Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

A boundary element-free method (BEFM) for three-dimensional elasticity problems

This study combines the boundary integral equation (BIE) method and improved moving least-squares (IMLS) approximation to present a direct meshless boundary integral equation method, the boundary element-free method (BEFM) for three-dimensional elasticity. Based on the improved moving least-squares approximation and the boundary integral equation for three-dimensional elasticity, the formulae of the boundary element-free method are given, and the numerical procedure is also shown. Unlike other meshless boundary integral equation methods, the BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus giving it a greater computational precision. Three selected numerical examples are presented to demonstrate the method.Aknowledgement The work in this project was fully supported by a grant from the Research Grants Council (RGC) of the Hong Kong Special Administrative Region, China (Project No. CityU 1011/02E).The work that is described in this paper was supported by Project No. CityU 1011/02E, which was awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China. The authors are grateful for the financial support.     

Boundary element‐free method (BEFM) for two‐dimensional elastodynamic analysis using Laplace transform

In this paper, we present a direct meshless method of boundary integral equation (BIE), known as the boundary element‐free method (BEFM), for two‐dimensional (2D) elastodynamic problems that combines the BIE method for 2D elastodynamics in the Laplace‐transformed domain and the improved moving least‐squares (IMLS) approximation. The formulae for the BEFM for 2D elastodynamic problems are given, and the numerical procedures are also shown. The BEFM is a direct numerical method, in which the basic unknown quantities are the real solutions of the nodal variables, and the boundary conditions can be implemented directly and easily that leads to a greater computational precision. For the purpose of demonstration, some selected numerical examples are solved using the BEFM. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method

The elastic bending of unstiffened and stiffened corrugated plates is studied in this paper, and a mesh-free Galerkin method is presented for the analyses. A corrugated plate is treated as an orthotropic plate that has different flexure properties in two perpendicular directions. The equivalent flexure properties are estimated by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plate is considered as a composite structure of an orthotropic plate with beams. By superimposing the strain energy of the orthotropic plate and the beams, and imposing the displacement compatibility conditions between the plate and the beams, the stiffness matrix of the structure is obtained. Because no mesh is needed in the proposed method, there is no limitation to the position of the stiffeners (beams). Changes in the positions of the stiffeners do not require the re-meshing of the plate. Several numerical examples are employed to show the accuracy and convergence of the proposed method. The computation results demonstrate good agreement with the solutions given by ANSYS, and different profiles of corrugated plates are considered.     

Buckling of braced monosymmetric cantilevers

The paper examines the elastic lateral buckling of monosymmetric cantilevers with a discrete intermediate brace. On the basis of the Timoshenko energy approach, the buckling capacities are determined by direct minimization of the ‘generalized Rayleigh quotient’. Solutions are expressed in terms of the easily calculated beam parameter, , and the degree of beam monosymmetry parameter, , which indicate readily the form of the monosymmetric section. The influences of lateral brace at different levels, of rotational brace and of full brace on the buckling capacities for varying brace locations, height of load application above the shear centre and the degrees of beam monosymmetry are investigated.     

Inelastic beam buckling experiments

The paper describes a series of experiments on the buckling of simply supported laterally continuous I-beams in the inelastic range. Nine beams were tested in three groups of three, each group having a different predominant moment gradient. Points of load application were prevented from moving laterally and twisting. Measurements of geometrical and material imperfections are included in this report. Results of a number of subsidiary experiments such as plastic moment and stub column tests are also presented. The results add to the small amount of test data presently available on such beams and provide a comparison with theoretical predictions. In particular, support is shown for the theoretical curves of Nethercot and Trahair and for the current trend to multiple design curves based on moment gradient.     

Numerical simulation of structural behaviour of transmission towers

Transmission towers are a vital component and management needs to assess the reliability and safety of these towers to minimise the risk of disruption to power supply that may result from in-service tower failure. Latticed transmission towers are constructed using angle section members which are eccentrically connected. Factors such as fabrication errors, inadequate joint details and variation of material properties are difficult to quantify. Consequently, proof-loading or full-scale testing of towers has traditionally formed an integral part of the tower design. The paper describes a nonlinear analytical technique to simulate and assess the ultimate structural response of latticed transmission towers. The technique may be used to verify new tower design and reduce or eliminate the need for full-scale tower testing. The method can also be used to assess the strength of existing towers, or to upgrade old and aging towers. The method has been calibrated with results from full-scale tower tests with good accuracy both in terms of the failure load and the failure mode. The method has been employed by electricity utilities in Australia and other countries to: (a) verify new tower design; (b) strengthen existing towers, and (c) upgrade old and aging towers.     

Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

This paper investigates the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Kármán geometric nonlinearity. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and estimated though the rule of mixture. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of FG-CNTRC beams with different end supports. A detailed parametric study is conducted to study the influences of nanotube volume fraction, vibration amplitude, slenderness ratio and end supports on the nonlinear free vibration characteristics of FG-CNTRC beams. The results for uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) beams are also provided for comparison. Numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fraction, vibration amplitude, slenderness ratio, end supports and CNT distribution on the nonlinear free vibration characteristics of FG-CNTRC beams.