Authors:L. Cveticanin; M. Zukovic; D. Cveticanin Pages: 3369 - 3379 Abstract: Abstract In this paper the energy harvester device with piezoelectric element is considered. In the device the mechanical energy of vibration is transformed into electric energy. The mechanical part of the system contains an oscillator which is coupled with a motor. The motor–oscillator system is of non-ideal type. Namely, the motion of the oscillator is affected by the motor excitation, but the oscillator also has an influence on the motion of the motor. In the paper the influence of nonlinear properties of the oscillator and of the piezoelement is considered. Analytical procedure based on averaging is developed. Special attention is given to averaging of the harvested energy of the system. The influence of the linear and of the nonlinear coupling piezoelectric parameter is considered. The Sommerfeld effect is treated. The region of unstable solutions is reduced by increasing the value of the nonlinear piezoelectric parameter. The analytically obtained solutions are compared with numerically obtained ones. They are in good agreement. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1878-4 Issue No:Vol. 228, No. 10 (2017)

Authors:Zai-lin Yang; Chong-qun Zhang; Guan-xi-xi Jiang; Pei-lei Yan; Yong Yang Pages: 3469 - 3481 Abstract: Abstract The complex function method is applied in the solution of the scattering problem for an irregularly shaped boundary in an infinite inhomogeneous elastic medium, which is deduced from the scattering problem in a homogeneous one. The potential function of the scattering wave which is generated by the irregularly boundary is obtained by applying the complex function method in the inhomogeneous medium. The reduced Helmholtz equation with variable coefficients is solved by separation of variables. Then, the potential function is expressed as the complex domain functions series. By truncating a set of infinite algebraic equations, the coefficient of the series are determined. In order to verify the validity of this method, the wave equation in a inhomogeneous medium is degenerated to the equation with constant coefficients. The domain function is discussed. The dynamic stress concentration factor around an elliptical cavity is calculated in an exponentially inhomogeneous medium. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1876-6 Issue No:Vol. 228, No. 10 (2017)

Authors:H. B. Zhao; H. Feng; F. Liu; Y. W. Liu; P. H. Wen Pages: 3483 - 3495 Abstract: Abstract A theoretical model is developed to investigate the effects of the nanoscale twin and the dislocation pileup at the twin boundary on crack blunting in nanocrystalline materials. In the model, the nanoscale twin as a stress source approximately equals a quadrupole of wedge disclination. Using the complex variable method, the complex form expressions of the stress field and the force field are derived. The critical stress intensity factors (SIFs) for the first dislocation emission from the crack tip are calculated. The effects of the dislocation pileup, disclination strength, twin size, twin orientation, twin position and crack length on the critical SIFs are discussed in detail. Moreover, the shielding/anti-shielding effect produced by the twin, the dislocation pileup at the twin boundary and the first dislocation emitted on the crack tip is discussed. The results show that both the twin and the dislocation pileup at the twin boundary would suppress the dislocation emission from the crack tip. The suppressive effect induced by the dislocation pileup at the twin boundary is much stronger that that by the twin. Meanwhile, the emission angle has a significant effect on the mode I shielding/anti-shielding effect on the crack tip a. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1874-8 Issue No:Vol. 228, No. 10 (2017)

Authors:Jianmin Long; Wen Chen Pages: 3533 - 3542 Abstract: Abstract In the present paper, the nanoindentation of an elastic half-space by a conical indenter is investigated with the influence of surface tension. Based on the solution of a point force acting on an elastic half-space with surface tension, the singular integral equation of this problem is formulated and is then solved numerically by using the Gauss–Chebyshev quadrature formula. Surface tension flattens the pressure distribution in the contact region. Compared to the result of the classical elasticity model, surface tension evidently decreases the normal displacement on the surface of the half-space. The explicit relations between load and contact radius, and between load and indent depth are derived, which are helpful to characterize the mechanical properties of the materials in nanoindentation. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1901-9 Issue No:Vol. 228, No. 10 (2017)

Authors:Arman Shojaei; Farshid Mossaiby; Mirco Zaccariotto; Ugo Galvanetto Pages: 3581 - 3593 Abstract: Abstract In this paper, the application of the meshless finite point method (FPM) to solve elastodynamic problems through an explicit velocity–Verlet time integration method is investigated. Strong form-based methods, such as the FPM, are generally less stable and accurate in terms of satisfaction of Neumann boundary conditions than weak form-based methods. This is due to the fact that in such types of methods, Neumann boundary conditions must be imposed by a series of equations which are different from the governing equations in the problem domain. In this paper, keeping all the advantages of FPM in terms of simplicity and efficiency, a new simple strategy for proper satisfaction of Neumann boundary conditions in time for elastodynamic problems is investigated. The method is described in detail, and several numerical examples are presented. Moreover, the accuracy of the method with reference to the solution of some 3D problems is discussed. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1894-4 Issue No:Vol. 228, No. 10 (2017)

Authors:T. V. Klimchuk; V. I. Ostrik Pages: 3619 - 3631 Abstract: Abstract This paper concerns the contact problem for an elastic strip with rigidly fixed bottom line. The upper strip line is pressed by the semi-infinite punch with rounded edge under uniformly distributed normal and tangential loads. The friction forces are taken into account in the contact area. The exact analytic solution is obtained by using the Wiener–Hopf method. A factorization of the functional equation coefficient is performed in the form of infinite products. We have found the distributions of the contact stress and of the tangential and normal stresses on the bottom strip line. Moreover, for the stress-free part of the upper strip line the normal displacement is calculated. The stress distribution inside the strip is derived in quadratures. Contours of principal shear stress are built, and the location of its maximum value is established in dependence on the rounding parameter of the punch edge and the friction coefficient. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1866-8 Issue No:Vol. 228, No. 10 (2017)

Authors:Vikas Goyat; Suresh Verma; R. K. Garg Pages: 3695 - 3707 Abstract: Abstract This work aims to analyse the stress concentration in an infinite panel having a rounded rectangular hole reinforced with a functionally graded material layer using the extended finite element method. Young’s modulus of the functionally graded material layer varies in normal direction to the hole with a power law function. The relation of stress concentration factor with hole parameters, layer thickness, and power law index is presented for uniaxial, biaxial, and shear loads. It is noticed that the reinforcement of the functionally graded material layer around the hole has a significant influence on the stress distribution, and the controlled variation in the material properties of the layer can significantly reduce the stress concentration. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1907-3 Issue No:Vol. 228, No. 10 (2017)

Authors:Nikolaos I. Ioakimidis Pages: 3709 - 3724 Abstract: Abstract The inverse buckling problem for a column is the problem where both the loading and the buckling mode are defined in advance (the latter generally in a polynomial form), and the flexural rigidity of the column is sought in a similar form with the help of the related ordinary differential equation. This problem was proposed and studied in many buckling problems by Elishakoff and his collaborators. A serious difficulty in its solution is that the resulting flexural rigidity should be positive along the column. Here in order to check this positivity, the modern computational method of quantifier elimination is proposed and used inside the computational environment offered by the computer algebra system Mathematica and mainly based on the Collins cylindrical algebraic decomposition algorithm. At first, the simple inverse buckling problem of an inhomogeneous column under a concentrated load is studied with respect to the aforementioned positivity requirement. Next, the much more difficult problem concerning a variable distributed loading is also studied both in the case of one parameter and in the case of two parameters in this loading. Parametric rational and trigonometric forms of the flexural rigidity are also studied. Naturally, the resulting conditions for the positivity of the flexural rigidity are rather simple for one loading parameter, but they may become sufficiently complicated for two loading parameters. The present computational approach constitutes a simple, efficient and mathematically rigorous way for the derivation of positivity conditions for the flexural rigidity of a column in a variety of inverse buckling problems. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1905-5 Issue No:Vol. 228, No. 10 (2017)

Authors:Eugen Magyari; Patrick Weidman Pages: 3725 - 3733 Abstract: Abstract Four problems are conceived which build on flows induced by moving boundaries. In the first problem, a stretching plate moves in the direction of stretching at speed \(u_0\) and in the transverse direction at speed \(v_0\) . The second problem superposes uniform shear flow of strength \(\omega _2\) transverse to the stretching plate. The third problem superposes uniform shear flow of strength \(\omega _1\) in the direction of stretching or opposite to it. For the second and third problems, we find a one-parameter family of wall shear stresses \(\lambda \) that satisfy the plate and far-field conditions. For these cases, unique solutions are selected by the Glauert criterion which requires that the wall shear stress be that for which the solutions asymptotically match the far-field conditions of the flow displaced by the stretching sheet. The fourth problem is uniform shear flow above a radially stretching sheet. Here also a unique solution is selected by the Glauert criterion. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1919-z Issue No:Vol. 228, No. 10 (2017)

Authors:Bence Béri; John Hogan; Gábor Stépán Pages: 3735 - 3740 Abstract: Abstract This paper investigates the structural stability of long boring or milling tools. The tool is modelled by a rotating cantilever beam that is subject to compression and torsion, manifested by semi-tangential torque. The three-dimensional mathematical model is based on Euler–Bernoulli beam theory considering a linear three-dimensional problem. We obtain a dimensionless relationship between the relative importance of rotation, compression, and torsion that reveals the stability boundaries of the system. PubDate: 2017-10-01 DOI: 10.1007/s00707-017-1902-8 Issue No:Vol. 228, No. 10 (2017)

Authors:W. S. Li; J. Zou; K. Y. Lee; X. F. Li Abstract: Abstract Asymmetric trapped modes in a waveguide of a cylindrical hollow tube with a local bulge are studied. The problem is converted to solving a nonaxisymmetric boundary value problem associated with the three-dimensional Helmholtz equation subject to Dirichlet boundary condition. The domain decomposition method and matching technique are invoked for an infinitely long tube with a bulge and a semi-infinitely long tube with an end bulge. Asymmetric trapped modes along with the frequencies are determined and can be decomposed into a linear combination of those with the n-fold periodic symmetry. For each n-fold periodic trapped mode, whether azimuthal trapped modes exist depends on the radius and width of the bulge. The influence of the bulge’s size on the frequencies and intensity location of localized vibration is analyzed. The obtained results can be extended to analyze bound states in quantum wires. PubDate: 2017-10-16 DOI: 10.1007/s00707-017-1999-9

Authors:Teodor M. Atanackovic; Stevan Pilipovic Abstract: Abstract We study the heat conduction with a general form of a constitutive equation containing fractional derivatives of real and complex order. Using the entropy inequality in a weak form, we derive sufficient conditions on the coefficients of a constitutive equation that guarantee that the second law of thermodynamics is satisfied. This equation, in special cases, reduces to known ones. Moreover, we present a solution of a temperature distribution problem in a semi-infinite rod with the proposed constitutive equation. PubDate: 2017-10-11 DOI: 10.1007/s00707-017-1959-4

Authors:Vikas Goyat; Suresh Verma; R. K. Garg Abstract: Abstract The stress concentration in an infinite panel having a pair of circular holes surrounded by a functionally graded material layer subjected to different load conditions using the extended finite element method is numerically analysed. Young’s modulus of the functionally graded material layer varies with a power law function, in the direction normal to the holes. To model the material properties and the hole boundary, a level set function is used. The relation of stress concentration factor with functionally graded material layer parameters (i.e. power law index, thickness of layer) and hole geometry parameters (i.e. normalised distance between holes, hole radius ratio) is discussed, and it is observed that the functionally graded material layer around the pair of circular holes results in a significant reduction in stress concentration. It is concluded that the proper selection of power law index and thickness of the functionally graded material layer helps in reducing the stress concentration factor to a great extent. PubDate: 2017-10-07 DOI: 10.1007/s00707-017-1974-5

Authors:Ciprian D. Coman Abstract: Abstract Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness \(\varepsilon >0\) . By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit \(\varepsilon \rightarrow {0}^+\) . It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations. PubDate: 2017-10-07 DOI: 10.1007/s00707-017-2036-8

Authors:S. N. Korobeynikov Abstract: Abstract The objective (Lagrangian and Eulerian) strain tensors, their rates, and conjugate stress tensors used in continuum mechanics equations are considered. These tensors are represented in the eigenprojections of the right and left stretch tensors \(\mathbf {U}\) and \(\mathbf {V}\) . The novelty of the research lies in the simultaneous derivation of expressions for Lagrangian versions of tensors and their Eulerian counterparts with decomposition of the obtained expressions into components coaxial and orthogonal to the tensors \(\mathbf {U}\) and \(\mathbf {V}\) . We consider the Lagrangian and Eulerian Doyle–Ericksen families of strain tensors, which, in turn, are subfamilies of the well-known Hill family of strain tensors. Basis-free expressions are obtained for the material rates of Lagrangian tensors from the previously introduced family of generalized strain tensors, whose subfamilies are the Lagrangian and Eulerian Hill families of strain tensors, and similar expressions are obtained for the Green–Naghdi rates of Eulerian strain tensors, which are Eulerian counterparts of the material rates of Lagrangian strain tensors. Basis-free expressions for stress tensors are derived from the classical definitions of the conjugacy of stress and strain tensors. Expressions are found for the Lagrangian and Eulerian symmetric Atluri stress tensors that do not have conjugate strain tensors from the Hill family, and the obtained expressions are decomposed into components coaxial and orthogonal to the tensors \(\mathbf {U}\) and \(\mathbf {V}\) . The ranges of allowed ratios of different principal stretches at which the Lagrangian and Eulerian Hencky and Atluri stress tensors approximate the rotated/standard Kirchhoff stress tensors are determined. It is shown that the range of allowed ratios for the Hencky stress tensors is wider than that for the Atluri stress tensors. PubDate: 2017-10-07 DOI: 10.1007/s00707-017-1972-7

Authors:M. Razizadeh; S. Mortazavi; H. Shahin Abstract: Abstract In this paper, the deformation, breakup of a drop in shear flow and drop pair coalescence are studied using a finite difference/front tracking method. The drop deformation in shear flow was first studied in a Stokes regime and was compared with experimental and numerical results. A new algorithm that changes the topology of the interface dynamically and globally was developed to study drop break-up in shear flow after reaching a critical limit. Break-up simulation was first carried out in a Stokes regime. To validate the method performance and topology changing algorithm, results were compared with other numerical methods. Moreover, by obtaining a critical capillary number at finite Reynolds numbers and comparing the results with available data in this area, good agreement was observed that shows the ability of the method and the present topology changing algorithm. Different coalescence regimes for drop pair collision were also captured using the present topology changing algorithm. The present method is capable to simulate other multiphase flow problems that to some extent include collision and breakup of drops. PubDate: 2017-10-07 DOI: 10.1007/s00707-017-1958-5

Authors:Valentina Motta; Leonie Malzacher Abstract: Abstract A real-time modeling and control architecture for coupled shear layer von Kármán instabilities on a wing section wake is developed. Previous wind tunnel experiments highlighted that these wake instabilities give rise to limit cycles on both local and resulting airloads. The two-state Van der Pol system is employed to model the self-sustained oscillations exhibited by the actual flow. Schemes featuring either one or two coupled Van der Pol oscillators in parallel are taken under consideration. Open-loop and closed-loop control laws to manipulate and reduce the self-sustained oscillations are extensively studied. An adaptive control scheme is developed to optimize the performance of the controller, according to the flow conditions. For the open-loop control scheme, the consistency with experimental tests performed on a wind tunnel model is shown. PubDate: 2017-10-06 DOI: 10.1007/s00707-017-1975-4

Authors:S. Sahmani; M. M. Aghdam Abstract: Abstract As one of the most important components of a cytoskeleton, microtubules made from tubular polymers of tubulin can be found throughout the cytoplasm of eukaryotic cells. The role of microtubules in maintaining the structures of a living cell under external mechanical load is essential, so it is necessary to anticipate their size-dependent mechanical characteristics. In the present study, the size-dependent nonlinear instability of microtubules embedded in the biomedium of a living cell and under hydrostatic pressure is analyzed at different temperatures. For this objective, a more comprehensive size-dependent elasticity theory such as nonlocal strain gradient theory of elasticity is implemented to a refined hyperbolic shear deformation shell theory. Through deduction of the nonclassical governing equations to boundary layer-type ones and then employing a two-stepped perturbation solving process, explicit analytical expressions are established for nonlocal strain gradient stability paths of hydrostatic pressurized microtubules surrounded by the cytoplasm of a living cell. It is observed that for a microtubule under hydrostatic pressure, an initial extension occurs in the prebuckling regime until the critical buckling pressure. The nonlocality size effect decreases this initial extension, but the strain gradient size dependency increases it. PubDate: 2017-10-06 DOI: 10.1007/s00707-017-1978-1

Authors:Eric Li; Z. C. He; G. R. Liu Abstract: Abstract A general evaluation technique (GET) for the stiffness matrix in the finite element methods (FEM) using a modified integration rule with alternate integration points \(r\in [0, 1]\) rather than the standard Gauss points is proposed. The GET is examined using quadrilateral elements for elasticity problems. For the first time, we have found that the desired softening and stiffening effect can be achieved with adjustments of the integration point r. This allows the FEM model to achieve better accuracy and handle special problems, such as hourglass instability and volumetric locking. Ideal regions for the integration point r are found to overcome the hourglass and volumetric locking issues for the overestimation problems. In addition, the exact solution of the FEM model with optimal r value in terms of strain energy can be always obtained for general overestimation problems of elasticity. More importantly, the optimal integration point r obtained from the static case can be directly applied to dynamic problems to improve the transient displacement significantly. The intensive numerical examples including the static, dynamic, compressible and nearly incompressible material problems are analyzed to verify the accuracy and properties of the GET. Furthermore, the implementation of the GET is extremely simple without increasing computational cost. PubDate: 2017-10-05 DOI: 10.1007/s00707-017-1977-2

Authors:Mohammad Reza Barati; Hossein Shahverdi Abstract: Abstract In this paper, new solutions are presented to examine large amplitude vibration of a porous nanoplate resting on a nonlinear hardening elastic foundation modeled by nonlinear four-variable plate theory. The closed-form expression of the nonlinear frequency is obtained using a novel Hamiltonian approach as well as homotopy perturbation method for the first time. Another novelty of these approaches is that they are needless of any iterative process. Based on a modified rule of mixture, the nanopores or nanovoids are considered in the model. Nonlinear governing equations of a four-variable nanoplate with von Karman geometric nonlinearity are obtained using Hamilton’s principle. The dependency of the nonlinear frequency on the porosities, scale parameter, maximum amplitude, material gradation, foundation parameters and geometrical parameters is explored. The proposed solution approach and also obtained results can be used in future investigations on nanostructures. PubDate: 2017-10-03 DOI: 10.1007/s00707-017-1952-y