Buckling of geometrically imperfect cylindrical shells — definition of a buckling load

On the basis of extensive buckling tests and analytical and numerical buckling analyses for composite cylinders it became desirable to provide a recommendation for the most reliable evaluation of stability limits for imperfect CFRP cylinders subjected to axial compression. This paper reports on different approaches including linear, non-linear and dynamic non-linear FE analysis results and discusses the related effects and potential difficulties.     

Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure

In this paper, an analytical solution is developed to determine deformations and stresses in circular disks made of functionally graded materials subjected to internal and/or external pressure. Taking mechanical properties of the materials of circular disks to be linear variations, the governing equation is derived from basic equations of axisymmetric, plane stress problems in elasticity. By transforming the governing equation into a hypergeometric equation, an accurate analytical solution of deformations and stresses in circular disks is obtained. The comparison with the numerical solution indicates that both approaches give very agreeable results, indicating correctness of the proposed analytical solution. The obtained analytical solution is employed to determine the radial displacement and stresses in circular disks subjected to external pressure, internal pressure, and internal and external pressure, respectively. How the radius ratio of circular disks affects deformations and stresses is also investigated.     

ADVANCES IN EXPERIMENTAL APPROACHES FOR INVESTIGATING CELL AGGREGATE MECHANICS

Cells tend to form hierarchy structures in native tissues.Formation of cell aggregates in vitro such as cancer spheroids and embryonic bodies provides a unique means to study the mechanical properties and biological behaviors/functions of their counterparts in vivo.In this paper,we review state-of-the-art experimental approaches to assess the mechanical properties and mechanically-induced responses of cell aggregates in vitro.These approaches are classified into five categories according to loading modality,including micropipette aspiration,centrifugation,compression loading,substrate distention,and fluid shear loading.We discussed the advantages and disadvantages of each approach,and the potential biomedical applications.Understanding of the mechanical behavior of cell aggregates provides insights to physical interactions between cells and integrity of biological functions,which may enable mechanical intervention for diseases such as atheromatosis and cancer.     

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

Thermally responsive liquid crystal elastomers(LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultra-thin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.     

A comparative study on parameter identification of fluid viscous dampers with different models

Fluid viscous dampers are extensively adopted as efficient and cheap energy dissipation devices in structural seismic protection. If we consider the usefulness of these passive control devices, the exact recognition of their mechanical behavior is of outstanding importance to provide a reliable support to design a very efficient protection strategy. In scientific and technical applications, many different constitutive models have been proposed and adopted till now to represent fluid viscous dampers, with different levels of complexity and accuracy. This paper focuses on parameter identification of fluid viscous dampers, comparing different existing literature models, with the aim to recognize the ability of these models to match experimental loops under different test specimens. The identification scheme is developed evaluating the experimental and the analytical values of the forces experienced by the device under investigation. The experimental force is recorded during the dynamic test, while the analytical one is obtained by applying a displacement time history to the candidate mechanical law. The identification procedure furnishes the device mechanical parameters by minimizing a suitable objective function, which represents a measure of the difference between the analytical and experimental forces. To solve the optimization problem, the particle swarm optimization is adopted, and the results obtained under various test conditions are shown. Some considerations about the agreement of different models with experimental data are furnished, and the sensitivity of identified parameters of analyzed models against the frequency excitation is evaluated and discussed.     

On poro-hyperelastic shear

The paper examines the problem of the shear of a porous hyperelastic material, the pore space of which is saturated with an incompressible fluid. Poro-hyperelasticity provides a suitable approach for modelling the mechanical behaviour of highly deformable materials in engineering applications and particularly soft tissues encountered in biomechanical applications. Unlike with the infinitesimal theory of poroelasticity, the application of pure shear generates pore fluid pressures that dissipate with time as fluid migrates either from or into the pore space due to the generated fluid pressure gradients. The analytical results provide benchmark problems that can be used to examine the accuracy of computational approaches.     

Review of Experimental Investigations on Compressibility of Arteries and Introduction of a New Apparatus

Arterial tissue incompressibility is a common notion used in numerical simulations and analytical studies. However, only a few experimental investigations have been performed to characterize arterial tissue incompressibility. Such studies have used various approaches, ranging from the initial purely mechanical measurements in 1954 to the more recent image-based analyses (2004). The results of these studies are rather diverse because different arteries have been tested (human/dog/mouse, carotid/pulmonary/iliac). This has therefore made accurate comparisons between studies challenging. In the first part of this report, a review of the experimental investigations on the compressibility of arteries is presented, with particular focus on the test rigs that have been used. In the second part of this report, a novel simple apparatus to test samples under physiological or supra-physiological conditions is described. Recommendations for a testing procedure are also provided. Finally, preliminary results on porcine renal arteries indicate significant levels of compressibility are possible (>10 %), thereby suggesting the need for further investigation.     

磁头精定位控制中压电致动特征的解析解

利用压电弹性介质的二维本构关系,对于分割电极片状压电致动器在恒定的反平行电场作用下的电-力致动特性,在对自由端边界作圣维南意义下的放松处理后,采用弹性力学的半逆求解方法,导出了其力-电耦合的静态位移和应力分布的解析解.通过将所得解析解与没有简化假设的有限元数值解进行比较,结果表明:所得解析解的致动特性（即自由端位移随外加电压的变化特征）与数值解的结果几乎完全重合,表明其二维解析解是有效和可靠的.     

AFM force spectroscopy and its applications on micro biomechanics

基于原子力显微镜技术的力谱技术是一种高灵敏度的力学检测方法.它能够以前所未有的精度, 在微观生物力学领域表征组织、细胞、生物膜、蛋白质、核酸、功能材料等目标对象, 探索其包括形貌、化学信息、导电性、静电力以及生物学特性在内的等信息, 并且能够对其进行分子级别精度的三维操纵. 从而对分子结构与构象变化, 分子间的相互作用以及反应历程实现单分子水平的实时--原位观测, 提供了其他测试方法不能完成的实验设计之可能性.本文首先介绍了原子力显微镜及其力谱技术的原理, 以及影响测量结果的各个参数的物理意义; 其次按照单个目标对象与配对目标对象的区分方式, 详细介绍了力谱技术在微观生物力学各个尺度上的研究进展; 之后介绍了力谱技术结合成像模式下的发展和应用; 最后对设备的改进和本研究领域发展方向进行了展望.     

An analytical design method of thin,isotropic press-fit retention sleeve for surface-mounted permanent magnet drives

Electric drives with surface-mounted permanent magnets feature magnet retention sleeves found in the air gap between the rotor and the stator. The design of these components, whose thickness affects the size of the magnetic air gap, has thus significant implications for the overall drive performance. The present work proposes a systematic analytical method for the mechanical design of press-fit retention sleeves for surface-mounted permanent magnet drives. The model relies on the premise that the sleeve is thin and mounted on a much stiffer rotor-magnet assembly. This leads to the assumption of constant thickness before and after the interference fit, as well as the only significant deformation being the hoop extension of the sleeve induced by the press fit. The proposed design method allows for rapid estimations of such sleeve parameters as the thickness and effective overlap, providing critical design points to be verified by subsequent high fidelity approaches. Accordingly, finite-element analysis results are provided as verification of the analytical approach, demonstrating very good agreement between the two approaches.     

原子力显微镜力谱技术及其在微观生物力学领域的应用

基于原子力显微镜技术的力谱技术是一种高灵敏度的力学检测方法.它能够以前所未有的精度, 在微观生物力学领域表征组织、细胞、生物膜、蛋白质、核酸、功能材料等目标对象, 探索其包括形貌、化学信息、导电性、静电力以及生物学特性在内的等信息, 并且能够对其进行分子级别精度的三维操纵. 从而对分子结构与构象变化, 分子间的相互作用以及反应历程实现单分子水平的实时--原位观测, 提供了其他测试方法不能完成的实验设计之可能性.本文首先介绍了原子力显微镜及其力谱技术的原理, 以及影响测量结果的各个参数的物理意义; 其次按照单个目标对象与配对目标对象的区分方式, 详细介绍了力谱技术在微观生物力学各个尺度上的研究进展; 之后介绍了力谱技术结合成像模式下的发展和应用; 最后对设备的改进和本研究领域发展方向进行了展望.      

A fully automated numerical tool for a comprehensive validation of homogenization models and its application to spherical particles reinforced composites

This paper presents a fully automated numerical tool for computing the accurate effective properties of two-phase linearly elastic composites reinforced by randomly distributed spherical particles. Virtual microstructures were randomly generated by an algorithm based on molecular dynamics. Composites effective properties were computed using a technique based on Fast Fourier Transforms (FFT). The predictions of the numerical tool were compared to those of analytical homogenization models for a broad range of phases mechanical properties contrasts and spheres volume fractions. It is found that none of the tested analytical models provides accurate estimates for the whole range of contrasts and volume fractions tested. Furthermore, no analytical homogenization models stands out of the others as being more accurate for the investigated range of volume fractions and contrasts. The new fully automated tool provides a unique means for computing, once and for all, the accurate properties of composites over a broad range of microstructures. In due course, the database generated with this tool might replace analytical homogenization models.     

Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data

Rubber-like materials consist of chain-like macromolecules that are more or less closely connected to each other via entanglements or cross-links. As an idealisation, this particular structure can be described as a completely random three-dimensional network. To capture the elastic and nearly incompressible mechanical behaviour of this material class, numerous phenomenological and micro-mechanically motivated models have been proposed in the literature. This contribution reviews fourteen selected representatives of these models, derives analytical stress–stretch relations for certain homogeneous deformation modes and summarises the details required for stress tensors and consistent tangent operators. The latter, although prevalently missing in the literature, are indispensable ingredients in utilising any kind of constitutive model for the numerical solution of boundary value problems by iterative approaches like the Newton–Raphson scheme. Furthermore, performance and validity of the models with regard to the classical experimental data on vulcanised rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944) are evaluated. These data are here considered as a prototype or worst-case scenario of highly nonlinear elastic behaviour, although inelastic characteristics are clearly observable but have been tacitly ignored by many other authors.     

A two-dimensional closed-form solution for the free-vibrations analysis of piezoelectric sandwich plates

This work presents a two-dimensional (2D) closed-form solution for the free-vibrations analysis of simply-supported piezoelectric sandwich plates. It has the originality to consider all components of the electric field and displacement, thus satisfying exactly the electric equilibrium equation. Besides, the formulation considers full layerwise first-order shear deformation theory and through-thickness quadratic electric potential. Its independent mechanical and electric variables are decomposed using Fourier series expansions, then substituted in the derived mechanical and electric 2D equations of motion. The resulting eigenvalue system is then condensed so that only nine mechanical unknowns are retained. After its validation on single- and three-layer piezoelectric, and hybrid sandwich plates, the present approach was then used to analyze thickness modes of a square sandwich plate with piezoceramic faces and elastic cross-ply composite core. It was found that only the first three thickness modes are global, thus can be modeled by the mixed equivalent single-layer/layerwise approach, often retained in the literature; the remaining higher thickness modes being characteristic of sandwich behavior; i.e., dominated by the deformations of either the core or the faces. These results, together with presented through-thickness variations of the mechanical and electric variables clearly recommend full layerwise modeling. Several numerical results are provided for future reference for validation of 2D approximate analytical or numerical approaches; in particular, of 2D piezoelectric adaptive finite elements.     

Temperature distribution of a simplified rotor due to a uniform heat source

In gas turbines, high combustion efficiency as well as operational safety are required. Thus, labyrinth seal systems with honeycomb liners are commonly used. In the case of rubbing events in the seal system, the components can be damaged due to cyclic thermal and mechanical loads. Temperature differences occurring at labyrinth seal fins during rubbing events can be determined by considering a single heat source acting periodically on the surface of a rotating cylinder. Existing literature analysing the temperature distribution on rotating cylindrical bodies due to a stationary heat source is reviewed. The temperature distribution on the circumference of a simplified labyrinth seal fin is calculated using an available and easy to implement analytical approach. A finite element model of the simplified labyrinth seal fin is created and the numerical results are compared to the analytical results. The temperature distributions calculated by the analytical and the numerical approaches coincide for low sliding velocities, while there are discrepancies of the calculated maximum temperatures for higher sliding velocities. The use of the analytical approach allows the conservative estimation of the maximum temperatures arising in labyrinth seal fins during rubbing events. At the same time, high calculation costs can be avoided.     

Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping

Friction-induced vibrations due to coupling modes can cause severe damage and are recognized as one of the most serious problems in industry. In order to avoid these problems, engineers must find a design to reduce or to eliminate mode coupling instabilities in braking systems. Though many researchers have studied the problem of friction-induced vibrations with experimental, analytical and numerical approaches, the effects of system parameters, and more particularly damping, on changes in stable-unstable regions and limit cycle amplitudes are not yet fully understood.The goal of this study is to propose a simple non-linear two-degree-of-freedom system with friction in order to examine the effects of damping on mode coupling instability. By determining eigenvalues of the linearized system and by obtaining the analytical expressions of the Routh–Hurwitz criterion, we will study the stability of the mechanical system's static solution and the evolution of the Hopf bifurcation point as functions of the structural damping and system parameters. It will be demonstrated that the effects of damping on mode coupling instability must be taken into account to avoid design errors. The results indicate that there exists, in some cases, an optimal structural damping ratio between the stable and unstable modes which decreases the unstable region. We also compare the evolution of the limit cycle amplitudes with structural damping and demonstrate that the stable or unstable dynamic behaviour of the coupled modes are completely dependent on structural damping.     

On-Chip Mechanical Characterization using an Electro-thermo-mechanical Actuator

A new micro-system for the on-chip mechanical characterization of thin polysilicon films was designed, fabricated and tested. The device contains a micro electro-thermo mechanical actuator which is able to load a specimen until rupture in purely tensile conditions. The elongation of the specimen is measured during the test through the capacitance variation of a set of parallel plate capacitors, while the force in the specimen can be computed starting from the applied voltage. Through a unique loading cycle in which the voltage is first increased until specimen rupture and then decreased, the new device allows for the determination of the specimen elastic stiffness and nominal tensile strength. The obtained experimental results were compared with values previously obtained by means of different on-chip test devices. Multi-physics FE simulations were performed for additional comparison with analytical formulae used in the data reduction procedure and with the obtained experimental results.     

An upper bound for validity limits of asymptotic analytical approaches based on normal form theory

Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.     

A comparison and extensions of algorithms for quantitative imaging of laminar damage in plates. I. Point spread functions and near field imaging

Real-time structural health monitoring (SHM) and safety prognostics require quantitative and continuously updated information on damage size and severity. A unified theoretical solution is presented for three distinct approaches that have been used for in situ imaging of structural damage in plate-like structures. These approaches are based on (i) linearised inverse scattering (or generalised diffraction tomography), (ii) beamforming, and (iii) reverse time migration. In all three approaches, the damaged region is regarded as a weak scatterer. Such an approach is appropriate for early damage detection that is of great practical interest. The linearised inverse is based on a rigorous mathematical formulation, whereas beamforming and reverse time migration are based on heuristic arguments, but the latter are more convenient for practical implementation. It is shown that, in the far-field approximation, the three imaging algorithms have a very similar mathematical structure. Analytical expressions are derived for the point spread functions (PSFs), which represent the reconstructed image for a point-like scatterer. Although the analytical expressions for the PSFs are different, the corresponding profiles are virtually identical. Based on these observed mathematical similarities, modified versions of the diffraction tomography and time-reversal algorithms are presented that combine the advantages of the various approaches. These modified algorithms are extensively evaluated using analytical solutions of a circular scatterer. The resulting algorithms are shown to provide accurate estimates for damage size and damage severity over a range of size and severity that is consistent with the weak scatterer approximation.     

Influence of Anisotropy on the Response Characteristics of Finite Cylinders Under Free Vibrations

A numerical–analytical approach is proposed to solve a problem on the free vibrations of cylindrical bodies. The approach is based on three-dimensional elastic theory and the semianalytic finite-element method. The free vibrations of isotropic and anisotropic solid cylinders of finite length are examined. It is studied how boundary conditions and mechanical and geometrical parameters affect the distribution of dynamic properties. The efficiency of the approach proposed is tested by comparing results produced by different approaches