Liyong Tong

A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures

The main objective of this article is to present an overview of the modelling that has been proposed by various workers in the field of smart or intelligent structures. Before the main discussion on the various models, some background information will be presented in relation to intelligent structures and the types of adaptive materials that are available. Although there are several categories of materials that can be implemented in intelligent structures, this article will focus on models that use piezoelectric materials as sensors and/or actuators (S/A). The modelling of the intelligent structures can be categorised in terms of the structural configuration (e.g., rod composites, fibre composites, monolithic structures, etc.) and also according to the type of modelling whether by finite element modelling or by analytical exact solutions. Models in this field of work had incorporated concepts from different background including three-dimensional linear elastic theory and dielectric theory to give rise to the linear piezoelectric model. Rules of Mixture and methods for calculating effective properties of fibre composites were extended to include piezoelectric fibre composite models. Classical Laminated Plate Theory was also adopted in laminated composite models where some laminae were piezoelectric materials. Exact solutions were applied to simple models and illustrated the potential of using piezoelectrics. Finite element techniques were used for more complicated problems that included complex geometries, nonlinear behaviour and dynamic control of the structure. The difference between induced strain and actuation strain is usually not addressed when using FE techniques, instead the piezoelectric strain can be regarded as an equivalent external force/moment or incorporated into the strain energy. In regard to control algorithms, the most common form applied by investigators in this field seems to be the negative velocity feedback control with single input and single output and some included linear quadratic control. More advanced control algorithms such as using multiple input and multiple output or even neural networks are less established.

Modelling for predicting the mechanical properties of textile composites : A review

Abstract Textile composite is one of the important materials used in industry and is made from textile substrates embedded in the matrices of different materials (see ref. 1 ). However, due to its complicated microstructure, understanding of mechanical properties of textile composite materials is still in its infant stage (see refs 2.3 ). Recently, many researchers have contributed to develop finite element analysis (FEA) and theoretical analysis models for predicting mechanical properties of textile composites, and to study the variation trends of mechanical property with major architectural parameters. In this paper, a review of recent developments and results in predicting mechanical properties of textile composites using finite element analysis and theoretical analysis methods, focusing on elastic behaviour for woven fabric composites, is presented. The predictive capability of various models, including earlier one-dimensional (1D) ‘mosaic model’ and more recent three-dimensional (3D) models, are discussed in this review.

Shape and topology optimization of compliant mechanisms using a parameterization level set method

In this paper, a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms. The structural shape boundary is implicitly embedded into a higher-dimensional scalar function as its zero level set, resultantly, establishing the level set model. By applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function, the temporal and spatial Hamilton-Jacobi equation from the conventional level set method is then discretized into a series of algebraic equations. Accordingly, the original shape and topology optimization is now fully transformed into a parameterization problem, namely, size optimization with the expansion coefficients of interpolants as a limited number of design variables. Design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints. The structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method. It is highlighted that the present method can not only inherit the merits of the implicit boundary representation, but also avoid some unfavorable features of the conventional discrete level set method, such as the CFL condition restriction, the re-initialization procedure and the velocity extension algorithm. Finally, an extensively investigated example is presented to demonstrate the benefits and advantages of the present method, especially, its capability of creating new holes inside the design domain.

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.

Design of piezoelectric actuators using a multiphase level set method of piecewise constants

This paper presents a multiphase level set method of piecewise constants for shape and topology optimization of multi-material piezoelectric actuators with in-plane motion. First, an indicator function which takes level sets of piecewise constants is used to implicitly represent structural boundaries of the multiple phases in the design domain. Compared with standard level set methods using n scalar functions to represent 2^n phases, each constant value in the present method denotes one material phase and 2^n phases can be represented by 2^n pre-defined constants. Thus, only one indicator function including different constant values is required to identify all structural boundaries between different material phases by making use of its discontinuities. In the context of designing smart actuators with in-plane motions, the optimization problem is defined mathematically as the minimization of a smooth energy functional under some specified constraints. Thus, the design optimization of the smart actuator is transferred into a numerical process by which the constant values of the indicator function are updated via a semi-implicit scheme with additive operator splitting (AOS) algorithm. In such a way, the different material phases are distributed simultaneously in the design domain until both the passive compliant host structure and embedded piezoelectric actuators are optimized. The compliant structure serves as a mechanical amplifier to enlarge the small strain stroke generated by piezoelectric actuators. The major advantage of the present method is to remove numerical difficulties associated with the solution of the Hamilton-Jacobi equations in most conventional level set methods, such as the CFL condition, the regularization procedure to retain a signed distance level set function and the non-differentiability related to the Heaviside and the Delta functions. Two widely studied examples are chosen to demonstrate the effectiveness of the present method.

Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation

This paper presents an experimental investigation of the mechanical behavior and failure mechanism of three-dimensional (3D) orthogonal woven CFRP composite panels. The 3D composite panels are preformed using Torayca T-300 (3K) carbon fiber, and then infused with the Epicote 828 epoxy resin. The nominal proportions of the stuffer yarn, the filler yarn and the warp weaver (or z yarn) are 1:1.2:0.2, respectively, and the overall fiber volume fraction is 43%. The 3D fiber architectures are measured and visualized in a micrograph form. Quasi-static tensile coupon tests are carried out to measure the in-plane Youngs modulus, Poissons ratio, tensile failure strengths and failure strains in both stuffer and filler yarn directions. Test results reveal that the average Youngs modulus in the filler yarn direction is higher than that in the stuffer yarn direction, and the average failure strain in the filler yarn direction is lower than that in the stuffer yarn direction. The average failure strength in the filler yarn direction is slightly higher than that in the stuffer yarn direction. The fracture surfaces are studied using the scanning electron microscope (SEM) and the failure mechanism are then discussed. It is noted by studying the fracture surface that the fracture surface is always perpendicular to the loading direction. The crack causes the z yarn/matrix interface to debond. Also, the fracture of specimen cut along the x- (or stuffer yarn) direction causes filler yarn/matrix interface to debond and stuffer yarn to break, and the fracture of specimen cut along the y- (or filler yarn) direction causes stuffer yarn/matrix interface to debond and filler yarn to break. The testing results are then used to validate the developed models in Parts II and III of these series papers. In Part II, simplified analytical and finite element models are proposed to predict the mechanical property and failure strengths for the 3D orthogonal woven CFRP composites. In Part III, a curved beam model resting on an elastic foundation is presented to predict the tensile strength in the filler direction, and then to investigate the effect of some geometrical parameters on the tensile failure strength in the filler yarn direction.

Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials

Abstract In this paper, two micro-electromechanics models, i.e. a rectangle model and a rectangle-cylinder model, are proposed for predicting the elastic, piezoelectric and dielectric constants for piezoelectric-fiber-reinforced composite (PFRC) materials under both single load and multiple load conditions. The closed-form formulae for these two models are derived by using a linear piezoelectric theory and iso-field assumptions. A comparison is carried out for the electroelastic constants predicted by the rectangle model under single load and multiple load conditions. A numerical study is also conducted to investigate the effects of geometrical parameters on the effective electroelastic constants, and to discuss the convergence of the rectangle-cylinder model. The results predicted using the present rectangle and rectangle-cylinder models correlate favorably with the finite-element analysis (FEA) results for the elastic constants, and with the existing experimental results for d33 and e33T/eo.

Vibration Control of Plates Using Discretely Distributed Piezoelectric Quasi-Modal Actuators/Sensors

A novel approach is presented for vibration control of smart plates using discretely distributed piezoelectric actuators and sensors. The new method consists of techniques for designing quasi-modal sensors and quasi-modal actuators. The modal coordinates and the modal velocities are obtained approximately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper voltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. The control spillover of the modal actuator is also estimated, and an upper bound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and actuator elements. In the optimality criteria the optimal locations and sizes of the sensor elements can be found by minimizing the observation error of the modal sensor, and those of the actuator elements can be obtained by minimizing both the control energy and the control spillover. The results obtained using the present optimal criteria show that they do not depend on the initial condition of vibration of the structures, nor do they depend on the control gains.

A semi-implicit level set method for structural shape and topology optimization

This paper proposes a new level set method for structural shape and topology optimization using a semi-implicit scheme. Structural boundary is represented implicitly as the zero level set of a higher-dimensional scalar function and an appropriate time-marching scheme is included to enable the discrete level set processing. In the present study, the Hamilton-Jacobi partial differential equation (PDE) is solved numerically using a semi-implicit additive operator splitting (AOS) scheme rather than explicit schemes in conventional level set methods. The main feature of the present method is it does not suffer from any time step size restriction, as all terms relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance. Hence, the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency. Resultantly, it allows enhanced relaxation on the time step size originally limited by the Courant-Friedrichs-Lewy (CFL) condition of the explicit schemes. The stability and computational efficiency can therefore be greatly improved in advancing the level set evolvements. Furthermore, the present method avoids additional cost to globally reinitialize the level set function for regularization purpose. It is noted that the periodically applied reinitializations are time-consuming procedures. In particular, the proposed method is capable of creating new holes freely inside the design domain via boundary incorporating, splitting and merging processes, which makes the final design independent of initial guess, and helps reduce the probability of converging to a local minimum. The availability of the present method is demonstrated with two widely studied examples in the framework of the structural stiffness designs.

Behavior of 3D orthogonal woven CFRP composites. Part II. FEA and analytical modeling approaches

Abstract In this paper, a 3D macro/micro finite element analysis (FEA) modeling approach and a 3D macro/micro analytical modeling approach are proposed for predicting the failure strengths of 3D orthogonal woven CFRP composites. These approaches include two different scale levels, macro- and micro-level. At the macro-level, a relatively coarse structural model is used to study the overall response of the structure. At the micro-level, the laminate block microstructure is modeled in detail for investigating the failure mechanisms of 3D orthogonal woven CFRP composites. The FEA and analytical models developed previously [Tan P, Tong L, Steven GP. Modeling approaches for 3D orthogonal woven composites, Journal of Reinforced Plastics and Composites, 1998:17;545–577] are employed to predict the mechanical properties of 3D orthogonal woven CFRP composites. All models presented in this paper are validated by comparing the relevant predictions with the experimental results, which were reported earlier in Part I of the paper [Tan P, Tong L, Steven GP. Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation, Composites, Part A: Applied Science and Manufacturing, 2000:31;259–71]. The comparison shows that there is a good agreement for the mechanical properties. An acceptable agreement exists for the failure strength in the x or stuffer yarn direction even though the FEA model gives a lower bound and the analytical model gives an upper bound. However, for the failure strength in the y or filler yarn direction, the difference between the predicted and experimental results is significant due to primarily ignoring of the waviness of filler yarn in the models. A curved beam model, which considers the waviness of the filler yarn, will be presented in Part III of the paper.