Mechanical & Materials Engineering Faculty Publications Copyright (c) 2013 University of Nebraska - Lincoln All rights reserved. http://digitalcommons.unl.edu/mechengfacpub Recent documents in Mechanical & Materials Engineering Faculty Publications en-us Sat, 04 May 2013 01:39:51 PDT 3600 High-Stress Shear-Induced Crystallization in Isotactic Polypropylene and Propylene/Ethylene Random Copolymers http://digitalcommons.unl.edu/mechengfacpub/91 http://digitalcommons.unl.edu/mechengfacpub/91 Thu, 02 May 2013 09:43:42 PDT Crystallization of an isotactic polypropylene (iPP) homopolymer and two propylene/ethylene random copolymers (RACO), induced by high-stress shear, was studied using in situ synchrotron wide-angle X-ray diffraction (WAXD) at 137 °C. The “depth sectioning” method (Fernandez-Ballester, Journal of Rheology 53:5 (2009), pp. 1229−1254) was applied in order to isolate the contributions of different layers in the stress gradient direction and to relate specific structural evolution to the corresponding local stress. This approach gives quantitative results in terms of the specific length of fibrillar nuclei as a function of the applied stress. As expected, crystallization becomes faster with increasing stress—from the inner to the outer layer—for all three materials. Stress-induced crystallization in a RACO with 7.3 mol % ethylene content was triggered at only 1 °C below its nominal melting temperature. The comparison of iPP and RACO’s with 3.4 and 7.3 mol % ethylene monomer reveals the effect of ethylene defects on high-stress shear induced crystallization at 137 °C. It is found that, for a given applied stress, the specific nuclei length formed by flow increases with ethylene content—which is attributed to a greater high molecular weight tail. However, the linear growth rate is significantly reduced by the presence of ethylene comonomers and it is found that this effect dominates the overall crystallization kinetics. Finally, a time lag is found between development of parent lamellae and the emergence of daughter lamellae, consistent with the concept of daughter lamellae nucleated by homoepitaxy on the lateral faces of existing parent lamellae.

Includes supporting information.

]]> Zhe Ma et al. Simulation of electrospun nanofiber deposition on stationary and moving substrates http://digitalcommons.unl.edu/mechengfacpub/90 http://digitalcommons.unl.edu/mechengfacpub/90 Tue, 19 Mar 2013 06:28:08 PDT Electrospinning produces continuous fibers with diameters from single nanometers to microns by jetting polymer solutions in high electric fields. Electrospun non-woven filamentary materials attract rapidly growing interest for broad range of applications. Properties of these materials depend on their nano- and microstructure that is determined in turn by the electric field and nanofiber collector. Despite critical importance, deposition of electrospun fibers on substrates has not yet been extensively studied theoretically and new methods of nanofiber collection continue to be developed mostly empirically. The objective of this Letter was to develop and demonstrate numerical simulation of electrospun nanofiber deposition on moving collectors. A dynamic model of nanofiber deposition onto a fast rotating drum was developed and used to simulate partial nanofiber alignment on this collector. The results were compared with the filamentary deposits in two classical stationary collection methods. Good agreement with experimental observations demonstrated predictive ability of simulations. The developed models can be used for the analysis of mechanisms of fiber deposition and alignment on substrates in various electric fields. Better understanding of dynamic nanofiber interaction with the electric field and collectors can lead to improved collector devices enabling one-step integrated nanomanufacturing of the designer nanofilamentary assemblies and architectures.

]]> Linhua Liu et al. Magnetic and magnetoelastic properties of Zn-doped cobalt-ferrites —CoFe<sub>2−x</sub>Zn<sub>x</sub>O<sub>4</sub> (x = 0, 0.1, 0.2, and 0.3) http://digitalcommons.unl.edu/mechengfacpub/89 http://digitalcommons.unl.edu/mechengfacpub/89 Mon, 11 Mar 2013 07:03:10 PDT Cobalt-ferrite (CoFe2O4) based materials are suitable candidates for magnetomechanical sensor applications owing to a strong sensitivity of their magnetostriction to an applied magnetic field. Zn-doped cobalt-ferrites, with nominal compositions CoFe2−xZnxO4 (x = 0–0.3), were synthesized by auto-combustion technique using Co- , Fe- , and Zn-nitrate as precursors. X-ray spectra analysis and Transmission electron microscopy studies revealed that the as-prepared powders were comprised of nano-crystalline (~25–30 nm) cubic-spinel phase with irregularly-shaped grains morphology along with minor impurity phases. Calcination (800 °C for 3 h) of the precursor followed by sintering (1300 °C for 12 h) resulted in a single phase cubic-spinel structure with average grain size ~2–4 μm, as revealed from scanning electron micrographs. The magnitude of coercive field decreases from ~540 Oe for x = 0 to 105 Oe for x = 0.30. Saturation magnetization initially increases and peaks to ~87 emu/g for x = 0.2 and then decreases. The peak value of magnetostriction monotonically decreases with increasing Zn content in the range 0.0–0.3; however the piezomagnetic coefficient (dλ/dH) reaches a maximum value of 105×10−9 Oe−1 for x = 0.1. The observed variation in piezomagnetic coefficient in the Zn substituted cobalt ferrite is related to the reduced anisotropy of the system. The Zn-doped cobalt-ferrite (x = 0.1) having high strain derivative could be a potential material for stress sensor application.

]]> Nalla Somaiah et al. Use of Environmental Scanning Electron Microscopy for in situ Observation of Interaction of Cells with Micro- and Nanoprobes http://digitalcommons.unl.edu/mechengfacpub/88 http://digitalcommons.unl.edu/mechengfacpub/88 Fri, 22 Feb 2013 07:07:52 PST Precision intracellular sensing, probing and manipulation offer unprecedented opportunities for advances in biological sciences. Next-generation ultra-fine probes will be capable of targeting individual cell organelles. Development of such probes as well as probes capable of penetrating through tough cell walls requires detailed knowledge of cell-probe interaction. This Letter evaluated the applicability of environmental scanning electron microscopy (ESEM) for cell and cell-probe interaction imaging. Several types of cells (plant and yeast cells as well as mouse spermatozoa) were successfully imaged in their natural state, with mouse spermatozoa observed by ESEM for the first time. Computerized stage applied to image was tough plant cell walls interactions with several probes. Substantial damage to the cell walls was observed as a result of microprobe penetration. The damage persisted after the probe withdrawal and there was residue of cellular content on the withdrawn probes. Several mechanisms of probe failure were observed in situ global buckling, localized bending followed by the tip break-off, and plastic deformation with permanent bending in the case of ultra-fine metal nanoprobe. The results demonstrate applicability of ESEM for high-resolution in situ imaging of cells. Observed mechanisms of cell damage and probe failure provide guidance for future development of probes for minimally-invasive intercellular probing.

]]> Alexander Goponenko et al. Effects of Arterial Strain and Stress in the Prediction of Restenosis Risk: Computer Modeling of Stent Trials http://digitalcommons.unl.edu/mechengfacpub/87 http://digitalcommons.unl.edu/mechengfacpub/87 Tue, 15 Jan 2013 10:38:59 PST Purpose — In-stenting restenosis is one of the major complications after stenting. Clinical trials of various stent designs have reported different restenosis rates. However, quantitative correlation between stent features and restenosis statistics is scant. In this work, it is hypothesized that stress concentrations on arterial wall caused artery injury, which initiates restenosis. The goal is to assess the correlation between stent-induced arterial stress and strain and the documented restenosis rates.

Methods — Six commercially available stents, including balloon-expandable stents and self-expanding stents, were virtually implanted into the arteries through finite element method. The resulted peak Von Mises stress, principal stress, principal logarithm strain, as well as percentage of intimal area with abnormal higher stress were monitored.

Results — Positive correlation between arterial stress and strain after stent implantations and the documented restenosis rates from the corresponding clinical trials was found regardless of stent types. No statistical significant difference was observed for various stress or strain parameters serving as indicators of artery injury.

Conclusions — In-stent restenosis are less likely to occur as arterial mechanics are least altered by stent implantations. Optimization of stent designs to minimize the stent-induced arterial stresses and strains can reduce the arterial injury, and thus reduce the occurrence of restenosis. This work improved our understanding of the stent-lesion interactions that regulate arterial mechanics and demonstrated that arterial stress and strain could predict the risk of instent restenosis.

]]> Shijia Zhao et al. On the Importance of Modeling Stent Procedure for Predicting Arterial Mechanics http://digitalcommons.unl.edu/mechengfacpub/86 http://digitalcommons.unl.edu/mechengfacpub/86 Mon, 14 Jan 2013 11:37:53 PST The stent-artery interactions have been increasingly studied using the finite element method for better understanding of the biomechanical environment changes on the artery and its implications. However, the deployment of balloon-expandable stents was generally simplified without considering the balloon-stent interactions, the initial crimping process of the stent, its overexpansion routinely used in the clinical practice, or its recoil process. In this work, the stenting procedure was mimicked by incorporating all the above-mentioned simplifications. The impact of various simplifications on the stent-induced arterial stresses was systematically investigated. The plastic strain history of stent and its resulted geometrical variations, as well as arterial mechanics were quantified and compared. Results showed the model without considering the stent crimping process underestimating the minimum stent diameter by 17.2%, and overestimating the maximum radial recoil by 144%. It was also suggested that overexpansion resulted in a larger stent diameter, but a greater radial recoil ratio and larger intimal area with high stress were also obtained along with the increase in degree of overexpansion.

]]> Shijia Zhao et al. Elastic–Plastic Analysis and Strength Evaluation of Adhesive Joints in Wind Turbine Blades http://digitalcommons.unl.edu/mechengfacpub/85 http://digitalcommons.unl.edu/mechengfacpub/85 Mon, 14 Jan 2013 11:24:38 PST The objective of this paper is to investigate the performance of adhesive joints of carbon/epoxy wind turbine blade subjected to combined bending and tension loadings through finite element method. The influence of adhesive material properties and geometrical details including fillet and imperfections was examined in terms of interlaminar stresses in the adhesive layer. The variation of stress intensity with change in adhesive shear modulus has also been investigated, while contour integral method was used for evaluating the stress intensity factors (SIF) at the imperfection tip. Furthermore, the strength of the joint was assessed through the crack initiation and propagation analysis. Results suggested that either adding a fillet or considering the plasticity led to the reduced peak stresses at the edge of the adhesive layer and redistributed the load to low stress regions. Inclusion of imperfections has resulted in high stress concentrations in the adhesive layer and reduction in the strength of the joint. Compared to the filleted adhesive, the strength of the joint reduced 2.4% and 4.8% considering a flat adhesive and filleted adhesive with through-thickness imperfection, respectively. Large shear modulus of the adhesive diminishes the fracture strength with the increased SIF.

]]> Yi Hua et al. Prediction of the Thermomechanical Behavior of Particle-Reinforced Metal Matrix Composites http://digitalcommons.unl.edu/mechengfacpub/84 http://digitalcommons.unl.edu/mechengfacpub/84 Mon, 14 Jan 2013 10:42:14 PST The objective of this paper was to predict the thermomechanical behavior of 2080 aluminum alloy reinforced with SiC particles using the Mori–Tanaka theory combined with the finite element method. The influences of particle volume fraction, stiffness, aspect ratio and orientation were examined in terms of effective Young’s modulus, Poisson’s ratio and coefficient of thermal expansion (CTE) of the composite. The microstructure induced local stress and strain field was obtained through the numerical models of the representative volume element. Results suggested that particle volume fraction had significant impact on the effective Young’s modulus, Poisson’s ratio and CTE of the composite. Stiffer particles could improve the effective Young’s modulus of the composite, while the overall sensitivity of the effective Poisson’s ratio and CTE with respect to the particle stiffness was minimal. Particles with larger aspect ratio generally led to a composite with increased effective Young’s modulus, as well as reduced Poisson’s ratio and CTE. The overall material properties of the composite were insensitive to the particle aspect ratio beyond 10. The particle orientations significantly impacted the effective material properties of the composite, especially along the longitudinal direction. Random 3D dispersed particles exhibited the effective isotropic behavior, whereas anisotropy has been observed for random 2D and unidirectional aligned particles. Our results could help create tailorable bulk composite.

]]> Yi Hua et al. The Influence of Heterogeneous Meninges on the Brain Mechanics under Primary Blast Loading http://digitalcommons.unl.edu/mechengfacpub/83 http://digitalcommons.unl.edu/mechengfacpub/83 Mon, 14 Jan 2013 09:55:48 PST In the modeling of brain mechanics subjected to primary blast waves, there is currently no consensus on how many biological components to be used in the brain–meninges–skull complex, and what type of constitutive models to be adopted. The objective of this study is to determine the role of layered meninges in damping the dynamic response of the brain under primary blast loadings. A composite structures composed of eight solid relevant layers (including the pia, cerebrospinal fluid (CSF), dura maters) with different mechanical properties are constructed to mimic the heterogeneous human head. A hyper-viscoelastic material model is developed to better represent the mechanical response of the brain tissue over a large strain/high frequency range applicable for blast scenarios. The effect of meninges on the brain response is examined. Results show that heterogeneous composite structures of the head have a major influence on the intracranial pressure, maximum shear stress, and maximum principal strain in the brain, which is associated with traumatic brain injuries. The meninges serving as protective layers are revealed by mitigating the dynamic response of the brain. In addition, appreciable changes of the pressure and maximum shear stress are observed on the material interfaces between layers of tissues. This may be attributed to the alternation of shock wave speed caused by the impedance mismatch.

]]> Linxia Gu et al. Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites http://digitalcommons.unl.edu/mechengfacpub/82 http://digitalcommons.unl.edu/mechengfacpub/82 Wed, 28 Nov 2012 12:38:29 PST We propose a computational method for a homogenized peridynamics description of fiber-reinforced composites and we use it to simulate dynamic brittle fracture and damage in these materials. With this model we analyze the dynamic effects induced by different types of dynamic loading on the fracture and damage behavior of unidirectional fiber-reinforced composites. In contrast to the results expected from quasi-static loading, the simulations show that dynamic conditions can lead to co-existence of and transitions between fracture modes; matrix shattering can happen before a splitting crack propagates. We observe matrix–fiber splitting fracture, matrix cracking, and crack migration in the matrix, including crack branching in the matrix similar to what is observed in recent dynamic experiments. The new model works for arbitrary fiber orientation relative to a uniform discretization grid and also works with random discretizations. The peridynamic composite model captures significant differences in the crack propagation behavior when dynamic loadings of different intensities are applied. An interesting result is branching of a splitting crack into two matrix cracks in transversely loaded samples. These cracks branch as in an isotropic material but here they migrate over the “fiber bonds” without breaking them. This behavior has been observed in recent experiments. The strong influence that elastic waves have on the matrix damage and crack propagation paths is discussed. No special criteria for splitting mode fracture (Mode II), crack curving, or crack arrest are needed, and yet we obtain all these modes of material failure as a direct result of the peridynamic simulations.

10 supplementary video files are attached (below).

]]> Wenke Hu et al. The Meaning, Selection, and Use of the Peridynamic Horizon and Its Relation to Crack Branching in Brittle Materials http://digitalcommons.unl.edu/mechengfacpub/81 http://digitalcommons.unl.edu/mechengfacpub/81 Tue, 27 Nov 2012 11:47:21 PST This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modeling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.

]]> Florin Bobaru et al. The formulation and computation of the nonlocal J-integral in bond-based peridynamics http://digitalcommons.unl.edu/mechengfacpub/80 http://digitalcommons.unl.edu/mechengfacpub/80 Tue, 20 Nov 2012 12:28:35 PST This work presents a rigorous derivation for the formulation of the J-integral in bond-based peridynamics using the crack infinitesimal virtual extension approach. We give a detailed description of an algorithm for computing this nonlocal version of the J-integral.We present convergence studies (m-convergence and δ-convergence) for two different geometries: a single edge-notch configuration and a double edge-notch sample.We compare the results with results based on the classical J-integral and obtained from FEM calculations that employ special elements near the crack tip.We identify the size of the nonlocal region for which the peridynamic J-integral value is near the classical FEM solutions.We discuss how the boundary conditions and the peridynamic “skin effect” may influence the peridynamic J-integral value.We also observe, computationally, the path-independence of the peridynamic J-integral.

]]> Wenke Hu et al. Numerical and Experimental Investigation of Vascular Suture Closure http://digitalcommons.unl.edu/mechengfacpub/79 http://digitalcommons.unl.edu/mechengfacpub/79 Tue, 23 Oct 2012 14:08:36 PDT Purpose — In order to optimize the performance of the suture for tissue closure, it is essential to develop strategies for devising new and improved techniques that can visualize and compare various suturing techniques. This paper describes an experimental and numerical investigation on the performance of sutured tissue.

Methods — In the experiments, two pieces of glutaraldehyde cross-linked bovine pericardium were sutured together through simple running suture and tensioned to study the performance of the sutured tissue. During testing, the tension load and the total displacement of the specimen were recorded. The strain field of the specimen was simultaneously captured using two high speed cameras and post processed using its associated image processing software. In addition, nonlinear hyperelastic material models for Shelhigh patch and cryopreserved human aorta were derived through least-square fitting into the tensile testing data. Three dimensional finite element models were developed to replicate the behavior of wound closure.

Results — The effect of tissue material mismatch, and stiffness of the suture thread on the mechanical behavior of sutured tissue was examined. The stain distributions obtained from simulation agrees with the captured surface strain map from experiments. A relative softer suture thread could reduce the peak stress concentrations at the knotting location.

Conclusions — The mechanical performance of sutured tissue depends on the level of mismatch in material stiffness between the native tissue and the replacement material

]]> Linxia Gu et al. A Few Transient Effects in AT-Cut Quartz Thickness-Shear Resonators http://digitalcommons.unl.edu/mechengfacpub/77 http://digitalcommons.unl.edu/mechengfacpub/77 Thu, 27 Sep 2012 13:45:56 PDT We study a few transient effects of AT-cut quartz thickness-shear resonators, including resonator turning on and turning off as well as voltage amplitude and frequency fluctuations. Mindlin’s two-dimensional plate equations are used and solved analytically. Both a sudden change and a gradual change of the driving voltage are studied. It is found that for a resonator with a frequency of 1.649430868 MHz and material quality factor of Q = 105, the characteristic time scale of the transient effects is of the order of 0.1 s.

]]> Runyu Zhang et al. Analysis of a Monolithic, Two-Dimensional Array of Quartz Crystal Microbalances Loaded by Mass Layers With Nonuniform Thickness http://digitalcommons.unl.edu/mechengfacpub/76 http://digitalcommons.unl.edu/mechengfacpub/76 Thu, 27 Sep 2012 13:40:28 PDT We study free thickness-shear vibrations of a monolithic, two-dimensional, and periodic array of quartz crystal microbalances loaded by mass layers with gradually varying thickness. A theoretical analysis is performed using Mindlin’s two-dimensional plate equation. It is shown that the problem is mathematically governed by Mathieu’s equation with a spatially varying coefficient. A periodic solution for resonant frequencies and modes is obtained and used to examine the effects of the mass layers. Results show that the vibration may be trapped or untrapped under the mass layers. The trapped modes decay differently in the two in-plane directions of the plate. The mode shapes and the decay rate of the trapped modes are sensitive to the mass layer thickness.

]]> Nan Liu et al. Frequency Shifts in Plate Crystal Resonators Induced by Electric, Magnetic, or Mechanical Fields in Surface Films http://digitalcommons.unl.edu/mechengfacpub/75 http://digitalcommons.unl.edu/mechengfacpub/75 Thu, 27 Sep 2012 13:38:37 PDT We study frequency shifts in plate crystal resonators with surface films. The films are multiphysical, including the effects of inertia, stiffness, intrinsic stress, piezoelectric coupling, and piezomagnetic coupling. Mindlin’s two-dimensional equations for a crystal plate with two elastic surface films are generalized to include the multiphysical effects of the films. They are used to study thickness-shear vibrations of a rotated Y-cut quartz plate with initial fields resulting from the mechanical, electric, and magnetic fields in the surface films. Frequency shifts caused by the initial fields are calculated and examined. Results show that plate crystal resonators with multiphysical surface films may be used for electric/magnetic field sensing.

]]> Nan Liu et al. Shear-Horizontal Vibration Modes of an Oblate Elliptical Cylinder and Energy Trapping in Contoured Acoustic Wave Resonators http://digitalcommons.unl.edu/mechengfacpub/74 http://digitalcommons.unl.edu/mechengfacpub/74 Thu, 27 Sep 2012 13:36:43 PDT We study shear-horizontal free vibrations of an elastic cylinder with an oblate elliptical cross section and a traction-free surface. Exact vibration modes and frequencies are obtained. The results show the existence of thickness-shear and thickness-twist modes. The energy-trapping behavior of these modes is examined. Trapped modes are found wherein the vibration energy is largely confined to the central portion of the cross section and little vibration energy is found at the edges. It is also shown that face-shear modes are not allowed in such a cylinder. The results are useful for the understanding of the energy trapping phenomenon in contoured acoustic wave resonators.

]]> Huijing He et al. <i>In Vivo</i> Demonstration of Surgical Task Assistance Using Miniature Robots http://digitalcommons.unl.edu/mechengfacpub/73 http://digitalcommons.unl.edu/mechengfacpub/73 Thu, 27 Sep 2012 13:33:46 PDT Laparoscopy is beneficial to patients as measured by less painful recovery and an earlier return to functional health compared to conventional open surgery.However, laparoscopy requires the manipulation of long, slender tools from outside the patient’s body. As a result, laparoscopy generally benefits only patients undergoing relatively simple procedures. An innovative approach to laparoscopy uses miniature in vivo robots that fit entirely inside the abdominal cavity. Our previous work demonstrated that a mobile, wireless robot platform can be successfully operated inside the abdominal cavity with different payloads (biopsy, camera, and physiological sensors). We hope that these robots are a step toward reducing the invasiveness of laparoscopy. The current study presents design details and results of laboratory and in vivo demonstrations of several new payload designs (clamping, cautery, and liquid delivery). Laboratory and in vivo cooperation demonstrations between multiple robots are also presented.

]]> Jeff A. Hawks et al. It’s Not What You Think: A Theory for Understanding the Lack of Interest among Domestic Students in the Engineering PhD http://digitalcommons.unl.edu/mechengfacpub/72 http://digitalcommons.unl.edu/mechengfacpub/72 Thu, 27 Sep 2012 13:30:38 PDT We live in a fast-paced world surrounded by technological advances. Engineers with advanced skills perform important functions in our society. However we know very little about how engineers consider obtaining advanced education and skills. The purpose of this study is to understand and develop a theory explaining the process domestic engineers undergo in developing an interest in obtaining a PhD in engineering. Our research was guided by the following central research question: What is the theory that explains the process of developing interest in doctoral-level engineering education for engineers? We used qualitative, grounded theory methods, to investigate the process of advanced engineering education interest. Interview data were collected from undergraduate engineering students, doctoral engineering students, engineering faculty, and engineers in industry with PhD degrees from seven institutional sites. Our theory explains that misperceptions, personal characteristics, and environmental elements are part of engineers’ interest in advanced education. Engineers must be exposed to these factors and must also actively process this information to develop interest. This theory provides a framework for understanding and promoting doctoral education for engineers. Implications for educators are offered.

]]> Michelle C. Howell Smith et al. Analysis Of Partially Electroded Piezoelectric Actuators With Nonuniform Thickness For The Purpose Of Reducing Actuating Shear Stress Concentration By Ansys http://digitalcommons.unl.edu/mechengfacpub/71 http://digitalcommons.unl.edu/mechengfacpub/71 Thu, 27 Sep 2012 13:28:04 PDT An elastic plate with thin piezoelectric films bonded on its two major surfaces is a typical smart structure which is used in actuation and sensing. The useful deformation of the smart structure is caused by the shear stress transferring from the actuators to the elastic plate. This shear stress is concentrated at two ends of the interface between the actuator and the plate. This concentration may induce undesirable delamination of the actuator from the plate. It was theoretically proved that actuators with partially covered electrodes have a much less concentrated actuating shear stress than that with fully ones. An actuator with nonuniform thickness was also found that may reduce the concentration of shear stress. The previous theoretical results were based on two simplified models. However, it is very difficult to get an analytical solution when the actuator owns the two characteristics at the same time, i.e. not only with partially covered electrodes, but also with an in-plane varied thickness. In this paper, we turn to use ANSYS to obtain useful numerical results from cases which are nearly impossible to be solved analytically. We study the effect of the electroded area of the actuator on reducing the concentrated shear stress. Moreover, we investigate the shear stress distribution under different variation of the actuator thickness. An optimal thickness profile is obtained. This work is considered as a frontier of smart structure.

]]> Nan Liu et al.