Showing papers in "Composites Part B-engineering in 1999"

Effect of fiber surface treatment on the fiber-matrix bond strength of natural fiber reinforced composites

Abstract: The interfacial shear strength (IFSS) between natural fibers and a thermoplastic matrix has been improved by the morphological and silane chemical modification of the fiber surface. An alkaline treatment was used to enhance both the matrix fiber wetting and the chemical surface modification in order to improve the physicochemical interactions at the fiber–matrix interphase. For characterization of the mechanical properties of such interphase, a modification of the micromechanical techniques commonly used in the characterization of the IFSS for circular-cross-section smooth fibers is proposed. The relationships developed for circular fibers were modified to incorporate the natural fiber perimeter instead of an equivalent fiber diameter. From the micromechanical test's results it was found that both surface modifications, preimpregnation and chemical, improves the fiber–matrix IFSS. Finally, the results obtained from the single fiber fragmentation test seem to better agree with the effective mechanical properties measured for the laminated material than those obtained with the pull out test.

Chemical modification of henequén fibers with an organosilane coupling agent

Abstract: Short henequen fibers were modified with a silane coupling agent in order to find out its deposition mechanism on the fiber surface and the influence of this chemical treatment on the mechanical properties of the composite. It was shown that the partial removal of lignin and other alkali soluble compounds from the fiber surface increases the adsorption of the silane coupling agent whereas the formation of polysiloxanes inhibits this process. The existence of a chemical bond between the coupling agent and the henequen fiber was confirmed by XPS and FTIR spectroscopy. It was further verified that the interaction between the fiber and the matrix is much stronger when the fiber surface topography is combined with the chemical modification of the fiber surface with a silane coupling agent.

Electromagnetic interference shielding using continuous carbon-fiber carbon-matrix and polymer-matrix composites

Abstract: A carbon-matrix composite with continuous carbon-fibers was found to be an excellent electromagnetic interference (EMI) shielding material with shielding effectiveness 124 dB, low surface impedance and high reflectivity in the frequency range from 0.3 MHz to 1.5 GHz. The shielding effectiveness of polymer-matrix composites with continuous carbon-fibers was less and that of polymer-matrix composites with discontinuous fillers was even less. The addition of 2.9 vol.% discontinuous 0.1 μm diameter carbon-filaments between the layers of conventional 7 μm diameter continuous carbon-fibers in a composite degraded the shielding effectiveness. The dominant mechanism of EMI shielding for both carbon-matrix and polymer-matrix continuous carbon-fiber composites is reflection.

Higher-order theory for functionally graded materials

Abstract: This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.

Effects of environmental aging on the properties of pultruded GFRP

Abstract: Pultruded glass–fiber-reinforced vinyl ester matrix composite coupons were subjected to environmental aging in order to study their durability since such composites are of interest for infrastructure applications. Specimens were tested as-received and after aging in water or salt solutions at room temperature (25°C) or in water at 75°C for various times. The flexural properties (strength and modulus) were determined for bending perpendicular to the 0° orientations (0° being the pull direction) for all aging conditions. In addition, flexural properties in the 90° orientation and tensile properties in the 0° orientation were also measured for the as-received specimens and the specimens exposed to selected aging conditions. Both strengths and moduli were generally found to decrease with environmental aging. Comparing the size of the fracture mirrors on the broken ends of the fibers in aged and un-aged samples suggested that environmental aging decreased the in situ fiber strength. In addition, examination of the failure surfaces and comparisons between the strength of the 90° specimens suggested that degradation of the fiber/matrix interphase region also occurred during the aging process.

An efficient implementation of the generalized method of cells for unidirectional, multi-phased composites with complex microstructures

Abstract: An efficient implementation of the generalized method of cells micromechanics model is presented that allows analysis of periodic unidirectional composites characterized by repeated unit cells containing thousands of subcells The original formulation, given in terms of Hill's strain concentration matrices that relate average subcell strains to the macroscopic stains, is reformulated in terms of the interfacial subcell tractions as the basic unknowns This is accomplished by expressing the displacement continuity equations in terms of the stresses and then imposing the traction continuity conditions directly The result is a mixed formulation wherein the unknown interfacial subcell traction components are related to the macroscopic strain components Because the stress field throughout the repeating unit cell is piece-wise uniform, the imposition of traction continuity conditions directly in the displacement continuity equations, expressed in terms of stresses, substantially reduces the number of unknown subcell traction (and stress) components, and thus the size of the system of equations that must be solved Further reduction in the size of the system of continuity equations is obtained by separating the normal and shear traction equations in those instances where the individual subcells are, at most, orthotropic Comparison of execution times obtained with the original and reformulated versions of the generalized method of cells demonstrates the new version's efficiency As demonstrated through examples, the reformulated version facilitates previously unattainable detailed analysis of the impact of fiber cross-section geometry and arrangement on the response of multi-phased unidirectional composites

Interfacial studies on surface modified Kevlar fibre/epoxy matrix composites

Abstract: Kevlar fibre/epoxy composites with superior interfacial strength were developed, by chemical treatment of the fibre surface with organic solvents. Multiple fibre pullout tests revealed that it is possible to raise the interfacial strength to 63 MPa from a value of 39 MPa normally exhibited by untreated Kevlar fibre/epoxy composites. A physicochemical and morphological characterization of the chemically treated fibre surface by microscopic and spectroscopic techniques, aids in the understanding of the observed interfacial properties. The importance of surface oxygen content in matrix bonding and mechanical interlocking of the fibre and matrix was established. Failure analysis of the pullout specimens reveals a strong correlation between the fracture features and the observed test data.

Applications of digital shearography for testing of composite structures

Abstract: This paper reviews shearography and its applications for testing of composite structures. Shearography is a laser-based technique for full-field measurement of surface deformation. Unlike holography, it does not require special vibration isolation; hence it can be employed in field/factory environments. The technique has already received considerable industrial acceptance for nondestructive testing of composite structures. In this application shearography reveals defects in an object by looking for defect-induced deformation anomalies. Other applications include strain measurement, material characterization, residual stress evaluation, vibration studies and 3-D shape measurement.

Stress waves in functionally gradient materials and its use for material characterization

Abstract: A method is presented to investigate elastic waves in functionally gradient material (FGM) plates excited by plane pressure wavelets The FGM plate was first divided into linearly inhomogeneous elements (LIEs) A general solution for the equation of motion governing the LIE was derived The general solution was then used together with the boundary and continuity conditions to obtain the displacement and stress in the frequency domain for an arbitrary FGM plate The response of the plate to a pressure wavelet was obtained using Fourier transform techniques Results obtained by the present method are compared with an existing method using homogeneous layer elements Relationships between the surface displacement response and the material mechanical properties of FGM plates were also obtained These relationships may be used for the material characterization of FGM plates

Mechanical properties of diamond-like carbon composite thin films prepared by pulsed laser deposition

Abstract: We have investigated the mechanical properties of diamond-like carbon (DLC) thin films that contain foreign atoms. The DLC films were prepared by pulsed laser deposition. A novel target design was adopted to incorporate foreign atoms into the DLC films during film deposition. Copper, titanium and silicon are chosen as the dopants. The chemical composition of the doped films was determined using Rutherford backscattering spectrometry, X-ray photoelectron spectroscopy and calibrated extrapolation. Experimental results of both visible and UV Raman are presented and discussed in terms of peak shape and position. The effect of dopants on the Raman spectrum is also analyzed. Optical microscopy of the pure DLC of a certain thickness showed severe buckling. A brief review of the theoretical background of adhesion is given and the possible mechanisms of adhesion that may work in DLC coatings are discussed. Qualitative scratch tests on the specimens show that pure DLC has quite poor adhesion due to the large compressive stress, while the doped DLC films exhibit much improved adhesion. Wear tests show improved wear resistance in the doped DLC coatings. Nanoindentation results give an average hardness above 40 GPa and effective Young's modulus above 200 GPa for pure DLC. The copper doped DLC films showed slightly decreased hardness and Young's modulus as compared to pure DLC films. Ti and Si can reduce the hardness and Young's modulus more than Cu. All these can be understood by analyzing the internal stress reduction as derived from Raman G-peak shift to lower wavenumbers. A preliminary model of the stress reduction mechanism is discussed.

Method for identification of elastic properties of laminates based on experiment design

Abstract: A numerical-experimental method for the identification of mechanical properties of laminated composites from the experimental results is developed. For the first time it is proposed to use the experiment design to solve the identification (inverse) problems. The basic idea of the proposed approach is that simple mathematical models (response surfaces) are determined only by using the finite element solutions in the reference points of the experiment design. Therefore, a significant reduction (about 50–100 times) in calculations of the identification functional can be achieved in comparison with the conventional methods of minimization. Numerical examples of identification of elastic properties of different laminates from the measured eigenfrequencies of plates are discussed.

Health monitoring and active control of composite structures using piezoceramic patches

Abstract: This paper presents new techniques under development for monitoring the health and suppressing the vibration of flexible composite structures. The techniques use piezoceramic patches bonded to the structure for actuation and sensing. Simulations and experiments are presented to demonstrate the utility of the methods for beam and panel structures. Limitations of piezoceramic materials are discussed, and suggestions are given for improving the techniques and for developing new uses of piezoceramic materials and smart structures.

Three-dimensional finite element analysis of double-lap composite adhesive bonded joint using submodeling approach

Abstract: Three-dimensional stress analysis is performed for double-lap composite-to-composite adhesive bonded joint exposed to uniaxial extension. The submodeling approach using 27-node solid element available in the recent versions of abaqus is utilized. Principal objectives are: to explore computational advantages provided by the multi-step submodeling approach and perform a comprehensive numerical study of three-dimensional (3D) stress variations in the joint structure, considering adhesive layers as 3D elastic entities. Numerical results obtained from the “global” analysis show fast displacement convergence everywhere in the joint, but do not clearly indicate if the stresses converge in the regions near the ends of the overlap. Besides the fact that a huge number of elements is required for the stress convergence study in the aforementioned regions, a serious computational obstacle have been also experienced: the element aspect ratio gets so high that the “zero or negative element volume error” is indicated, and results become unreliable. In order to overcome these problems, a multi-step submodeling approach is further explored. Its application has allowed to convincingly demonstrate that some stress components are not converging along certain lines belonging to the ends of the overlap. Additional numerical study performed with a two-dimensional plane stress formulation has shown that when taking into account a spew fillet, stress distributions near the end of the overlap change radically. It is concluded that submodeling approach provides an efficient computational tool for enhancing stress analysis in the sites of high stress gradients.

Optimization of material composition of FGM hollow circular cylinder under thermal loading: a neural network approach

Abstract: A neural network is applied to a optimization problem of material compositions for a hollow circular cylinder of functionally graded material. Using the analytical procedure of a laminated cylinder model, the analytical temperature solution for the cylinder is derived approximately. The thermal stress components are formulated making use of the Airy’s stress function method. As the optimization problem of minimizing the thermal stress distribution, the numerical calculations are carried out making use of neural network, and the optimum material composition is determined under arbitrary temperature range and temperature rise. In addition, the results obtained by neural network and ordinary nonlinear programming method are compared.

Localized damage response of composite sandwich plates

Abstract: The objective of this article is to derive closed-form solutions for the deformation and fracture responses of a composite sandwich plate subjected to static indentation of a hemispherical-nose indenter. The composite sandwich is modeled as an infinite, orthotropic, elastic plate resting on a rigid-plastic foundation. The facesheet deflection is several times the laminate thickness so that bending moments may be neglected and only membrane forces are considered in the facesheet. The rigid-plastic foundation force is given by the honeycomb crushing resistance. The deformation of the facesheet is found by using the principle of minimum potential energy. The elastic strain energy resulting from the membrane forces in the facesheet, the plastic work dissipated in crushing the honeycomb, and the external work are evaluated using an appropriate shape function for the facesheet deflection. The relations between the indentation load and the transverse deflection and length of deformation are obtained by minimization of the total potential energy. Minimization of the total potential energy has to be done numerically because of an implicit expression for the contact radius between the hemispherical-nose indenter and the facesheet of the honeycomb. An approximate solution for the load–indentation response is derived by assuming an average value of the contact radius. For the particular composite sandwich plates and indenters considered, the difference between the numerical and approximate solutions is about 3%. Furthermore, the approximate predictions are within 15% of the experimental results. Conservative estimates of the failure loads which cause cracking of the facesheet are predicted using the Maximum Stress and Tsai–Hill Criteria. The equations derived by the above failure criteria yield important design considerations for composite sandwich plates. It was observed that the failure load increases with the square of the ply thickness and indenter radius and is inversely proportional to the crushing resistance of honeycomb.

On free vibration of a rotating truncated circular orthotropic conical shell

Abstract: This article presents a method to study the free vibration of a rotating truncated circular orthotropic conical shell with simply-supported boundary conditions at both ends. Based on the Love first approximation theory and considering the centrifugal and Coriolis accelerations as well as the initial hoop tension, this article studies the frequency characteristics for various geometric and material properties. A detailed discussion is also made for the effects of material orthotropy and cone angle on the frequency characteristics. The present method proves to be reliable and accurate by comparing with available results in the literature.

The use of Fabry Perot fiber optic sensors to monitor residual strains during pultrusion of FRP composites

Abstract: This paper describes the use of an embedded optical sensor to measure the process induced strain in pultruded carbon fiber reinforced composite rods The survivability of Fabry Perot optical sensors in the pultrusion process, real time strain monitoring during the pultrusion process and residual strain measurements within the composite rods, were the three objectives of the research Strain profiles were recorded for individual experiments as the sensors traveled through the pultrusion die, and for the cool down period after the sensor had exited the die For the total pultrusion process, the residual strain after cooling was found to present somewhat of a problem For several experiments, the residual strain after exiting the pultrusion die was in the range of +200 to 400 microstrain, after which the sensors ceased to function Calculations indicated that the radial shrinkage of the carbon fiber rods was sufficient to cause failure of the glass capillary portion of the Fabry Perot sensors A novel method of reinforcing the Fabry Perot sensors before being pultruded was successful in allowing the sensors to survive the total process with only a slightly negative residual strain

Apparent negative electrical resistance in carbon fiber composites

Abstract: Apparent negative electrical resistance was observed, quantified, and controlled through composite engineering. Its mechanism involves electrons traveling in the unexpected direction relative to the applied voltage gradient, due to backflow across a composite interface. The observation was made in the through-thickness direction of a continuous carbon fiber epoxy–matrix two-lamina composite, such that the fibers in the adjacent laminae were not in the same direction and that the curing pressure during composite fabrication was unusually high (1.4 MPa). At a usual curing pressure (0.13 MPa), the resistance was positive. At an intermediate curing pressure (0.33 MPa), the apparent resistance was either positive or negative, depending on the current direction, due to non-uniformity in the thickness within a junction. The magnitude of the apparent negative resistance decreased with increasing temperature. Appropriate apparent negative and positive resistances in series, as provided by more than two laminae, allowed tailoring of the total apparent resistance. Apparent negative resistance was also observed in carbon fiber cement-matrix composites and in bare carbon fibers held together by pressure. Relevant applications are electrical, optical, structural and electrochemical.

Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis

Abstract: The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C 1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and torsional studies. The geometric nonlinearity based on von Karman’s assumptions is incorporated in the formulation while retaining the linear behavior for the material. The finite element employed here is based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam. The transverse shear deformation in the form of trigonometric sine function is introduced in the formulation to define the transverse shear strain. The governing equations of motion for the dynamic analysis are obtained using Lagrange’s equation of motion. The solution for nonlinear equations is sought by using an algorithmdirect iteration technique suitably modified for eigenvalue problems, based on the QR algorithm. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear modulus and thickness of the core of the sandwich beam, aspect ratios, boundary conditions, and lay-up in the case of laminates on the system loss factors. q 1999 Elsevier Science Ltd. All rights reserved.

Design and manufacturing considerations for ply drops in composite structures

Abstract: Thickness variations are required to optimize the design of modern laminated composite structures. These thickness variations are accomplished by dropping plies along the length to match varying in-plane and bending loads. This results in a structure which is matched to stiffness and loading requirements. Unfortunately, these ply drops produce internal and local stress concentrations as a consequence of geometric discontinuities and shear lag. In this study, we explore various factors for design of composite structures with ply drops. These factors include: thicknesses, ply stacking sequences, ply drop geometries and manufacturing considerations. In addition, fatigue loading is considered with respect to delamination initiation and growth. A strong sensitivity to the position and the manufacturing details of ply drops is shown for fatigue damage initiation and growth. All studies were conducted on a low-cost E-glass/polyester composite system. The results indicate that it will be difficult to completely suppress damage and delamination initiation in service. However, it was found that, in many cases, there is a threshold loading under which there is little growth after initiation is noted. Factors affecting this threshold are analyzed via the virtual crack closure method in Finite Element Analysis and verified experimentally. Design rules for ply dropping are presented on the basis of these results.

The hardnesses and elastic moduli of pulsed laser deposited multilayer AlN/TiN thin films

Abstract: The hardnesses and elastic moduli of multiple aluminum nitride (AlN) and titanium nitride (TiN) thin film bilayers of various periodicities deposited on silicon (111) and sapphire (0001) were investigated using nanoindentation based on a continuous stiffness measurement technique. Multiple bilayer thin films of AlN/TiN were grown by the pulsed laser deposition method. X-ray diffraction analysis revealed that the deposited thin films were highly textured polycrystalline oriented along the [0001] and [111] axes for aluminum nitride and titanium nitride, respectively. The AlN/TiN multiple layer hardness measurements ranged from 18 to 23 GPa, compared to single component film hardnesses of 34 and 24 GPa for TiN and AlN, respectively. The elastic moduli measured were 290–340 and 275–290 GPa for multiple layer AlN/TiN thin films deposited on sapphire (0001) and silicon (111), respectively.

Delamination buckling analysis of general laminated composite beams by differential quadrature method

Abstract: This article focuses on the application of the differential quadrature method (DQM) for the buckling analysis of one-dimensional (1D) composite laminated beam-plates. The DQM formulation of the problem is presented. The formulation accounts for the effects of shear deformation and bending-extension coupling. The governing 1D differential equations were transferred into a system of linear algebraic eigenvalue equations. A standard eigen-solver was used to obtain the delamination buckling loads and the associated mode shapes. Several case studies were used to investigate some of the parameters that affect the buckling response of such composite beams. The study demonstrates the excellent accuracy and efficiency that can be obtained by applying the DQM to treat delamination buckling of composites.

Enhancement of pre-buckling behavior of composite beams with geometric imperfections using piezoelectric actuators

Abstract: The non-linear behavior of slightly crooked slender composite beams with piezoelectric actuators is addressed. Von Karman non-linear strain–displacement relations and linear constitutive relations for both the piezoelectric and composite materials are used. The piezoelectric control of crooked beams subjected to axial compression renders its equilibrium path as close as possible to that of the ideal perfect beam. A modal analysis demonstrates that, through the application of suitable voltages to the actuators, the elimination of certain buckling mode contributions to the beam response is feasible and highly desirable. The equilibrium path of imperfect structures is shown to be dramatically changed via piezoelectric control; this has potential applications in the post-buckling of structures with negative slope of the secondary equilibrium path.

Effect of silicon carbide volume fraction on the work hardening behaviour of thermomechanically processed aluminium-based metal–matrix composites

Abstract: An understanding of the work hardening behaviour of particulate reinforced metal–matrix composites is crucial in optimizing the parameters for deformation processing of these materials. In the case of particulate-reinforced aluminium composites, the microstructure and mechanical properties can be altered by thermomechanical treatments as well as by changing the reinforcement volume fraction. In this study metal–matrix composites with different levels of reinforcement were synthesized by the disintegrated melt deposition technique. The as-processed composites were then extruded and their mechanical properties evaluated. A modified continuum model was then used to relate the work hardening behaviour of the composites to microstructural parameters. The model is shown to be applicable for all the composite materials investigated in the present study.

Vibration analysis and control of flexible beam by using smart damping structures

Abstract: The temperature effects on frequency, loss factor and control of a flexible beam with a constrained viscoelastic layer and shape memory alloy layer (SMA) are discussed. It is shown that the temperature in the SMA (actuation) layer is very important in the determination of frequency and loss factor of such a structure. The effects of damping layer shear modulus and damping layer height as affected by the temperature are also discussed. As temperature plays such an important role, it is, therefore, imperative to evaluate temperature effects on the control of the system as well. Results with and without active control are discussed.

Transient response of stiffened composite plates subjected to low velocity impact

Abstract: This article deals with the transient response of a stiffened composite plate subjected to low velocity impact. An approximate solution for the prediction of plate response to low velocity impact is presented. This solution includes the combined action of the plate and stiffeners as well as the effects of the contact and transverse shear deformation. A finite element (FE) approach is also proposed. In the FE approach, an impact force function based on Hertz contact law is linked into a commercial FE code, which facilitates the study of a more realistic model. Results predicted by the present solution for a simplified stiffened plate are compared with those by the FE approach for a realistic stiffened plate. Effects of the stiffener spacing and thickness, anisotropic material properties, impact mass and contact stiffness on the impact response are also examined.

Application of model updating techniques in dynamics for the identification of elastic constants of composite materials

Abstract: This work consists of the identification of the stiffness properties of composite materials from dynamic tests. Unknown coefficients are identified by a technique of model updating. The formulation used (modal approach) is based on the minimization of the eigensolution residuals (sensitivity method). This technique allows the simultaneous identification of several properties from a single test. Stiffness properties of extension, bending, twisting and transverse shear have been identified. A discussion of the different identification approaches of elastic constants of composite materials from dynamic tests has been presented. Important points of the model updating in dynamics have been addressed: generalized mass errors, placement of sensors and approximate reanalysis of eigensolutions. Results obtained by numerical simulations show the efficiency of the proposed methodology.

Temperature/light sensing using carbon fiber polymer-matrix composite

Abstract: A polymer (epoxy)-matrix composite with the top two laminae of continuous carbon fibers in a crossply configuration was found to be a temperature sensor. Each junction between crossply fiber tow groups of adjacent laminae is a sensor, while the fiber groups serve as electrical leads. A junction array provided by two crossply laminae allows sensing of the temperature/light distribution. The contact electrical resistivity of the junction decreases reversibly upon heating (whether using light or hot plate to heat), due to the activation energy involved in the jump of electrons across the junction. The contact resistivity decreases with increasing pressure during composite fabrication, due to the increase in pressure exerted by fibers of one lamina on those of the other lamina. The absolute value of the fractional change in contact resistivity per degree C increases with increasing pressure during composite fabrication, due to decrease in composite thickness, increase in fiber volume fraction and consequent increases in interlaminar stress and activation energy. A junction between unidirectional fiber tow groups of adjacent laminae is much less effective for temperature/light sensing, due to the absence of interlaminar stress.

Development of the boundary element method for 2D piezoelectricity

Abstract: The analytical and numerical foundations are laid out for the formulation of the boundary element method (BEM) for plane piezoelectric solids. We extend a physical interpretation of Somigliana's identity to piezoelectricity and give a direct formulation of the BEM in terms of the continuous distributions of point forces/charges and displacement/electric potential discontinuities in the infinite piezoelectric domain. We adopt Stroh's complex variable formalism for piezoelectricity to derive the point force/charge and the displacement/electric potential discontinuity, their dipoles and continuous distributions systematically. The duality relations between the force/charge and the displacement/electric potential solutions, embedded in the Stroh formalism, are exploited as the foundations for the analytic and the numerical approaches to the piezoelectric boundary value problems in two dimensions. These approaches enable us to solve important problems of piezoelectricity with arbitrary geometry and composition.

Modeling of smart composite box beams with nonlinear induced strain

Abstract: A new smart composite box beam model is developed to investigate the behavior of helicopter rotor blades built around the active box beam. Piezoelectric actuators and sensors are surface bonded on the walls of the composite box beam. The new theory, based on a refined higher order displacement field of a plate with eccentricity, is a three-dimensional model which approximates the elasticity solution so that the box beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warpings are included automatically in the formulation. The formulations also include nonlinear induced strain effects of piezoelectric actuators. The procedure is implemented using finite element method. The developed theory is used to model the load carrying member of helicopter rotor blades with moderately thick-walled sections. Static analysis of the smart box beam under varying degrees of actuation has been performed. Very good overall agreement is observed with available experimental data for thin-walled sections without embedded actuators. The results show that piezoelectric actuation significantly reduces the deflection along the box beam span and therefore can be used to control the magnitude of rotor blade vibrations. The nonlinear actuation effect is found to be closely related to the material stiffness of the primary structure.