Authors:Friedrich Pfeiffer Abstract: Many processes in machines and mechanisms are accompanied by impacts with friction. They arise by short-time contacts between two or more bodies, and they generate energy losses mainly due to friction in tangential contact directions. During the last three decades, a couple of impact models based on the theory of rigid body contacts were established connected with the names of Moreau, Fremond, and Glocker, which all work quite satisfactorily with respect to practical applications. In the following, we shall establish the basic equations, discuss several structural issues, and consider the energy behavior of impulsive motion. Measurements verify the theoretical ideas very nicely. An application will be given, too. PubDate: 2017-11-23 DOI: 10.1007/s00707-017-1989-y

Authors:Hans Irschik; Rudolf Heuer Abstract: In the present paper, we consider nonlocal linear elastic Kirchhoff plates, where we restrict to thin, isotropic, and homogeneous plates under the action of static transverse forces, utilizing the differential equation form of the Eringen nonlocal continuum theory. For the case of simply supported plates of polygonal planform, we derive analogies between the solutions of the nonlocal Kirchhoff theory and its local counterpart. First, we extend the Marcus decomposition method for local Kirchhoff plates, where we show that, analogous to the local case considered by Marcus, the moment sum and the nonlocal deflection are both governed by Poisson boundary value problems, which correspond to auxiliary (local) membrane problems. In the present context, it eventually follows that there is a nonvanishing term responsible for a correction of the deflection due to the nonlocal effect, while the moments and shear forces of the local and the nonlocal plate coincide. The nonlocal correction of the deflection turns out to be governed by a membrane-type boundary value problem again. From this fact, it follows immediately that the correction for the deflection due to the nonlocal effect can be derived alternatively from both the local deflection and the local moment sum, which represents a substantial simplification of the nonlocal computations. For the sake of demonstration, we consider examples with closed form solutions. We first consider (as limiting case) infinite plates under the action of single forces, where the singular behavior of Green’s function of the nonlocal Kirchhoff theory can be clarified. Then we discuss the bending of nonlocal plate strips for comparison sake, as well as equilateral triangular plates. To our best knowledge, no results for bending of nonlocal triangular plates have been presented in the literature so far. The present paper has been strongly influenced by a former contribution on analogies between simply supported polygonal Kirchhoff plates rigid in shear and shear-deformable plate solutions. This paper was co-authored together with our teacher, the late Professor Franz Ziegler, to whom we dedicate the present paper. In light of this latter contribution, and extending an idea promoted by Professor Franz Ziegler and his co-workers in the framework of various other fields, we finally show in the Appendix that the deflections of simply supported nonlocal Kirchhoff plates can be considered as deflections of a local “background” Kirchhoff plate under the action of additional fictitious eigenstrain loadings, such as thermal moments. PubDate: 2017-11-22 DOI: 10.1007/s00707-017-2005-2

Authors:Christian Bucher Abstract: A purely kinematic approach to the formulation of plane stress/strain triangular elements with three nodes as well as tetrahedral elements with four nodes including rotational degrees of freedom is presented. The class of elements is shown to perform comparably well in several well-established test cases. Essentially, the displacement interpolation functions are cubic allowing for more flexibility in the displacement-based formulation. The in-plane triangle can be augmented by a plate bending element to form an efficient triangular shell element. PubDate: 2017-11-21 DOI: 10.1007/s00707-017-2045-7

Authors:Chethan Gouder; U. Saravanan Abstract: Here mixture theory is used to capture the changes in cement concrete exposed to sodium sulfate till cracks develop. Toward this, the mixture is assumed to be made of eleven constituents of which the sodium sulfate and water move relative to themselves and the remaining nine solid constituents. The nine solid constituents constrained to move together are the eight relevant chemical constituents in concrete that react with sodium sulfate and all the other remaining chemical constituents of concrete that do not react with sulfates. Constitutive assumptions needed to be made within this mixture theory framework are the same as those reported by Gouder and Saravanan (Acta Mech 227(11):3123–3146, 2016). Within this framework of mixture theory, the radial ingress and reaction of sodium sulfate solution with the concrete cylinder sealed at top and bottom, exposed to a constant concentration of sodium sulfate at its outer surface, are formulated. The resulting nonlinear governing differential equations are converted into a system of nonlinear algebraic equations using a forward finite difference scheme in space and a backward difference in time. The nonlinear algebraic equations are solved simultaneously using constrained minimization technique till the water reaches the center of the cylinder. The results obtained for ingress without chemical reactions agree with those predicted by Fick’s equation. The axial expansion of the cylinder and the increase in the value of Young’s modulus of the part of concrete which reacted with sulfates agree qualitatively with the experiments. PubDate: 2017-11-21 DOI: 10.1007/s00707-017-2035-9

Authors:Alexander K. Belyaev; Vladimir V. Eliseev Abstract: The behavior of an oil drill string is considered on example of a rotating flexible shaft in a rigid tube. The tube (a model of the borehole) is assumed to be an arbitrary space curve, and the shaft is considered as a nonlinear elastic Cosserat rod. The nonlinear dynamic equations for the shaft are derived and solved by means of computer mathematics. The boundary value problem for the quasi-static rotation is reduced to the ordinary differential equation (ODE). The shooting method is applied for solving the obtained nonlinear ODE. The quasi-static rotation is shown to exhibit jumps for some sets of parameters. The dynamic problem is solved by the differential-difference method. The rotation behavior, the resultant forces, and moments in the rod as well as the contact reaction of the inner surface of the tube are determined. The differences between the static and dynamic solutions are demonstrated. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2003-4

Authors:S. Iino; S. Yahiro; T. Nishikawa; T. Tsuji Abstract: It is important to measure the defect of objects. The radiated sound from the impacted body has many types of information, and it also has the information of the defect. Therefore, in this study, we propose a method in order to identify the position and the size of the defect in the impacted body by measuring the radiated sound pressure. In the proposed method, we calculate the time dependence of the radiated sound pressure from the impacted body with the supposed defect by using FEM analysis. The defect position and size can be given in order to match the time dependence of the sound pressure with the measured sound pressure. In order to obtain much information involved in the defect, it is necessary to measure the sound pressure in the wide range. However, it is difficult to prepare hundreds of microphones to measure the radiated sound distribution. Thus, we constructed the measuring system of the sound pressure distribution by moving a microphone and applying the same impact force to the body. In this system, we can measure fictionally the sound pressure distribution on the plane over \(200\hbox { mm}\times 200\hbox { mm}\) area with \(2~\upmu \hbox {m}\) resolution. The efficiency of the proposed method is confirmed by some experiments. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2023-0

Authors:N. D. Anh; N. N. Linh Abstract: This paper introduces and discusses a weighted form of the dual mean-square error criterion by considering weighted contributions of forward and return replacements adjusted by a specific non-dimensional weight coefficient. The simplicity and accuracy of the proposed weighted dual equivalent linearization technique are checked on several random vibration systems in comparison with other criteria. It is shown that the corresponding accuracy can be significantly improved for a large range of nonlinearity of investigated vibration systems. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2009-y

Authors:S. Casciati; L. Faravelli; M. Vece Abstract: A rich literature studies shape memory alloy (SMA) wires for their potential use in dampers devices able to reduce wind, rain, and traffic-induced oscillations of stayed cables. Restrainers for bridges and improved aseismic devices also exploit alloy components. Thus, SMAs should be regarded as materials susceptible to storage in the yard. In this paper, the authors discuss the evolution of SMA macroscopic behavior as caused by a long-time storage of the product as acquired. The study discriminates between wires of different diameters, because the flat cycles shown by thin wires (i.e., diameter \(\le 0.5\,\hbox {mm}\) ) and the non-classical S-shaped cycles of thick wires (of diameter 2.46 mm in this paper) answer differently to environmental modifications. The hysteretic behavior of some specimens of wires, of diameter 2.46 mm, is here investigated to mark the unpredictability of the consequence of a long-time storage, which could prevent from the practical exploitation of such alloys in civil engineering. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-1993-2

Authors:Yu Su; George J. Weng Abstract: The frequency dependence of the electromechanical response of a barium titanate nano-thin film was studied through phase-field simulation. A two-dimensional phase-field model based on Landau–Devonshire energy density function was established in this work. The time-dependent Ginzburg–Landau equation was utilized to calculate the dynamics of the microstructure upon the application of an AC electric field. A segment of barium titanate thin film was modeled with 20 nm in thickness and 80 nm in width. Periodic boundary conditions were applied to both ends of the nano-thin film to represent an infinite length-to-thickness ratio. It was observed from the phase-field results that the loading frequency of the electric field can noticeably affect the hysteresis and butterfly loops of the nano-thin film through competition with the electric dipole evolution. A high-frequency electric field tends to yield a close-to-linear response of the thin film. Meanwhile, it was discovered that the existence of \(180^{\circ }\) domain walls and their dynamics (oscillation) within the thin film have remarkable influence on the overall response. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2000-7

Authors:Ashirbad Swain; Tarapada Roy Abstract: The present article deals with the viscoelastic modeling and dynamic responses of the carbon nanotubes (CNTs)-based carbon fiber-reinforced polymer (CNTs-CFRP) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of CNTs-based polymer matrix phase. Further, the strength of material method has been employed to formulate the viscoelastic material behavior of the homogenized hybrid CNTs-CFRP composite materials. An eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials. Frequency- and temperature-dependent material properties of such hybrid composite materials have been obtained and analyzed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters on the material properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-based proposed composite materials. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2051-9

Authors:Qiushi Fu; Jiang Qian; Dimitri E. Beskos Abstract: The formulation of constitutive models for anisotropic materials such as masonry is a problem of large complexity. One possible way is to define linear transformations on the stress tensors using fourth-order transformation tensors that carry all the anisotropic information of the material. In the present paper, a new type of evolutionary linear transformation tensor is defined, which can change the values of its components along with the evolution of internal variables. This means the transformation laws are defined according to the current plastic and damage levels, and allows the constitutive model to describe totally different hardening and softening behaviours of the material along different directions. First, a general procedure of formulation of anisotropic constitutive models is given. Second, as a specific example, an orthotropic plastic–damage constitutive model for masonry is presented. Finally, the proposed constitutive model is validated by comparing finite element results with experimental ones pertaining to simple masonry structures under static and cyclic loading. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-1995-0

Authors:Yang Sun; Xueming Yu; Wenbing Jia; Xianhui Wang; Mabao Liu Abstract: In this investigation, general approximate solutions for the stress intensity factor (SIF) and configuration force (CF) are derived, respectively, based on the Eshelby theory for the interaction between an inhomogeneous inclusion of arbitrary shape undergoing a stress-free transformation strain and plane stress mode II crack. For common inclusion shapes, some simplified approximate formulae are also developed. Then, the relationship between the normalized CF and SIF is discussed, as well as the effects of inclusion shape, location, and size on the CF and SIF of a plane stress mode II crack. To give deep insight into the complex three-dimensional interaction between an inclusion undergoing a stress-free transformation strain and a crack, two typical cases of the triaxial stress state are analyzed, and no significant difference occurs among most engineering materials. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2041-y

Authors:Jing Yang; Qin Fan; Liangcai Zeng; Leon M. Keer; Kun Zhou Abstract: The plastic zones of crack tips play a significant role in the fracture behavior of material. This paper proposes a semi-analytic solution for the plastic zones and stress distribution of an infinite space with multiple cracks and inhomogeneous inclusions under remote stress. In this solution, cracks can be treated as a distribution of edge dislocations with unknown densities according to the distributed dislocation technique, while inhomogeneous inclusions can be modeled as homogeneous inclusions with initial eigenstrain plus the unknown equivalent eigenstrain by using the equivalent inclusion method. These unknowns can be obtained by using the conjugate gradient method. The plastic zones ahead of crack tips are one-dimensional slender strips, and their sizes can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the applied load based on the Dugdale model of small-scale yielding. It is found that the plastic zones of crack tips are significantly affected by Young’s modulus and the positions of inhomogeneous inclusions. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-1983-4

Authors:M. Bateni; M. R. Eslami Abstract: The present paper is aimed to make a detail analysis on the correct simulation of the associated natural thermal boundary conditions and their interesting effects on the thermally nonlinear generalized thermoelastic response of a continuum medium. The paper presents some explanations regarding the literally conventional thermal boundary conditions associated with Cattaneo’s heat conduction law. The importance of modeling the natural thermal boundary conditions is investigated by applying three practical thermal loads to a homogeneous one-dimensional layer. The results of the investigations are illustrated by propagation of thermoelastic waves through the layers. These results clearly show the profound effects of the correct statement of natural thermal boundary conditions on the thermoelastic response of the layer. It is shown that these effects intensify the importance of thermally nonlinear generalized thermoelastic analyses. PubDate: 2017-11-17 DOI: 10.1007/s00707-017-2001-6

Authors:C. R. Bocking; M. G. Blyth Abstract: A mathematical model of oxygen uptake by bacteria in agricultural soils is presented with the goal of predicting anaerobic regions in which denitrification occurs. In an environment with a plentiful supply of oxygen, micro-organisms consume oxygen through normal respiration. When the local oxygen concentration falls below a threshold level, denitrification may take place leading to the release of nitrous oxide, a potent agent for global warming. A two-dimensional model is presented in which one or more circular soil aggregates are located at a distance below the ground level at which the prevailing oxygen concentration is prescribed. The level of denitrification is estimated by computing the area of any anaerobic cores, which may develop in the interior of the aggregates. The oxygen distribution throughout the model soil is calculated first for an aggregated soil for which the ratio of the oxygen diffusivities between an aggregate and its surround is small via an asymptotic analysis. Second, the case of a non-aggregated soil featuring one or more microbial hotspots, for which the diffusion ratio is arbitrary, is examined numerically using the boundary-element method. Calculations with multiple aggregates demonstrate a sheltering effect whereby some aggregates receive less oxygen than their neighbours. In the case of an infinite regular triangular network representing an aggregated soil, it is shown that there is an optimal inter-aggregate spacing which minimises the total anaerobic core area. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-2042-x

Authors:A. Kaveh Abstract: In this paper, some graph theoretical (topological) transformations are presented for simplifying certain problems involved in structural analysis. For each case, the main problem is stated and the proposed topological transformation is established. Once the required topological analysis is completed, a back transformation results in the solution for the main problem. The transformations studied here employ (i) models drawn on a lower dimensional space, (ii) models embedded on higher dimensional spaces and (iii) interchange models which have simpler connectivity properties than the corresponding original structural models. All these transformations are illustrated utilizing simple examples. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-1991-4

Authors:N. Jamia; P. Rajendran; S. El-Borgi; M. I. Friswell Abstract: The dynamic response of a bladed disk is very sensitive to the symmetry of identical blades. If the properties of one or more blades vary slightly then the response can increase substantially, which is known as mistuning. Mistuning in bladed disks due to manufacturing tolerances has been extensively studied, with emphasis on response and fatigue life prediction. Damage to blades can also cause mistuning but has received only limited attention. The identification of mistuning in rotating bladed disks is a challenging and an on-going topic of investigation. This study proposes a Wavelet Energy-Based Mistuning Index (WEBMI) which is obtained from the wavelet packet transforms of both tuned and mistuned blade responses, and requires only output response signals. The proposed mistuning index is demonstrated on a lumped parameter model of a bladed disk, and mistuning was represented by altering the stiffness or mass of individual blades. Mistuning to single and multiple blades with different locations and severities was simulated. Gaussian white noise was added to the response signal to test robustness. Finally, experiments were conducted to validate the feasibility of the proposed method. The results demonstrate that the WEBMI is sensitive enough to identify subtle mistuning as small as 0.5% in single and multiple locations. Furthermore, the mistuning index increases monotonically with increases in mistuning severity. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-2059-1

Authors:T. Cui; P. Verberne; S. A. Meguid Abstract: An extensive experimental program and molecular dynamics (MD) simulations have been conducted to ascertain the effect of water absorption upon the mechanical degradation of thermoset polymers. Mechanical tests were conducted to determine the degradation of the mechanical properties at regular testing intervals for up to 300 days of water immersion. The outcome of our studies reveals the following: (i) a decrease in the elastic modulus and the tensile strength as a result of the plasticization of the considered epoxy caused by water-induced swelling, and (ii) a reduction of approximately 50% in the fracture strain due to water ingression. SEM micrographs of the fracture surface revealed an abundance of aggregates, crazes, and microcracks as a result of aging in water. Meanwhile, AFM images further depicted step and stacked lamellar topological features of the fracture surface. In addition to the plasticization effect, there is a partial recovery of the elastic modulus at certain water absorption content. Such anti-plasticization effect of water molecules on the epoxy was demonstrated by both experiments and MD simulations. The elastic properties of the epoxy with and without different water contents were predicted by MD simulations, and the results corresponded with the experimental aging trend. The MD predictions further revealed that the water diffusion coefficient decreases with the increase in the epoxy density. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-1997-y

Authors:Alberto Di Matteo; Thomas Furtmüller; Christoph Adam; Antonina Pirrotta Abstract: In this paper, the use of a tuned liquid column damper (TLCD) as a cost-effective means to control the seismic response of a base-isolated structure is studied. A straightforward direct approach for the optimal design of such a device is proposed, considering a white noise model of the base excitation. On this base, a direct optimization procedure of the TLCD design parameters is performed and optimal design charts are presented as a ready-to-use practical design tool. Comparison with the optimal parameters obtained considering a classical iterative statistical linearization technique proves the reliability of the proposed approach. The performance of the base-isolated TLCD-controlled structure is examined and compared with that of the simple base-isolated one (without TLCD), using a set of 44 recorded ground motions as base excitation. Theoretical and numerical results show that the TLCD is rather effective in reducing the response of base-isolated structures under strong earthquakes. Therefore, considering its advantageous characteristics and its overall beneficial effects, TLCDs can be considered as practical and appealing means to control the seismic response of base-isolated structures. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-1980-7

Authors:John T. Katsikadelis; Nick G. Babouskos Abstract: In this paper, the boundary element method (BEM) is developed for the flutter analysis of thick anisotropic plates modeled by Mindlin’s theory. Such plates describe the response of laminated plates consisting of layers of anisotropic materials, which are extensively used in various modern engineering applications. The plate is subjected to aerodynamic pressure due to supersonic air flow, a follower-type load. The governing equations are three coupled linear partial differential equations of second order subjected to three boundary conditions besides the initial conditions. The boundary value problem is solved using the analog equation method. Thus, following the principle of the analog equation, the original equations are substituted by three uncoupled Poisson’s equations under fictitious loads, which are subsequently, solved using the conventional BEM for Poisson’s equation. Various thick and thin laminated plate problems are studied using the proposed method. The obtained numerical results demonstrate the efficiency of the solution procedure, validate its accuracy and give a revealing insight into the dynamic response of the thick laminated plates under follower loads. PubDate: 2017-11-15 DOI: 10.1007/s00707-017-1988-z