CPW) line. A static electromechanical model considering the residual stress effects is developed to predict the effective stiffness constant and the critical collapse voltage of the bridge for several typical bridge geometries. The deformation of the bridge and its contact behavior with the dielectric layer are analyzed using the finite element method (FEM) in order to explore a good contact field with different bridge geometries. Furthermore, a nonlinear dynamic model that captures the effects of electrostatic forces, elastic deformation, residual stress, inertia, and squeeze film damping is developed, and is used for predicting the switching speed (including the switching-down and the switching-up time) and the Q -factor. The effects of variation of important parameters on the mechanical performance have been studied in detail, and the results are expected to be useful in the design of optimum shunt capacitive micromachined switch. The results may also be useful in the design of actuators with membranes or bridges.

Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method

In this paper, we adopt the first-order shear deformation theory in the moving least squares differential quadrature (MLSDQ) procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates. The transverse deflection and two rotations of the laminate are independently approximated with the moving least squares (MLS) approximation. The weighting coefficients used in the MLSDQ approximation are obtained through the fast computation of the MLS shape functions and their partial derivatives. The natural frequencies of vibration are computed for various laminated plates and compared with the available published results. Through numerical experiments, the capability and efficiency of the MLSDQ method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined. Effects of the size of support, order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated.

Resonance analysis of multi-layered graphene sheets used as nanoscale resonators.

A stacked plate model for the vibration of multi-layered graphene sheets (MLGSs), in which the van der Waals (vdW) interaction between layers is described by an explicit formula, is presented. Explicit formulae are derived for predicting the natural frequencies of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the natural frequencies. The natural frequencies are calculated for various numbers of layered graphene sheets, and the results show that the vdW interaction has no influence on the lowest natural frequency (classical frequency) of an MLGS but plays a significant role in all higher natural frequencies (resonant frequencies) for a given combination of m and n. The vibration modes that are associated with the classical frequencies for each sheet of an MLGS are identical. In contrast, the vibration modes that are associated with the resonant frequencies are non-identical and give various vibration patterns, which indicates that MLGSs are highly suited to use as high frequency resonators.