Authors:Qingjun Hao; Wenjie Zhai; Zhaobo Chen Abstract: Abstract In this paper, free vibration of connected double-beam system under general boundary conditions is investigated by a modified Fourier–Ritz approach. The effects of the restrained stiffness of the springs and the elastic layer stiffness on modal properties are incorporated in the current framework. The displacement components can be expressed as Fourier cosine series plus auxiliary polynomial functions, which aim to eliminate the discontinuities of displacement and its derivatives at both ends and to enhance the convergence of the results effectively. Numerical examples were presented and discussed for several different geometric and material properties as well as distinct boundary conditions. The effectiveness and rapid convergence of the present method can be verified from the results. Numerous new results for connected double-beam system with arbitrary boundary conditions are presented. PubDate: 2018-01-04 DOI: 10.1007/s00419-017-1339-5

Authors:Andreas Lehn; Marcel Mahner; Bernhard Schweizer Abstract: Abstract The performance of air foil thrust bearings (AFTBs) is studied for aligned, distorted and misaligned operating conditions on the basis of a very detailed numerical model for the foil sandwich. The exact geometry of the bump foil is modeled by a Reissner–Mindlin-type shell theory. A penalty-type contact formulation including frictional effects is applied for the contact between top foil and bump foil as well as between bump foil and base plate. The minimal film thickness within the thrust bearing is used as a criterion for comparing different air foil thrust bearings with rigid thrust bearings. If the rotor disk and the base plate are perfectly parallel (aligned conditions), AFTBs are proved to have always a lower load capacity than (optimized) rigid thrust bearings due to unequal bump foil deformations and top foil sagging effects. This finding is in contradiction to previous works based on simplified foil models, which claimed AFTBs to be superior to rigid thrust bearings. Furthermore, for both operating conditions—thermally induced distortions of the rotor disk as well as misalignment—an individual pad of an AFTB is found to be unable to effectively compensate for the disturbance in the gap function. Consequently, a tailoring of the stiffness distribution in the AFTB is shown to be of limiting effect. Instead, the overall compliance of the pads in an AFTB is demonstrated to be the essential reason for the superior behavior of AFTBs to rigid thrust bearings under misaligned conditions. PubDate: 2018-01-04 DOI: 10.1007/s00419-017-1337-7

Authors:Sonia Parvanova; Georgi Vasilev; Petia Dineva Pages: 1947 - 1964 Abstract: 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: 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: 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: 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: 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: 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:Roohollah Ghaedamini; Aazam Ghassemi; Amir Atrian Abstract: Abstract Residual stresses in composite constructions are created because of non-uniform contraction of layers during cooling from curing to ambient temperature. The aim of this study is to investigate the feasibility of incremental ring-core method to estimate non-uniform residual stresses in various laminates of polymer matrix composites. To carry out this test, glass/epoxy specimens were selected in two different types of symmetric cross-ply laminate \(\left( \left[ 0^{\circ }_{4}/90^{\circ }_{4}\right] _{S}\right) \) and symmetric quasi-isotropic laminate \(\left( \left[ 0^{\circ }_{2}/\pm 45^{\circ }/90^{\circ }_{2}\right] _{S}\right) \) . The samples were created using hand layup and vacuum bagging. By experimental tests, released strains measured during milling process and coefficient factors for every annular groove machining operations were obtained by finite element modeling. As well, residual stresses were calculated by classical lamination plate theory. For symmetric cross-ply, the maximum difference between experimental and theoretical results was about 16%, which was observed in the first and eighth layers. Symmetric quasi-isotropic specimen showed also good agreement between the results and the maximum measurement error of 8% was observed. For the mentioned two cases, summation of components of the residual stress in all directions is near to zero. The results of this study show that in the ring-core method, because of the nature and higher volume of material removal than other methods, values of residual stress released are higher and the results have a good consistency compared with the theoretical values. PubDate: 2017-12-29 DOI: 10.1007/s00419-017-1340-z

Authors:Kerimcan Celebi; Durmus Yarimpabuc; Naki Tutuncu Abstract: Abstract A novel approach is employed in the free vibration analysis of simply supported functionally graded beams. Modulus of elasticity, density of material, and Poisson’s ratio may change arbitrarily in the thickness direction. The equations of motion are derived using the plane elasticity theory. The governing differential equations have variable coefficients, which are functions of material properties. Analytical solutions of such equations are limited to specific material properties. Hence, numerical approaches must be adopted to solve the problem on hand. The complementary functions method will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Solutions thus obtained are compared to closed-form benchmark solutions available in the literature and finite element software solutions to validate the method presented. Subsequently, it is demonstrated that the method is efficiently applicable to material properties changing arbitrarily through the thickness with continuous derivatives. PubDate: 2017-12-21 DOI: 10.1007/s00419-017-1338-6

Authors:Marina Rakočević; Svetislav Popović Abstract: Abstract This paper presents the analysis of simply supported rectangular laminated composite plates loaded perpendicularly to the middle plane using a new computational method based on Reddy’s layerwise theory. The stress–strain analysis was based on the analytical solution of equations of the layerwise theory, where the plates with an antisymmetric layer arrangement were analysed. Each of the layers contains continuous fibres oriented in one of two mutually orthogonal directions. The results obtained by applying above-mentioned computational procedure have been compared with the results obtained using three different models of finite elements of the ANSYS software package. The quantified limits of the computational method in terms of the impact of plate thickness, the number of layers and the aspect ratio of the plate on the accuracy, convergence and stability of primary variables—components of displacement, and secondary variables—components of stress, have been analysed in the paper. PubDate: 2017-12-16 DOI: 10.1007/s00419-017-1334-x

Authors:Wenjun Yang; Taotao Hu; Xu Liang; Shengping Shen Abstract: Abstract Flexoelectricity becomes remarkable in nanoscale dielectrics where strong strain gradients are expected. The effect of flexoelectricity on elastic plane waves propagating in nanoscale layered phononic crystals is discussed in the current work. The fundamental governing equations and boundary conditions are derived from the virtual work principle. Detailed calculations are performed for nanoscale two-layered and three-layered phononic crystals using the transfer matrix method. Numerical results indicate that phononic crystals possess frequency pass bands and stop bands. For nanoscale layered phononic crystals, flexoelectricity increases the middle frequency regardless of the thickness ratio, whereas the flexoelectric effect on the bandwidth depends on the thickness ratio, which implies that there is an optimal thickness ratio to maximize the bandwidth. In addition, the middle frequency and bandwidth decrease with an increase in the unit cell thickness if the thickness ratio is fixed. Hence, considering the flexoelectric effect on band structures of nanoscale phononic crystals may provide guidance in manipulating elastic wave propagation and facilitate potential applications in phononic crystal devices. PubDate: 2017-12-12 DOI: 10.1007/s00419-017-1332-z

Authors:Lei Zhao; Zunyi Zhao; Lianyong Xu; Yongdian Han; Hongyang Jing Abstract: Abstract The interaction and combination of multiple embedded cracks would accelerate cracks growth and shortened the components life. In this study, the interaction of the multiple embedded cracks in a finite thickness plate subjected to remote tensile loading in the creep regime was investigated using comprehensive finite element calculations. In addition, the features of cracks and material properties (e.g., crack aspect ratios a / c, relative crack depth a / t, relative distance s / c and creep hardening exponent n) were considered. The results revealed that the creep interaction factor distribution was asymmetric along the crack front. In addition, the creep interaction factor increased as the crack depth and creep hardening exponent increased and gradually decreased as the position away from the each other. However, the crack shape changing from elliptical shape to circular shape had slight impact. Furthermore, based on the comprehensive analyses, an empirical formula to determine the multiple interaction level considering the crack configurations and the material properties was proposed for the embedded cracks operating at elevated temperatures. PubDate: 2017-12-12 DOI: 10.1007/s00419-017-1335-9

Authors:Francesco Foti; Luca Martinelli Abstract: Abstract Cables are widely used lightweight and efficient structural members affected by various nonlinearities. This paper is devoted to the development of a finite element approach to the study of the nonlinear dynamic behavior of cable structures under wind loading. Firstly, the formulation of a co-rotational beam-cable element is presented to account for cable geometrical nonlinearities within the context of an Updated Lagrangian approach. The Euler–Bernoulli kinematics is adopted in the co-rotated frame assuming small or moderate displacements and strains. Secondly, the formulation of an aerodynamic element, meant to be superimposed to the mechanical beam element, is developed to fully account for the nonlinearity of the aerodynamic forces. The wind interaction forces are computed within the framework of the quasi-steady theory. Appropriate procedures for applying the aforementioned elements in static and dynamic analyses are presented and applied to the study of the static configuration and the galloping vibrations of a suspended cable under steady and turbulent wind conditions. The results point out the importance of the first anti-symmetric in-plane mode on the galloping response of the iconic selected structure, and reveal the role of the mechanical and aerodynamic model by comparison with a different discretization based on cable finite elements. A mechanical model, such as the proposed co-rotational finite element formulation, which includes the description of torsional rotations is required to properly model the aerodynamic loads in dynamic galloping analyses under steady wind. The mechanical and aerodynamic assumptions, instead, play a less important role in the case of turbulent wind conditions, leading to an eminently buffeting response entailing a strong effect of the swing of the structure. PubDate: 2017-12-11 DOI: 10.1007/s00419-017-1333-y

Authors:Jiangen Lv; Houjun Kang Abstract: Abstract In this paper, the one-to-one interaction of a cable-stayed arch structure under the cable’s primary resonance is investigated. Based on the coupling condition at the arch tip, the partial differential equations governing the planar motion of the system are derived using the extended Hamiltonian principle, while with the application of the Galerkin method, these equations are transformed into a set of ordinary equations. Applying the method of multiple scales to these ordinary equations, the first approximated solutions and solvability condition are obtained. The one-to-one interaction between the cable and the arch is investigated under simultaneous internal and external resonances for an actual cable-stayed arch structure. Based on the shooting method and the pseudo-arclength algorithm, the dynamic solutions of the system are obtained, and a period-doubling route to chaos is analyzed. The effects of the cable’s initial tension, inclination angle, the arch’s rise-to-span ratio and intersection angle between the cable and the arch are explored, and the results show that the interaction response mainly depends on specific parameters. PubDate: 2017-12-11 DOI: 10.1007/s00419-017-1328-8

Authors:H. R. Majidi; M. R. Ayatollahi; A. R. Torabi Abstract: Abstract The aim of the present study is to assess the suitability of the extended finite element method (XFEM) combined with the cohesive zone model (CZM) and also the incremental method together with the maximum tangential stress (MTS) criterion in predicting the fracture load and crack trajectory of key-hole notched brittle components subjected to mixed mode I/II loading with negative mode I contributions. For this purpose, a total number of 63 fracture test results, reported recently in the literature on the key-hole notched Brazilian disk (Key-BD) specimens made of the general-purpose polystyrene (GPPS) under mixed mode I/II loading with negative mode I contributions, are first collected. Then, the experimentally obtained fracture loads of the tested GPPS specimens are theoretically predicted by means of XFEM combined with CZM. Additionally, the crack trajectory in the tested Key-BD specimens is predicted by using both XFEM combined with CZM and the incremental method combined with MTS criterion. Finally, it is shown that both the fracture load and the crack trajectory could successfully be predicted by means of the two proposed methods for different notch geometries. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1329-7

Authors:Lifeng Ma; Biao Wang; Alexander M. Korsunsky Abstract: Abstract Analytical solution for a rigid line inclusion embedded in an infinite-extended plane under non-uniform loading is still a challenging problem in inclusion mechanics, which has both theoretical and applied significance in material engineering. In this paper, by directly employing Kolosov–Muskhelishvili stress potentials, a rigid line inclusion interacting with a generalized singularity is addressed in the framework of plane deformation, with the help of the superposition principle. It should be pointed out that the generalized singularity in this study can represent a point force, an edge dislocation, a point moment, a point nucleus of strain, and even remote uniform load, etc. The solutions can be used as kernel functions for integral equation formulations of rigid line inclusion–substrate system models using the Green’s function method. With this framework, stress field and stress intensity factors at the line inclusion ends are analyzed. The application of the solutions is demonstrated with two simple examples: (i) the rigid line inclusion under remote loading is studied, and it is strictly confirmed with rigorous proof that the remote shear load will not arouse stress concentration; (ii) a rigid line inclusion interacting with a dislocation is investigated, and the full solution is given. These examples also partially validate the general solution derived this study. PubDate: 2017-12-01 DOI: 10.1007/s00419-017-1330-1

Authors:Ankur Jaiswal; H. P. Jawale Abstract: 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: 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: 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