Abstract: This paper addresses the problem of characterizing the mechanical behaviour and collapse of symmetric circular and pointed masonry arches subject to their own weight. The influence on the arch’s collapse features of its shape and thickness, as well as the friction between the arch’s voussoirs, is analysed. The safety level of arches is then investigated by suitably reworking in semi-analytical form the graphical method of the stability area proposed by the renowned nineteenth century French scholar, Durand-Claye. According to Durand-Claye’s method, the arch is safe if along any given joint both the bending moment and shear force do not exceed the values determined by some given limit condition. The equilibrium conditions corresponding to all possible symmetric collapse modes are individuated. As was expected, pointed and circular arches exhibit different collapse behaviours, in terms of both collapse modes and safe domain. The limit values of arch thickness and friction coefficient are determined and the results obtained consistently compared with those published by Michon in 1857. PubDate: 2019-02-15

Authors:Hakan Ozbasaran Abstract: Design of the slender members requires calculation of buckling loads in addition to stress and deflection demand/capacity ratios. The Rayleigh–Ritz Method, which allows one to present approximate closed-form solutions for certain cases, is one of the simplest methods for this purpose. This study evaluates the buckling analysis of the I-section prismatic beam–columns with the Rayleigh–Ritz Method in detail. First, algebraic, trigonometric, and exponential trial functions for various restraint configurations are derived carefully in finite series form. Then, an iterative procedure to calculate buckling loads and modes is described. Finally, a software is developed with Mathematica and the sensitivity of the results and performance to trial function type and the number of terms is investigated over 1000 computer-generated numerical examples, which include doubly and singly symmetric sections, simply supported and cantilever members, intermediate torsional and lateral restraints, transversal concentrated and distributed loads acting above/below the shear center, and axial loads. PubDate: 2019-02-14 DOI: 10.1007/s00419-019-01508-1

Authors:Siyuan Bao; Shuodao Wang Abstract: A unified solution procedure applicable for analyzing the free transverse vibration of both rectangular and annular sectorial plates is presented in this study. For the annular sectorial plate, the basic theory is simplified by a variable transformation in the radial direction. The analogies of coordinate system, geometry and potential energy between the two different shapes are drawn and then unified in one framework by introducing the shape parameter. A generalized solving procedure for the two shapes becomes feasible under the unified framework. The solution adopts the spectro-geometric form that has the advantage of describing the geometry of structure by mathematical or design parameters. The assumed displacement field and its derivatives are continuous and smooth in the entire domain, thereby accelerating the convergence. In this study, the admissible functions are formulated in simple trigonometric forms of the mass and stiffness matrices for both rectangular and annular sectorial plates can be obtained, thereby making the method computationally effective, especially for analyzing annular sectorial plates. The generality, accuracy and efficiency of the unified approach for both shapes are fully demonstrated and verified through benchmark examples involving classical and elastic boundary conditions. PubDate: 2019-02-14 DOI: 10.1007/s00419-019-01519-y

Authors:Mohammad Tahaye Abadi Abstract: This paper presents an analytic solution method to evaluate transient response of the joints in the truss-type structural networks. The analytic method models the wave propagation along the elastic members connected to the joints and derives the functions for the reflection and transmission coefficients for the structural joints. The coefficients of wave reflection and transmission across the joints are functions of material properties and geometrical parameters of the elements connected to the joint. The present analytic solution considers the effects of abrupt change in material properties as well as the alignment of connected elements on the transmission and reflection coefficients of the joints. The analytic solution method derives the functions for the transmission and reflection coefficients at the connection point of two different coaxial elements as well as the joints in planar and space frame structures. PubDate: 2019-02-12 DOI: 10.1007/s00419-019-01525-0

Authors:Xu Wang; Peter Schiavone Abstract: We consider a coated rigid inclusion inserted into an elastic matrix subjected to uniform remote anti-plane shear stresses and examine whether the inclusion can be made neutral (meaning that its introduction will not disturb the original uniform stress field in the surrounding uncut matrix) despite the presence of partial debonding along the inclusion–coating interface. Our analysis involves the introduction of a conformal mapping function (expressed in terms of a Laurent series) for the (thick) coating, a Laurent series expansion for the corresponding Plemelj function and simple matrix algebra. Our method demonstrates that coated neutral inclusions continue to be available under these challenging yet more realistic physical conditions. Numerical results are presented to demonstrate the feasibility of the solution method. PubDate: 2019-02-09 DOI: 10.1007/s00419-019-01524-1

Authors:Matthias Labusch; Jörg Schröder; Doru C. Lupascu Abstract: A computational homogenization analysis for the simulation of porous magneto-electric composite materials is presented. These materials combine two or more ferroic states with each other enabling a coupling between magnetization and electric polarization. This magneto-electric coupling finds application in sensor technology or data storage devices. Since most single-phase multiferroics show coupling at very low temperatures beyond technically relevant applications, two-phase composites, consisting of a ferroelectric and a ferromagnetic phases, are manufactured. They generate a strain-induced magneto-electric coupling at room temperature. The performance and reliability of these materials is influenced by defects or pores, which can arise during the manufacturing process. We analyze the impact of pores on the magnitude of the magneto-electric coupling coefficient. In order to determine the effective properties of the composite, a two-scale finite element ( \(\hbox {FE}^2\) ) homogenization approach is performed. It combines the macroscopic and microscopic scale by direct incorporation of the microscopic morphology. We derive the basic equations for the localization and the homogenization of the individual field variables and give an algorithmic expression for the effective tangent moduli. We discuss the influence of pores on the magneto-electric coupling in two-phase composites by analyzing numerical examples. PubDate: 2019-02-08 DOI: 10.1007/s00419-018-01500-1

Authors:M. Amara; O. Bouledroua; M. Hadj Meliani; Z. Azari; M. Tahar Abbess; G. Pluvinage; Z. Bozic Abstract: On the basis of the calculation of the stress field around the corrosion-damaged areas on the external part of a pipeline used for the transport of hydrocarbons, an analysis of the effect of the level of post-repair burst pressure by composite patches is proposed. This work examines some points of views on the burst pressure standards calculation on real test on pipeline with external corrosion defects. This study divided to three parts. In the first, an inspection is given for a real pipe exhibiting a surface corrosion defect. The corrosion defects were collected and divided into six important defects. The internal pressure has increased to the burst of pipeline. The second part illustrated a numerical study of the defects interaction effect on the safety of pipeline. The third part of this study is showing a finite element analysis of repaired pipe using the composite repair; we will study the effect of the composite sleeve number on the structural integrity of the pipe. The principle of failure assessment (FAD) diagram is described, and particularly, the definition of the non- dimensional applied crack tip loading \({k}_{\mathrm{r}}\) , the non- dimensional net applied stress (or load) \({S}_{\mathrm{r}}\) or \({L}_{\mathrm{r}}\) is given. The interest lays in the fact that many pipes defects are scratch or gouge types. In the FAD, results demonstrated that the composite repair method does not affect the interpolation curve and, at the same time, had a slightly effect on the function point. PubDate: 2019-02-07 DOI: 10.1007/s00419-019-01518-z

Authors:Bingqiang Li; Hui Ma; Xi Yu; Jin Zeng; Xumin Guo; Bangchun Wen Abstract: A dynamic model of a rotor-blade system is established considering the effect of nonlinear supports at both ends. In the proposed model, the shaft is modeled as a rotating beam where the gyroscopic effect is considered, while the shear deformation is ignored. The blades are modeled as Euler–Bernoulli beams where the centrifugal stiffening effect is considered. The equations of motion of the system are derived by Hamilton principle, and then, Coleman and complex transformations are adopted to obtain the reduced-order system. The nonlinear vibration and stability of the system are studied by multiple scales method. The influences of the normal rubbing force, friction coefficient, damping and support stiffness on the response of the rotor-blade system are investigated. The results show that the original hardening type of nonlinearity may be enhanced or transformed into softening type due to the positive or negative nonlinear stiffness terms of the bearing. Compared with the system with higher support stiffness, the damping of the bearing has a more powerful effect on the system stability under lower support stiffness. With the increase in rubbing force and support stiffness, the jump-down frequency, resonant peak and the frequency range in which the system has unstable responses increase. PubDate: 2019-02-07 DOI: 10.1007/s00419-019-01509-0

Authors:Stanislav Kotšmíd; Pavel Beňo Abstract: This paper presents a theoretical and experimental analysis of buckling load of the square wooden beams. The buckling tests were conducted on the wooden beams with three different lengths, and the critical buckling load was determined on the basis of the measured relation between the axial displacement and axial load. Analytical solutions for the critical buckling load of the beams were derived using the Euler–Bernoulli beam theory and Timoshenko beam theory. When deriving the models, both small and large deformation theories were considered. Moreover, the effect of a grain orientation was included in the models. The results show that the selected solution was in agreement with the values measured from the experiment. The paper provides a review of mathematical models and gives us a comparison between the theories and experiments with subsequent recommendations for practice. PubDate: 2019-02-07 DOI: 10.1007/s00419-019-01523-2

Authors:Jinyu Zhou; Wujun Chen; Jianhui Hu; Bing Zhao; Tengfei Zhang Abstract: Force finding of cable–strut structures is to identify self-equilibrated pre-stress states for structures with given shape, which is a crucial step in the structural design of flexible structures since pre-stresses significantly affect their mechanical behaviors. Utilizing symmetry properties of structures is generally considered as a practical way to facilitate the force finding process. To indicate the symmetric feature of structures, an algebraic indicator is proposed in the context of the equilibrium matrix theory. Furthermore, it is found that the orthogonal projection onto the null space of the equilibrium matrix could show the symmetry properties of structures geometrically. Then, a symmetry-based method of computing feasible pre-stress states is developed in the light of the above orthogonal projection. Finally, the proposed method is applied on three examples to confirm its validity and accuracy. PubDate: 2019-02-07 DOI: 10.1007/s00419-019-01517-0

Authors:Vishal Boddu; Paul Steinmann Abstract: The presence of a spontaneous and switchable polarization is the defining property of a ferroelectric material. Such materials are indispensable in a countless number of industrial and scientific applications. Furthermore, the enhancement of ferroelectric property at reduced dimensions is crucial for continuous advancement in nanoelectronic applications. In this work, we investigate the onset of out-of-plane ferroelectricity in open-circuited stress-free BaTiO \(_3\) ultrathin films by performing molecular dynamics simulations using the core–shell model potential. In doing so, we try to obtain electric polarization hysteresis loops using an appropriate range of external electric loading. It is found that out-of-plane ferroelectricity is suppressed in ultrathin films with thickness 10 or less than 10 unit cells, indicating that there exists a critical thickness for the emergence of out-of-plane ferroelectricity in ultrathin films. It is also found that the ultrathin films exhibit asymmetrical hysteresis loops slightly above the critical thickness. PubDate: 2019-02-04 DOI: 10.1007/s00419-019-01522-3

Authors:Alexander B. Freidin; Leah L. Sharipova Abstract: We relate two problems which arise from different branches of mechanics of materials: construction of limiting phase transformation surfaces in strain space and stress–strain diagrams for stress-induced phase transitions and optimal design of two-phase 3D composites in the sense of minimizing its energy. In Antimonov et al. (Int J Eng Sci 98:153–182, 2015) for the case of isotropic phases, it was shown that given a new phase volume fraction and depending on average strain, the strain energy of a two-phase linear-elastic composite is minimized by either direct or inclined simple laminates, direct or skew second-rank laminates or third-rank laminates. Then these results were applied for the construction of direct and reverse transformations limiting surfaces in strain space for elastic solids undergoing phase transformations by additional minimization with respect to the new phase volume fraction and finding the strains at which minimizing volume fraction equals zero or one. In the present paper we construct stress–strain diagrams on various straining paths at which a material undergoes the phase transformation. We demonstrate that an additional degree of freedom—new phase volume fraction—may crucially result in instability of two-phase microstructures even if the microstructures are energy minimizers for composites with given volume fractions of phases. This in turn may lead to incompleteness of monotonic phase transformations and broken stress–strain diagrams. We study how such a behavior depends on a loading path and chemical energies of the phases. PubDate: 2019-01-24 DOI: 10.1007/s00419-019-01510-7

Authors:Kyong-Ho Chang; Seong-Uk Kang; Zhen-Ming Wang; Shazia Muzaffer; Mikihito Hirohata Abstract: The results of a fatigue finite element analysis (FEA) based on the continuum damage mechanics of welding tubular members are presented. The effects of welding joint type on fatigue life and crack location were investigated. The initial mechanical state of a welded tubular member was simulated to identify initial welding imperfections such as welding residual stress and welding deformation using three-dimensional (3D) thermal elasto-plastic large-deformation FEA. The temperature history, which was simulated by using a 3D nonsteady heat conduction FEA, was used in the thermal elasto-plastic analysis as the initial thermal load. The welding joint type effects on fatigue life and crack location of a tubular member were investigated using 3D fatigue FEA. The effect of welding joint type on fatigue strength was also observed. It clarified that fatigue life was different depending on the joint type. Moreover, crack initiation and crack propagating direction of welded T- and K-type tube members were investigated. It was found that crack initiation takes place at different positions depending on the welding joint type. The 3D fatigue FEA method presented here is helpful in identifying fatigue crack location and ascertaining fatigue life. PubDate: 2019-01-21 DOI: 10.1007/s00419-019-01513-4

Authors:Andrej Cherkaev; Michael Ryvkin Abstract: The paper demonstrates a rational design of an isotropic heterogeneous beam lattice that is fault-tolerant and energy-absorbing. Combining triangular and hexagonal structures, we calculate elastic moduli of obtained hybrid heterogeneous structures; simulate the development of flaws in that composite lattice subjected to a uniform uniaxial deformation; investigate its damage evolution; measure various characteristics of damage that estimate fault tolerance; discuss the trade-off between stiffness and fault tolerance. A design is found that develops a cloud of small evenly spread flaws instead of a crack. PubDate: 2019-01-21 DOI: 10.1007/s00419-018-1428-0

Authors:Vuong Nguyen Van Do; Kyong-Ho Chang; Chin-Hyung Lee Abstract: This study introduces an accurate and effective mesh-free approximation based on the radial point interpolation method (RPIM) to predict the post-buckling responses of FGM plates in mechanical edge compression. In the RPIM, a new radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. The equilibrium and governing equations for the plate are derived by using the higher-order shear deformation theory in which a new hybrid type transverse shear function is incorporated in order to better represent the displacement fields. A von Kármán type nonlinear equation which accounts for both the geometric nonlinearity and the initial geometric imperfection is constructed. A solution procedure based on the total Lagrangian formulation to trace the post-buckling path, which utilizes the modified Newton–Raphson method, is designed. The numerical results illustrate the accuracy of the proposed meshless method for predicting the post-buckling behavior of FGM plates. PubDate: 2019-01-17 DOI: 10.1007/s00419-019-01512-5

Authors:I. Comez; K. B. Yilmaz; M. A. Güler; B. Yildirim Abstract: In this study, contact problem for a homogeneous orthotropic layer loaded by a rigid cylindrical stamp is considered. The rigid cylindrical stamp slides over the contacting medium whose bottom surface is fixed to the ground in all directions. Using the integral transformation technique, the contact problem is formulated analytically into a singular integral equation. The resulting integral equation is converted to algebraic equations by using Gauss–Jacobi integration formulas and solved numerically. In addition to the analytical formulation, a finite element method (FEM) study is also conducted. The results that are obtained using FEM are compared with the results found using analytical formulation. It is found that the results obtained from analytical formulation and FEM study are in good agreement with each other. The primary intention of this paper is to demonstrate the effects of orthotropic material properties, geometrical properties and the coefficient of friction on the stresses generated due to the sliding motion of the rigid cylindrical stamp. The results of this study may provide benchmark results for engineers to be used in tribology applications involving friction and wear mechanisms. PubDate: 2019-01-17 DOI: 10.1007/s00419-019-01511-6

Authors:Zhenyong Lu; Xiaodong Wang; Lei Hou; Yushu Chen; Xiyu Liu Abstract: This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system. PubDate: 2019-01-09 DOI: 10.1007/s00419-018-01501-0

Authors:Maciej Klemiato; Piotr Czubak Abstract: Vibratory conveyors are very important elements of production lines. Very often there is a need to change the feed transport velocity, especially in the case of feeders, or to alter the transport direction in the case of symmetric production lines. The transport possibilities of the new vibratory conveyor, allowing fast changes of the velocity and direction of transporting, solely by changes of the angular velocity of the excitation vibrator, and patented by the authors, are analysed in this paper. The innovatory control method allowing fast changes of the transport direction and good stabilisation of the given velocity, without the need to pass through its resonance frequencies, is presented. This new solution increases the safety and functionality of machine operations. PubDate: 2019-01-04 DOI: 10.1007/s00419-018-01507-8

Authors:Michele De Angelo; Emilio Barchiesi; Ivan Giorgio; B. Emek Abali Abstract: Mechanical properties are investigated for a class of microstructured materials with promising applications. Specifically, we consider a composite material with orthogonal, mutually interconnected fibers building a pantographic substructure. In order to predict the behavior of such a system in three-dimensional continuum, a reduced-order model is introduced by means of a bi-dimensional elastic surface accurately describing large deformations. The properties of this reduced-order model are characterized by an elastic energy density that involves second space derivatives of the displacement for capturing the resistance of twisted and bent fibers in plane as well as out of plane. For determining the coefficients in the elastic energy of the reduced-order model, we utilize a numerical inverse analysis and make use of ad hoc computational experiments performed by a direct numerical simulation on the microscale with detailed modeling of the pantographic substructure. This reduced-order model represents a homogenized material on macro-scale with its substructure on microscale. The homogenized model is capable of describing materials response at a significantly less computational cost than the direct numerical simulations. PubDate: 2019-01-03 DOI: 10.1007/s00419-018-01506-9