Authors:Sonia Parvanova; Georgi Vasilev; Petia Dineva Pages: 1947 - 1964 Abstract: The paper deals with numerical evaluation of the scattered wave and dynamic stress concentration fields in a finite anisotropic solid containing multiple nano-cavities. 2D plane-strain state and in-plane wave motion are assumed. The proposed mechanical model combines classical elastodynamic theory for the bulk general anisotropic solid and the Gurtin–Murdoch theory of surface elasticity assuming localized constitutive equation for the infinitely thin interface between the cavity and the matrix. The developed computational methodology is based on the following: (a) displacement boundary integral equations along existing boundaries using the analytically derived through Radon transform fundamental solution of the equation of motion of the bulk anisotropic solid; (b) non-classical boundary conditions of the Gurtin–Murdoch model along the interface between the matrix and cavities taking into consideration a jump in the stresses as one moves from the bulk material to the cavity due to the presence of surface elasticity; and (c) elastic-viscoelastic correspondence principle. The accuracy of the developed software is proven by comparisons of the obtained results solved by boundary element method and finite element method. A detailed parametric study reveals the sensitivity of the wave field to different key factors such as size, number and configuration of the cavities, surface and bulk material properties. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1303-4 Issue No:Vol. 87, No. 12 (2017)

Authors:Fabio C. Figueiredo; Lavinia A. Borges Pages: 1965 - 1977 Abstract: The aim of this paper is to propose a limit analysis formulation concerning prescription of non-homogeneous velocities and unilateral conditions with friction at structures’ contact interfaces. This formulation is especially suitable for determining the limit state conditions in structures in which the external action is defined by prescribed velocities on boundaries, particularly if the contact interface is not planar and the force distribution is not known a priori. The requirement of body’s non-penetrability is attended by applying the unilateral conditions at normal direction and a sliding rule based on Coulomb friction law at tangential direction. Under limit state, if there is sliding between the contact surfaces, the external collapse power is consumed by plastic and friction dissipation. As applications, the influence of friction coefficient at tool–specimen interface at scratch test problem and the lateral resistance of a soil due to lateral movement of a partially embedded pipe are investigated. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1304-3 Issue No:Vol. 87, No. 12 (2017)

Authors:R. Bagheri Pages: 1979 - 1992 Abstract: A piezoelectric half-plane weakened by several horizontal cracks is investigated under anti-plane mechanical and in-plane electrical impacts. The distributed dislocation and integral transform techniques are employed to construct integral equations of the multiple dynamic cracks embedded in the piezoelectric half-plane. At first, the stress and the electric fields in the piezoelectric half-plane are calculated by using pattern. Then, by determining distributed dislocation density on the crack surface, a system of singular integral equations with Cauchy-type singularity is derived. The dynamic field stress intensity factors are determined by using the numerical Laplace inversion and dislocation densities. Finally, several examples are solved and the effects of the geometrical parameters and cracks configuration are graphically obtained upon the dynamic field intensity factors. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1305-2 Issue No:Vol. 87, No. 12 (2017)

Authors:İsa Çömez Pages: 1993 - 2002 Abstract: In this study, frictional moving contact problem for a rigid cylindrical punch and an elastic layer is considered. The punch is subjected to concentrated normal and tangential force, and moves steadily with a constant subsonic velocity on the boundary. The problem is reduced to a singular integral equation of the second kind, in which the contact stress and the contact area are the unknowns, and it is treated using Fourier transforms and the boundary conditions for the problem. The numerical solution of the singular integral equation is obtained by using the Gauss–Jacobi integration formulas. Numerical results for the contact stress and the contact area are given. The results show that with increasing values of relative moving velocity, contact width between the moving punch and the layer increases, whereas contact stress decreases. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1306-1 Issue No:Vol. 87, No. 12 (2017)

Authors:Chang-Gon Jeong; Seong-Kyun Kim; Joo-Hee Lee; Jong-Woong Kim; In-Sung Luke Yeo Pages: 2003 - 2009 Abstract: Screw loosening, which is closely associated with the preload of an abutment screw, is one of the most frequent complications in clinical implantology. The aim of the present study was to investigate the preload prediction of a joint screw assembly between an implant and abutment based on a mechanical analysis. A mechanical formula was determined to relate preload, the dependent variable, to the tightening–loosening torque difference, the independent variable. To confirm the equation, 15 implant–abutment assemblies were prepared. These assemblies were divided into five groups based on tightening torques, and joint screw loosening torques were recorded. Preload values of the assemblies were calculated using a mechanical formula and compared with those previously obtained from direct measurements. In addition, the recommended tightening torque was deduced to prevent screw loosening using the linear relation between tightening torque and the tightening–loosening torque difference. Theoretically calculated preload values were similar to those directly estimated using devices to measure preload. Every predicted preload was insufficient in preventing screw loosening. However, the theoretical preload for prevention was clinically unavailable. These results indicate that prevention of screw loosening requires repeated tightening of the abutment screw. Moreover, this study suggests a useful tool to predict preload, which was practically applicable to the implant–abutment assembly, in dental implantology. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1307-0 Issue No:Vol. 87, No. 12 (2017)

Authors:Qianqian Sui; Changliang Lai; Hualin Fan Pages: 2011 - 2024 Abstract: To reveal free vibration modes and fundamental frequency of one-dimensional periodic IsoTruss tubular composite structures (ITTCSs), finite element modeling method and dynamic equivalent models were developed. ITTCS has two typical vibration modes: (a) shell-like modes and (b) beam-like modes. Short ITTCS and large inclinations of helical members easily induce shell-like vibration modes, while long ITTCS and small inclinations easily induce beam-like vibration modes. For shell-like vibration, the fundamental frequency is decided by the inclination, while the length has little influence. For beam-like vibration, the fundamental frequency depends on the column length and the inclination has slight influence. Dynamic continuum beam-like model and shell-like model were developed to predict the fundamental frequency of the IsoTruss structure. The predictions are consistent with the numerical simulations, and these models can be applied in engineering to instruct the dynamic design of the IsoTruss structure. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1308-z Issue No:Vol. 87, No. 12 (2017)

Authors:Xianjie Shi; Chunli Li; Fengjun Wang; Dongyan Shi Pages: 1781 - 1796 Abstract: The objective of this investigation is to apply the spectro-geometric method to study the vibration behavior of the annular sector plates with arbitrary boundary restraints on the basis of the three-dimensional theory of elasticity. All the classical homogeneous boundary conditions can be universally considered as the special cases when the stiffness for each of restraining springs is set equal to either zero or infinity in this study. Under the current solution framework, each displacement of the annular sector plate is, regardless of boundary conditions, invariantly expanded as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series and all the series expanded coefficients are determined with the Rayleigh–Ritz procedure. The present solution method can be generally applied to a broad range of annular sector plates, regardless of their thicknesses and sector angles. The current results are compared with those previously published in literature and the finite element analysis data to validate the current formulation. More results for plates with different boundary restraints and geometrical parameters are presented, which may serve as benchmark solutions for others. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1286-1 Issue No:Vol. 87, No. 11 (2017)

Authors:K. Mercan; H. M. Numanoglu; B. Akgöz; C. Demir; Ö. Civalek Pages: 1797 - 1814 Abstract: In the present paper, buckling analysis of silicon carbide nanowires has been investigated including size effect. The size effect has been taken into consideration by using different size-dependent continuum theories. These theories are modified couple stress theory, modified strain gradient theory, nonlocal elasticity theory, surface elasticity theory, and nonlocal surface elasticity theory. Analyses have been made for a continuum model which is embedded in double-parameter elastic foundation. The foundation has been modeled by using both Winkler- and Pasternak-type elastic foundation models. Simply supported boundary conditions have been used. Buckling equations have been obtained by using energy principle and solved via Navier’s solution procedure. Results are given and compared in figures and tables. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1288-z Issue No:Vol. 87, No. 11 (2017)

Authors:S. Suresh Kumar; H. Ashwin Clement; R. Karthik Pages: 1815 - 1828 Abstract: In real time, aircraft panels are mainly subjected to fatigue loading induced by the pressurization cycle. When two cracks approach one another, their stress fields influence each other and produce enhancing or shielding effect depending on the position of the cracks. In the present work, an attempt has been made to determine the effect of plate curvature on mixed mode stress intensity factor (SIF) of multiple cracks in a riveted joint using numerical and experimental methods. Diametrically opposite surface cracks of various crack depth ratios [(a / t); ‘a’ crack length and ‘t’ thickness of the plate] were considered for a typical longitudinal splice joint. ‘Frictional contact interaction’ was defined between rivet hole, rivet head-sheet, between sheet surfaces and stringer to sheet interfaces in order to simulate the service conditions. At lower crack depths, [ \(({a}/{t}) =2\) ] higher SIF was observed for biaxial loading compared to uniaxial loading. Marginal influence of loading condition was observed for deep cracks [ \(({a}/{t})=5\) ]. SIF values of curved panels were observed to be higher than that of flat panel irrespective of the crack depths considered the present work. This is mainly due to ‘flattening’ of curved plate when loading. It was also noticed that, the presence of stiffener reduces the in plane (mode-II) and out of plane (mode-III) shear fracture considerably for curved panel as it exerts compressive force on the joint. To validate the numerical observations, experiments were conducted on a Al 2024-T3 specimens to determine the fatigue crack growth rate and it showed a good correlation with numerical methods. The experimental results also indicated a higher crack growth rate for curved panel compared to flat panel which is mainly due to additional bending stress at the rivet hole region caused by eccentric loading. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1289-y Issue No:Vol. 87, No. 11 (2017)

Authors:T. Apatay; E. Arslan; W. Mack Pages: 1829 - 1843 Abstract: For given geometry of a shrink fit, a further essential design parameter is the interface pressure between inclusion and hub to reliably transfer a moment under all operating conditions in the specific application. Hence, in general a large interface pressure shall be achieved, and this may be facilitated by an elastic–plastic design. Furthermore, minimizing the weight of the device becomes increasingly important in engineering, too. To achieve both objectives, in the present semi-analytical study of a shrink fit with solid inclusion a combined elastic–plastic design and use of a functionally graded hub is proposed. As is shown, by appropriate grading not only the weight of the hub can be reduced noticeably as compared to a homogeneous one but also a much better behavior at rotation can be achieved, and admitting partial plasticization can further improve the performance; as an example, a shrink fit with steel/aluminum FGM-hub is discussed comprehensively. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1290-5 Issue No:Vol. 87, No. 11 (2017)

Authors:Chang-Sheng Lin Pages: 1845 - 1857 Abstract: The topic of this paper is the accuracy improvements in parametric estimation of systems with modal interference. A channel-expansion technique has been previously used in the Ibrahim time domain method to well perform the modal identification. However, the error involved in the determination of system order from the frequency response function or the Fourier spectrum associated with each of the response channels would generally lead to a distortion in the modal identification, especially for a system with modal interference. In the present paper, the singular value decomposition in conjunction with least-squares analysis is introduced in the procedure of Ibrahim time domain method to obtain the system matrix and determine the system order. Also, the phase angle diagram of frequency response function can be employed to distinguish the structural modes influenced by modal interference and then avoid the phenomenon of omitted modes from the distortion of system order determined by frequency response function. Numerical simulations, including two examples of a model of the motor vehicle, and a linear two-dimensional model of one-half of a railway vehicle, confirm the validity of the proposed method for modal identification of a system with modal interference. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1292-3 Issue No:Vol. 87, No. 11 (2017)

Authors:V. I. Fabrikant Pages: 1859 - 1869 Abstract: A general solution is obtained for a magneto-electro-elastic half-space \(x_{3}\ge 0\) subjected to arbitrary point forces or arbitrary point dislocations, as well as electric and magnetic influence by using two-dimensional Fourier transform. The final results are presented as single integrals over a unit circle. Using the theory of generalized functions, all basic parameters at the half-space boundary are defined in a finite form, and no computation of any integral is needed. Knowledge of Green’s functions in finite form allows us to derive the governing integral equations for the normal and tangential contact and crack problems, as well as to establish certain relationship between the kernels of the relevant integral equations. We also established some interesting general properties of the determinants, which might be new. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1293-2 Issue No:Vol. 87, No. 11 (2017)

Authors:Alireza Ebrahimi; Mahdi Heydari; Mehdi Behzad Pages: 1871 - 1889 Abstract: In this paper, the forced vibration of a cracked rotor with an open edge crack has been studied by a new continuous model for flexural vibration of cracked rotors proposed in Ebrahimi et al. (J Sound Vib 333:3522–3535, 2014). The cracked rotor behavior under the external excitation of gravity and unbalance forces is presented. Since the governing equation is linear, using the superposition principle the responses of the cracked rotor to the gravity and unbalance forces are calculated separately. Then, the total response is calculated by summing these two responses. Each of these two responses is found by using a modified Galerkin method. The effect of the crack in the presence of the gravity and unbalance forces on the time response, frequency spectrum, frequency response curve and orbit diagram of the rotor is analyzed. Results can be used for the crack identification of rotors. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1295-0 Issue No:Vol. 87, No. 11 (2017)

Authors:Airong Liu; Mark Andrew Bradford; Yong-Lin Pi Pages: 1909 - 1928 Abstract: Nonlinear in-plane multiple equilibria and buckling of pinned–fixed shallow circular arches under an arbitrary radial concentrated load are investigated. Analytical solutions for the multiple nonlinear equilibria, buckling and limit points are derived. New findings are: (1) pinned–fixed shallow arches under the arbitrary concentrated load have multiple stable and unstable equilibria; (2) the position of the arbitrary concentrated load and the modified slenderness of the arch influence the number of multiple equilibria and limit points as well as the first buckling load significantly; (3) a pinned–fixed arch under the arbitrary concentrated load can buckle in a limit point instability mode, but not in a bifurcation mode; (4) when the load is located between the crown and the pinned end, the buckling load is lower than that when the load is located between the crown and the fixed end, and (5) in addition to limit points, the nonlinear equilibria of pinned–fixed arches under the arbitrary concentrated load have inflexion points, which corresponds to specific modified slenderness switching the number of equilibria and limit points or switching buckling and no buckling behaviour. The analytical solutions for inflexion points and specific modified slenderness, and for the corresponding load, axial force and displacement are also derived for the first time in the literature. Comparisons with the finite element results have shown that the analytical solutions can accurately predict the multiple equilibria, limit points, inflexion points, and buckling load of shallow pinned–fixed arches under the arbitrary concentrated load. PubDate: 2017-11-01 DOI: 10.1007/s00419-017-1300-7 Issue No:Vol. 87, No. 11 (2017)

Authors:F. D. Fischer; G. A. Zickler; J. Svoboda Abstract: The ensemble of interstitial atoms as C attracted to a dislocation is well established as “Cottrell cloud” phenomenon. The deposition of the interstitial atoms in octahedral or tetrahedral positions in a bcc lattice may yield a remarkable internal stress state according to their anisotropic misfit eigenstrains. The stress fields of the atoms may then lead to a significant change in the stress field, e.g., around a dislocation. In such a case, the interstitial atoms are situated near the dislocation core in cylindrical volume elements along the dislocation line. As the occupancy of the sites in each cylinder by interstitial atoms can be considered as constant, also the eigenstrain state tensor is constant in the cylinder. A complete set of analytical expressions for the eigenstress state inside and outside of the cylinder is presented. The resultant stress field is then given by superposition, which allows also the determination of the interaction energy between the Cottrell cloud and the dislocation. PubDate: 2017-11-08 DOI: 10.1007/s00419-017-1318-x

Authors:Jędrzej Mączak; Marcin Jasiński Abstract: The paper is presenting a methodology for developing model-based method of gear fault diagnostics. First the simulation model of the helical gearbox is discussed allowing analysis of the phenomena taking place during teeth mating in the presence of manufacturing and assembly errors. It includes observation of influence of errors on the generated signals. The model was initially used to analyze the teeth contact in the presence of pitch errors and later to verify the sensitiveness of proposed diagnostic methods and their availability to detect the fatigue damages of teeth. The common feature of discussed approach is the direct use of time signal processing algorithms, and in contrary to the methods based on spectral analysis it allows precise localization of gear defects like pitting and tooth fracture associating them to the particular pinion or gear teeth. Their advantage is the simplicity and speed of action that is of great significance for the implementation in the autonomous transmission diagnostic systems and diagnostic systems working online. Presented methods of signal processing were first tested on a simulation model of the gear assembly and later verified during the experiments on a back-to-back test stand. PubDate: 2017-11-07 DOI: 10.1007/s00419-017-1321-2

Authors:M. Beerhorst; M. Seibel; C. Mittelstedt Abstract: This paper presents approximate solutions for the postbuckling behavior of a plate consisting of laminated composites with symmetrical, balanced lay-up loaded in longitudinal compression. The transversal edges of the plate are simply supported, one longitudinal edge is free and the opposite one is rotationally restrained. Key to obtain an explicit and thus highly computational efficient solution is the use of a shape function with only few variables. First, the shape function is inserted into the compatibility condition of in-plane strains to derive a closed-form solution of Airy’s stress function. Then, the equilibrium condition is approximated with the Galerkin procedure yielding a load–deflection relationship. Subsequently, other state variables such as in-plane displacements and stresses can be obtained. Overall, results for displacements and strains show very good agreement with detailed nonlinear finite element analyses. PubDate: 2017-11-07 DOI: 10.1007/s00419-017-1319-9

Authors:Ankur Jaiswal; H. P. Jawale Abstract: Kinematic mechanisms are synthesized for a task. Function generation provides precise displacement at output links that obeys a given functional relations. This article describes the synthesis of four-bar mechanism for the hyperbolic function generation with four and five accuracy point, which is further optimized using least square method. This research is concerned with development of mathematical formulation based on Freudenstein–Chebyshev approximation theory, extended to four- and five-point synthesis function generation problem. The objective function is analyzed for the structural error between the generated function and the desired function. Resulting nonlinear equations are converted into set of linear equations applying the compatibility conditions and are solved using Gauss elimination method. The formulation is proposed for five position synthesis for algebraic and trigonometric function generation problem. Associated structural error is estimated. Comparison of estimated error through the formulation is carried out with the reported errors through graphical method. The error for hyperbolic function is estimated. Attempt is made to minimize the error through simple of least square technique. The results obtained are compared with Freudenstein–Chebyshev approximation method. Three hyperbolic functions, namely sinh(x), cosh(x) and tanh(x), are used to demonstrate the effectiveness of the proposed synthesis method. PubDate: 2017-10-24 DOI: 10.1007/s00419-017-1310-5

Authors:Xiangyu Luo; Guoxin Zhang Abstract: The effective bulk modulus K of brittle porous materials such as concrete is related to the matrix bulk modulus \(K_\mathrm{m}\) and is affected by factors such as the pore shape and Poisson’s ratio. Basing on Walsh functions and the complex variable function solution for the square pore, this paper derives a formula for calculating the effective bulk modulus of a medium with square pores under planar arrangement condition. Meanwhile, the effective bulk modulus of a model with a random pore distribution is calculated using a numerical method. The results of the numerical calculation and the formula are compared with the results of tests and numerical simulations from previous studies. The results show that there is a critical porosity for the theoretical formula; when the porosity is lower than the critical porosity, the results of the single-pore formula match the test and numerical results well, whereas when the porosity exceeds the critical porosity, the results of the multi-pore formula match the test and numerical results; when the porosity is greater than 0.45, the results of the numerical simulation deviate significantly from those of the theoretical formula. A verification of the numerical results versus the theoretical results shows that the square pore formula is an excellent representation of the relationship between the effective bulk modulus and the matrix bulk modulus for porous media such as concrete within limits. PubDate: 2017-10-07 DOI: 10.1007/s00419-017-1309-y

Authors:Francesco Castellani; Lorenzo Scappaticci; Nicola Bartolini; Davide Astolfi Abstract: This work is devoted to the dynamics of a hydraulic monotube shock absorber, whose design resembles racecar vehicles dampers, prototyped at the University of Perugia for scientific purposes. A physical approach is adopted for numerical modeling of the global operation of the device, and the model is validated against a comprehensive test bench experimental campaign, conducted at velocities and frequencies typical of racecar vehicles. The main peculiarity of the prototype is that it is built in Plexiglas, and therefore, it has transparent walls allowing experimental tests with optical acquisition through high-speed camera. This provides a completely novel perspective, because it is possible to observe the evolution of the internal behavior, through the optical access, jointly with standard experimental test approaches. These experimental techniques are especially fit for the analysis of the cavitation phenomenon: the influence of the main boundary conditions (compensation pressure, fluid temperature) on the onset and the evolution of cavitation is investigated. Further, the influence of cavitation, according to its evolution, on the performances of the device is investigated. In particular, it is further shown that the optical acquisition is fundamental to have insight on the incipient and evolving phases of cavitation, which cannot be observed through the common techniques found in the literature. PubDate: 2017-10-07 DOI: 10.1007/s00419-017-1302-5