Authors:A. Nasrnia; F. Haji Aboutalebi Pages: 1461 - 1475 Abstract: Abstract In brittle or quasi-brittle materials, mechanical fracture phenomenon occurs suddenly and without any warning. Therefore, prediction of brittle materials failure is an essential challenge confronting design engineers. In this research, using the conventional finite element method (CFEM) and extended finite element method (XFEM) based on linear elastic fracture mechanics, rupture behavior of U-notch specimens under mixed mode loadings are numerically and practically studied. As the main contribution and objective of the current study, two different fracture criteria established on CFEM and six various criteria founded on XFEM are employed to numerically predict load carrying capacity and crack initiation angle of the U-notch samples. Also, the load carrying capacity and crack initiation angle are experimentally obtained from tensile tests of the U-notch instances under planar mixed mode loading to verify the simulation results. The empirical results are compared with the corresponding estimated values achieved by CFEM and XFEM methods which permit to assess the accuracy of the mentioned criteria in predicting the load carrying capacity and crack initiation angle of U-notch coupons subjected to mixed mode loadings, as the novelty of the investigation. The comparison shows that although both the CFEM and XFEM can properly predict the load carrying capacity and crack initiation angle, applying the XFEM in addition to reduce the computational costs and mesh sensitivity is more precise. Besides, a comparison between the XFEM results denotes that stress-based models are significantly more accurate than strain-based types in predicting the load carrying capacity and crack initiation angle of the U-notch instances under mixed mode loading. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1381-y Issue No:Vol. 88, No. 9 (2018)

Authors:Ranita Roy; Soumen De; B. N. Mandal Pages: 1477 - 1489 Abstract: Abstract The problem of water wave scattering by three thin vertical barriers present in infinitely deep water is investigated assuming linear theory. Out of the three, two outer barriers are partially immersed and the inner one is fully submerged and extends infinitely downwards. Havelock’s expansion of water wave potential along with inversion formulae is employed to reduce the problem into a set of linear first-kind integral equations which are solved approximately by using single-term Galerkin approximation technique. Very accurate numerical estimates for the reflection and transmission coefficients are then obtained. The numerical results obtained for various arrangements of the three vertical barriers are depicted graphically in several figures against the wavenumber. These figures exhibit that the reflection coefficient vanishes at discrete wavenumbers only when the two outer barriers are identical. Few known results of a single submerged wall with a gap, single fully submerged barrier extending infinitely downwards, and two barriers partially immersed up to the same depth in deep water are recovered as special cases. This establishes the correctness of the method employed here. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1382-x Issue No:Vol. 88, No. 9 (2018)

Authors:Mousa Rezaee; Vahid Shaterian-Alghalandis Pages: 1491 - 1506 Abstract: Abstract In this paper, by analyzing the geometrically nonlinear vibrations of a cracked beam under harmonic excitation, a new crack sensitive parameter is introduced to recognize the open edge crack in a beam. The beam is assumed to be clamped at both ends, so that, increasing the amplitude of vibration results in stretching of the beam longitudinally and causes the beam vibrations to be geometrically nonlinear. By extracting the nonlinear forced vibration equations and solving them using perturbation method, the steady state response of the beam to harmonic excitation with a frequency close to one of the three first natural frequencies is obtained analytically. These responses are then Hilbert transformed, and instantaneous amplitudes are obtained in each case. Based on these data, a new parameter is extracted which is shown to be dependent only on the modal parameters of the cracked beam. Then, this parameter which we call it “Crack Index” is used to detect the crack in a beam under the geometrically nonlinear vibration. It is shown that while the amount of data needed to obtain the crack indexes is the same as those needed to obtain the natural frequencies, these indexes are much more sensitive to crack than the modal parameters. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1383-9 Issue No:Vol. 88, No. 9 (2018)

Authors:Guannan Wang Pages: 1525 - 1543 Abstract: Abstract This work presents the elastic solutions for the separable problems, where certain coordinate variables in the boundary and continuity conditions in terms of series representations can be eliminated to simplify the systems of equations. The definition of “separable problems” is clarified, which is mainly because the internal displacement or stress fields and the outer boundary conditions share similar patterns of series expansions in the same coordinate systems. Several types of separable problems are illustrated in the introduction to show the applicability and importance of the present theory. The multilayered hollow cylinders are employed to explain the procedure of solving similar types of boundary value problems. A special application of the multilayered cylinders is to embed them into an infinite plate with a hole at the center, where a layer-by-layer functional gradation along the radial direction could lead to the reduction of the stress concentrations. Besides validating the accuracy of the derivations against the solution of a continuously graded cylinder and the original Kirsch solutions, the effects of the geometrical and material properties on the stress distributions are also tested. The idea of solving separable problems can significantly contribute to the theoretical analysis and design of discretely graded structures with various geometries. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1385-7 Issue No:Vol. 88, No. 9 (2018)

Authors:Fabio Di Carlo; Simona Coccia; Zila Rinaldi Pages: 1545 - 1558 Abstract: Abstract In this work, the collapse load of a masonry arch subjected to an actual horizontal displacement of the supports is assessed, in the deformed configuration of the structure, by means of limit analysis theory. Masonry is modelled as a rigid in compression, no-tension material and avoiding the occurrence of sliding failures. A numerical tool, based on the approach of the kinematical theorem of the collapse state, is proposed for the collapse computation of circular arches subjected to dead loads and to incremental concentrated load applied at their crown. A parametric study has been carried out in order to develop a deeper understanding of the influence of the involved parameters. It is shown that the existence of a kinematically admissible collapse mechanism is correlated to a thickness/mean radius ratio dependent on the value of the actual horizontal displacement of the supports. In the paper, a relationship between these two last parameters is proposed. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1386-6 Issue No:Vol. 88, No. 9 (2018)

Authors:Amit Kumar; Santosh Kapuria Pages: 1573 - 1594 Abstract: Abstract We present an enriched finite element (FE) formulation applicable for general wave propagation problems in one- and two-dimensional domains, using local element domain spatial harmonic enrichment functions which satisfy the partition of unity condition. It allows prescription of boundary conditions in the same way as in the conventional FE method. The method is assessed for different classes of wave propagation problems such as impact and high frequency-guided wave propagation in bars and plates, and surface and body wave propagation in semi-infinite solid media for which the classical FE method either fails to yield accurate results or is prohibitively expensive. It is shown that the present formulation gives accurate solutions to the former and shows significant improvement in computational efficiency for the latter category of problems. The performance is also assessed against other special FEs such as the spectral FE and a recently proposed enriched FE with global harmonic basis functions. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1388-4 Issue No:Vol. 88, No. 9 (2018)

Authors:Junnan Lv; Li Yu; Wei Du; Qun Li Pages: 1637 - 1656 Abstract: Abstract The conversion problem of plane strain fracture toughness ( \(K_\mathrm{IC}\) ) which is necessarily measured according to ASTM standards, to lower constraint applications generally existing in engineering structures, has led to extensive material and labor costs. The present paper explores and quantifies the crack-tip constraint effects by the crack-tip plastic zone to serve the prediction of material’s fracture toughness. Firstly, the approximate three-dimensional crack front displacement fields are obtained by using the variable separation method. The three-dimensional stress field is then used to predict the shape and size of the crack-tip plastic zone. Secondly, the two-dimensional in-plane and the three-dimensional out-of-plane geometric constraint effects are quantified separately, and two constraint factors, i.e., \(\alpha _\mathrm{in}\) and \(\alpha _\mathrm{out}\) are proposed. A series of configurations of the two-dimensional and three-dimensional crack-tip plastic zones that vary with the specimen’s geometric size (plate width, thickness, etc.) are presented, which will facilitate a better understanding of the crack-tip constraint effect. Finally, the present method is applied to elucidate the significant “thickness effect” of the X70 pipeline steel’s fracture toughness by using the out-of-plane constraint factor \(\alpha _\mathrm{out}\) . The corresponding results are compared with the experimentally measured and FEM-predicted fracture toughness \(K_\mathrm{C}\) . It is concluded that the parameters \(\alpha _\mathrm{out}\) and the fracture toughness \(K_\mathrm{C}\) can be correlated with each other, which will be beneficial to the prediction of material’s fracture toughness and the avoidance of experimental costs. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1392-8 Issue No:Vol. 88, No. 9 (2018)

Authors:Ulrich Werner Pages: 1657 - 1682 Abstract: Abstract In the paper, the vibration control of induction motors with sleeve bearings—mounted on soft steel frame foundations—using active motor foot mounts is analyzed. The presented model is based on a multibody model, considering electromagnetic influence, stiffness, and rotating damping of the rotor, stiffness and damping of the bearing housings with end shields, of the oil film in the sleeve bearings, and of the foundation. Additionally, the stiffness and damping of the motor foot mounts—which are positioned between the motor feet and the steel frame foundation—are considered, as well as the controlled forces which are applied in the vibration system by the motor foot mounts, using PD-controllers. The aim of the paper is to unite all these influences in a mathematical model, including the control system. Based on a numerical example, it can be shown that the vibration behavior of soft mounted induction motors can be clearly improved and that critical speeds in the speed range can be avoided, using active motor foot mounts. PubDate: 2018-09-01 DOI: 10.1007/s00419-018-1393-7 Issue No:Vol. 88, No. 9 (2018)

Authors:A. B. Movchan; R. C. McPhedran; G. Carta; R. V. Craster Abstract: Abstract In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring–mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring–mass resonators can be tuned to produce a “negative inertia” input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes. PubDate: 2018-09-20 DOI: 10.1007/s00419-018-1465-8

Authors:F. Mottaghian; A. Darvizeh; A. Alijani Abstract: Abstract A new one-dimensional finite element model is developed to investigate the nonlinear elastic response of cracked beams. Classical and continuum-based approaches are adopted into four different nonlinear theories to derive relationships which characterize the influence of initial cracks on the bending behavior of beams subjected to quasi-static loading. A linear rotational spring is used to simulate the crack whose stiffness factor is considered in terms of the geometric parameters of the crack. A cracked element is subdivided into two sub-elements, and the conditions of continuity are maintained in the crack position. By implementing a novel technique in this element, the tangent and secant stiffness matrices and the internal force vector are originally enriched due to the crack properties. Some case studies are performed to compare the rate of convergence, the accuracy of the theories, the difference in results obtained from linear and nonlinear analyses and the effects of the depth and the position of single and double cracks on the deflection pattern. PubDate: 2018-09-20 DOI: 10.1007/s00419-018-1460-0

Authors:Silvio Tschisgale; Louis Thiry; Jochen Fröhlich Abstract: Abstract The present paper provides a collision model for Cosserat rods, able to represent a very general collision response, including frictional effects as well as multiple simultaneous collisions of a large number of rods. The proposed collision model falls into the category of constraint-based collision models. This concept is extended to a general class of objects sharing properties of rigid and deformable bodies, here undertaken for viscoelastic Cosserat rods. The collision constraints are imposed by collision impulses added to the external loads of the equations of motion of the colliding objects. No iterations between the equations of motion and the collision model are required. Both parts are executed in a staggered manner, so that the collision model is well separated from the equations of motion. Hence, existing solvers for Cosserat rods or similar objects can easily be extended, so that the range of application is significantly enlarged to the collisional regime. Extensive validations are presented using various test cases, ranging from a collision of a single rod with a wall to more realistic configurations with multiple simultaneous collisions of numerous rods. PubDate: 2018-09-19 DOI: 10.1007/s00419-018-1458-7

Authors:T. Bartel; R. Schulte; A. Menzel; B. Kiefer; B. Svendsen Abstract: Abstract This contribution deals with investigations on enhanced Fischer–Burmeister nonlinear complementarity problem (NCP) functions applied to a rate-dependent laminate-based material model for ferroelectrics. The framework is based on the modelling and parametrisation of the material’s microstructure via laminates together with the respective volume fractions. These volume fractions are treated as internal-state variables and are subject to several inequality constraints which can be treated in terms of Karush–Kuhn–Tucker conditions. The Fischer–Burmeister NCP function provides a sophisticated scheme to incorporate Karush–Kuhn–Tucker-type conditions into calculations of internal-state variables. However, these functions are prone to numerical instabilities in their original form. Therefore, some enhanced formulations of the Fischer–Burmeister ansatz are discussed and compared to each other in this contribution. PubDate: 2018-09-18 DOI: 10.1007/s00419-018-1466-7

Authors:Christoph Schopphoven; Kerstin Birster; Rouven Schweitzer; Christian Lux; Shilin Huang; Markus Kästner; Günter Auernhammer; Andreas Tschöpe Abstract: Abstract Magnetic nanocomposites were prepared by dispersing uniaxial ferromagnetic Ni nanorods in poly(acrylamide) hydrogels. Field alignment of the nanorods during polymerization resulted in a magnetic texture which was explored for field-induced deformations in the elastic composite. At very low particle volume fraction \(<10^{-6}\) , the magnetic torque resulted in a local rotation of the nanorods, measured by optical transmission of linearly polarized light, with a field- and orientation dependence in agreement with the Stoner–Wohlfarth model. The local rotation was virtually unaffected by an increase in the volume fraction to \(\sim 10^{-4}\) which suggested negligible interparticle interactions or mutual compensation of opposing contributions. Elastic interactions, mediated by the deformation of the matrix, were investigated by FEM simulations for nanorods of different aspect ratio and relative spatial positions. Complementary experiments were performed by measuring the rotation of individual nanorods using laser scanning confocal microscopy. The results suggest interparticle interactions to be negligible in textured nanorod composites up to a volume fraction of \(10^{-4}\) . Macroscopic deformations of Ni nanorod/hydrogel magnetic actuators in this concentration regime are expected to be solely determined by the intrinsic properties of the nanorods which was demonstrated using the example of a torsion cylinder. PubDate: 2018-09-17 DOI: 10.1007/s00419-018-1461-z

Authors:Andrej Cherkaev; Michael Ryvkin Abstract: Abstract The paper studies damage propagation in brittle elastic beam lattices, using the quasistatic approach. The lattice is subjected to a remote tensile loading; the beams in the lattice are bent and stretched. An introduced initial flaw in a stressed lattice causes an overstress of neighboring beams. When one of the overstressed beams fails, it is eliminated from the lattice; then, the process repeats. When several beams are overstressed, one has to choose which beam to eliminate. The paper studies and compares damage propagation under various criteria of the elimination of the overstressed beams. These criteria account for the stress level, randomness of beams properties, and decay of strength due to micro-damage accumulation during the loading history. A numerical study is performed using discrete Fourier transform approach. We compare damage patterns in triangular stretch-dominated and hexagonal bending-dominated lattices. We discuss quantitative characterization of the damage pattern for different criteria. We find that the randomness in the beam stiffness increases fault tolerance, and we outline conditions restricting the most dangerous straight linear crack-like pattern. PubDate: 2018-09-17 DOI: 10.1007/s00419-018-1429-z

Authors:Jiaxing Cheng; Bin Sun; Mengyun Wang; Zhaoxia Li Abstract: Abstract In this paper, a fracture problem in a rectangular plate of functionally graded piezoelectric/piezomagnetic material is investigated. The physical parameters of FGM are assumed to continuously vary along the axis-x. Two magneto-electric types of crack surface are considered, permeable type and impermeable type. A semi-inverse method is used to reduce the problem to power-series equations with the boundary collocation method employed, as numerical method, to calculate these equations in the finite region. The effects on fracture behavior of the gradient parameter, combing magneto-electric loads and two types of crack surface, are investigated. An increase in the gradient parameter is accompanied by a decrease in the ability of FGM to fracture. Increasing the magnetic load, as opposed to the electric load, promotes crack initiation and growth. Under the magneto-electrically permeable assumption, the electric and magnetic loads have no impact on the potentials field in terms of the crack singularity. On the other hand, when impermeable type is involved, the electric and magnetic loads make a critical contribution to the crack tip singularity. PubDate: 2018-09-17 DOI: 10.1007/s00419-018-1462-y

Authors:Barbara Kaltenbacher; Pavel Krejčí Abstract: Abstract The problem of optimal energy harvesting for a piezoelectric element driven by mechanical vibrations is stated in terms of an ODE system with hysteresis under the time derivative coupling a mechanical oscillator with an electric circuit with or without inductance. In the piezoelectric constitutive law, both the self-similar piezoelectric butterfly character of the hysteresis curves and feedback effects are taken into account in a thermodynamically consistent way. The physical parameters of the harvester are chosen to be the control variable, and the goal is to maximize the harvested energy for a given mechanical load and a given time interval. If hysteresis is modeled by the Preisach operator, the system is shown to be well-posed with continuous data dependence. For the special case of the play operator, we derive first-order necessary optimality conditions and an explicit form of the gradient of the total harvested energy functional in terms of solutions to the adjoint system. PubDate: 2018-09-17 DOI: 10.1007/s00419-018-1459-6

Authors:Dmitry Borin; Gennady Stepanov; Eike Dohmen Abstract: Abstract This study focusses on a magnetoactive elastomeric composite based on a polydimethylsiloxane matrix highly filled with a mixed magnetic powder. The powder contains a mixture of carbonyl iron and magnetically hard NdFeB alloy spherical microparticles. Magnetoactive elastomer samples with different ratios of the magnetically hard and soft filler were synthesized and characterized using dynamic axial loading. Behavior of the composites was compared with the behavior of a conventional magnetorheological elastomer based solely on magnetically soft particles. It was found that the passive state and active state properties of the magnetoactive composites with mixed powders can be separately tuned. The passive state properties may be changed by pre-magnetization of the magnetically hard particles influencing composite’s remanence, while the active state properties can be controlled by applying external magnetic field. The range of passive tuning and active control depends on the amount of magnetically hard and soft components. Using external fields up to 1500 mT for a pre-magnetization and fields up to 240 mT for investigation of the active control, it was found that the passive change of samples’ storage modulus and loss factor may reach up to \(\sim \) 30–100%, while within active control these parameters can be changed up to \(\sim \) 50–200%. PubDate: 2018-09-12 DOI: 10.1007/s00419-018-1456-9

Authors:B. Shekastehband Abstract: Abstract A major deficiency of tensegrity structures which may prevent wide spread application of them in practice is their low structural efficiency in terms of initial stiffness and ultimate strength. Further, the collapse of these structures can be initiated by the buckling of a few struts, which may propagate to other elements of these systems and finally cause overall collapse. Using force-limiting devices (FLDs) and high-stiffness cables can be the primary enhancement techniques for abrupt collapse prevention as well as achieving efficient behavior to ensure the satisfactory performance of these structures exposed to extreme events. In the present study, static and dynamic collapse analyses have been conducted to evaluate the effects of FLDs and high-stiffness cables on the collapse behavior and structural efficiency of these structures. From the results, it is found that an increase of 145% in the cable elastic modulus increases the initial stiffness of tensegrity structures by approximately 135%. Using FLDs in a small selection of the most critical struts can lead to increases of up to 52% in tensegrity structures strength. Irrespective of cable stiffness, using FLDs can be more beneficial in altering the collapse mechanism of these structures. PubDate: 2018-09-11 DOI: 10.1007/s00419-018-1455-x

Authors:Marina Bošković; Radovan R. Bulatović; Slaviša Šalinić; Goran R. Miodragović; Gordana M. Bogdanović Abstract: Abstract This paper presents an optimization technique for dynamic balancing of a four-bar mechanism for the purpose of minimization of joint reactions, shaking forces and shaking moment. Joint reaction forces were determined by using a new method which can be applied in rigid planar closed-loop kinematic chains with revolute joints, and it is based on the use of absolute angles of rotation. The problem of balancing the obtained joint reaction forces was then solved as a multi-objective optimization problem. Kinematic and dynamic parameters of the four-bar linkage were taken as design variables. Three cases with simultaneous minimization of several objective functions were considered. The new hybrid algorithm named Hybrid Cuckoo Search and Firefly Algorithm (H-CS-FA) was used for solving the defined optimization problem in accordance with the given constraints. The appropriate selection of objective functions (three cases) and the application of the proposed algorithm resulted in a significant reduction of the values of joint reactions, shaking forces, shaking moment and driving torque. A concrete numerical example was used to show the efficiency of the new hybrid algorithm. The results obtained by H-CS-FA are compared with those obtained by using basic algorithms in the hybridization process (CS and FA) which proved the superiority of the newly proposed optimization procedure. PubDate: 2018-09-11 DOI: 10.1007/s00419-018-1457-8

Authors:Xuejuan Niu; Wenfeng Pan; Yang Li Abstract: Abstract Steered-fiber placement has been a very interesting approach to enhance the mechanical properties of fiber-reinforced composite structures, especially with holes. Based on flow field theory and the Levenberg–Marquardt algorithm, the fiber orientations on a variable stiffness (VS) ply in a composite plate with a central hole are represented and optimized. The fiber orientations on the VS plies are aligned with those of the maximum principal stress as much as possible. By transforming the complex planning problem of curvilinear trajectory into the function design of a scalar field, this method leads to better efficiency and general optimization. Comparative failure analysis based on the MCT criterion shows that the VS model has a 197% higher capability for initial damage and a 97% higher capability for ultimate load. The contour plots of the failure state and the load–displacement plots also certify the validity and the feasibilities of the proposed VS planning method. PubDate: 2018-09-06 DOI: 10.1007/s00419-018-1454-y