Authors:Ibrahim Goda; Jean-François Ganghoffer Pages: 2101 - 2121 Abstract: As a living tissue, bone is subjected to internal evolutions of its trabecular architecture under normal everyday mechanical loadings leading to damage. The repeating bone remodeling cycle aims at repairing the damaged zones in order to maintain bone structural integrity; this activity of sensing the peak stress at locations where damage or microcracks have occurred, removing old bone and apposing new bone is achieved thanks to a complicated machinery at the cellular level involving specialized cells (osteocytes, osteoclasts, and osteoblasts). This work aims at developing an integrated remodeling-to-fracture model to simulate the bone remodeling process, considering trabecular bone anisotropy. The effective anisotropic continuum mechanical properties of the trabecular bone are derived from an initially discrete planar hexagonal structure representative of femur bone microstructure, relying on the asymptotic homogenization technique. This leads to scaling laws of the effective elastic properties of bone versus effective density at an intermediate mesoscopic scale. An evolution law for the local bone apparent density is formulated in the framework of the thermodynamics of irreversible processes, whereby the driving force for density evolutions is identified as the local strain energy density weighted by the locally accumulated microdamage. We adopt a classical nonlinear damage model for high cycle fatigue under purely elastic strains, where the assumed homogeneous damage is related to the number of cycles bone experiences. Based on this model, we simulate bone remodeling for the chosen initial microstructure, showing the influence of the external mechanical stimuli on the evolution of the density of bone and the incidence of this evolution on trabecular bone effective mechanical properties. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1438-y Issue No:Vol. 88, No. 12 (2018)

Authors:Baisheng Wu; Yang Zhou; C. W. Lim; Weipeng Sun Pages: 2123 - 2134 Abstract: New and expressive analytical approximate solutions to resonance response of harmonically forced strongly odd nonlinear oscillators are proposed. This method combines Newton’s iteration with the harmonic balance method. Unlike the classical harmonic balance method, accurate and explicit analytical approximate solutions are established because linearization of the governing nonlinear differential equation is conducted prior to harmonic balancing. The approach yields simple linear algebraic equations instead of nonlinear algebraic equations which have no analytical solution. With carefully constructed corrective measures, only one single iteration is required to obtain very accurate analytical approximate solutions to resonance response. It is found that since determination of stability of the initial approximate solution that resulted from the single-term harmonic balance can lead to erroneous conclusions, correction to the solution is necessary. Three examples are presented to illustrate the applicability and effectiveness of the proposed technique. Specially, for oscillations in high-energy orbits of the bistable Duffing oscillator, the proposed method can also give excellent analytical approximate solutions. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1439-x Issue No:Vol. 88, No. 12 (2018)

Authors:Georgios A. Drosopoulos; Georgios E. Stavroulakis Pages: 2135 - 2152 Abstract: A computational homogenization method is presented in this article, for the investigation of localization phenomena arising in periodic masonry structures. The damage of the macroscopic, structural scale is represented by cohesive cracks, simulated by the extended finite element method. The cohesive traction–separation law along these cracks is built numerically, using a mesoscopic, fine scale, masonry model discretized by classical finite elements. It consists of stone blocks and the mortar joints, simulated by unilateral contact interfaces crossing the boundaries of the mesoscopic structure, assigned a tensile traction–separation softening law. The anisotropic damage induced by the mortar joints can be depicted by this method. In addition, the non-penetration condition between the stone blocks is incorporated in the averaging relations. Sophisticated damage patterns, depicted by several continuous macro-cracks in the masonry structure, can also be represented by the proposed approach. Finally, results are compared well with experimental investigation published in the literature. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1440-4 Issue No:Vol. 88, No. 12 (2018)

Authors:Carmine Maria Pappalardo; Domenico Guida Pages: 2153 - 2177 Abstract: The goal of this investigation is to perform a comparative analysis of the principal methodologies employed for the analytical formulation and the numerical solution of the equations of motion of rigid multibody mechanical systems. In particular, three formulation approaches are considered in this work for the analytical formulation of the equations of motion. The multibody formulation strategies discussed in this paper are the Reference Point Coordinate Formulation with Euler Angles (RPCF-EA), the Reference Point Coordinate Formulation with Euler Parameters (RPCF-EP), and the Natural Absolute Coordinate Formulation (NACF). Moreover, five computational algorithms are considered in this investigation for the development of effective and efficient solution procedures suitable for the numerical solution of the equations of motion. The multibody computational algorithms discussed in this paper are the Augmented Formulation (AF), the Embedding Technique (ET), the Amalgamated Formulation (AMF), the Projection Method (PM), and the Udwadia-Kalaba Equations (UKE). The multibody formulation approaches and solution procedures analyzed in this work are compared in terms of generality, versatility, ease of implementation, accuracy, effectiveness, and efficiency. In order to perform a general comparative study, four benchmark multibody systems are considered as numerical examples. The comparative study carried out in this paper demonstrates that all the methodologies considered can handle general multibody problems, are computationally effective and efficient, and lead to consistent numerical solutions. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1441-3 Issue No:Vol. 88, No. 12 (2018)

Authors:Chao Fu; Xiao Yang Pages: 2179 - 2198 Abstract: In this paper, the Kant higher-order beam theory is applied to model each segment of the partial-interaction composite beams, aiming to capture as possible fidelity as the plane stress model. On this basis, the weak-form equation is obtained through the principle of virtual work. Besides, the weak-form quadrature element (WQE), as a counterpart of the conventional finite element (CFE), is derived and implemented to more efficiently solve problems, including free vibration eigenvalue analysis and dynamic responses prediction to moving loads. After the verification of all the programs developed, a series of numerical examples are given to investigate the WQE’s superiority on convergence rate and numerical smoothness over the CFE. At the end of the paper, the influences of structural damping and loads’ moving speed on impact factor of two-span continuous beams are analyzed. Numerical results show that the proposed WQE, due to the variable-order interpolation of the element, possesses overwhelmingly higher computational efficiency than the CFE, and the numerical smoothness problem in the internal force analysis is significantly alleviated by WQE method. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1443-1 Issue No:Vol. 88, No. 12 (2018)

Authors:Pengcheng Liu; Hongnian Yu; Shuang Cang Pages: 2199 - 2219 Abstract: This paper studies the nonlinear dynamics of a two-degree-of-freedom vibro-driven capsule system. The capsule is capable of rectilinear locomotion benefiting from the periodic motion of the driving pendulum and the sliding friction between the capsule and the environmental surface in contact. Primary attentions are devoted to the dynamic analysis of the motion and stick-slip effect of the capsule system. Following a modal decoupling procedure, a profile of periodic responses is obtained. Subsequently, this work emphasizes the influences of elasticity and viscosity on the dynamic responses in a mobile system, whose implicit qualitative properties are identified using bifurcation diagrams and Poincaré sections. A locomotion-performance index is proposed and evaluated to identify the optimal viscoelastic parameters. It is found that the dynamic behaviour of the capsule system is mainly periodic, and the desired forward motion of the capsule can be achieved through optimal selection of the elasticity and viscosity coefficients. In view of the stick-slip motion, the critical equilibrium and its dynamic behaviours, different regions of oscillations of the driving pendulum are identified, with the attention focusing on the critical region where linearities are absent and nonlinearities dominate the dynamic behaviour of the pendulum. The conditions for stick-slip motions to achieve a pure forward motion are investigated. The proposed approach can be adopted in designing and selecting of suitable operating parameters for vibro-driven or joint-actuated mechanical systems. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1444-0 Issue No:Vol. 88, No. 12 (2018)

Authors:R. R. Labibov; Yu. A. Chernyakov; A. E. Sheveleva; A. G. Shevchenko Pages: 2221 - 2230 Abstract: Model of slip band propagation in materials with yielding plateau is introduced. Development of a slip band is modeled in a form of loss of stability during transition of the material from an elastic state to hardening. This transition is the generalization of crack mode I development model by Novozhilov (J Appl Math Mech 3:201–210, 1969) in elastic solids. Possibility for slip bands of limited length is shown in the model in contrast to ideal plasticity model that only leads to infinite slip bands. Problems of localization in a form of slip bands in a state for the pure shear and for intermaterial layer are considered. For different external loads and various mechanical properties of the interlayer, the lengths of the localization zone of plastic deformations, the graphs of the tangential displacement jump in this zone, and the shear stress on their continuation are found. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1445-z Issue No:Vol. 88, No. 12 (2018)

Authors:Mohammad Hadi Izadi; Shahrokh Hosseini-Hashemi; Moharam Habibnejad Korayem Pages: 2231 - 2246 Abstract: In this study, the free vibration analysis of two joined laminated conical shells is investigated. Five equilibrium equations for each conical shell have been derived in a particular coordinate system; using Hamilton’s principle and first-order shear deformation theorem. The analytical solutions are obtained in the form of power series based on separation of variables method. The boundary conditions at both ends of the joined shells and the continuity conditions, at the conical shells contact, are extracted from energy formulations. As a result, the non-dimensional natural frequencies are studied for cross-ply laminated shells. The effects of semi-vertex angle, circumferential modes, number of layers, thickness, length of shells and different boundary conditions on non-dimensional frequencies are considered. As a comparing result, the non-dimensional frequencies and mode shapes are extracted using finite element method (FEM). The results are compared and verified with the previous available results in other researches. The results reveal a good agreement among analytical solutions, FEM and other results. The output of this paper can be used for analyzing cylindrical–conical shells in addition to joined conical shells. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1446-y Issue No:Vol. 88, No. 12 (2018)

Authors:Zhongwei Zhao; Jinjia Wu; Bing Liang; Haiqing Liu; Qingwei Sun Pages: 2247 - 2260 Abstract: The post-tensioned energy dissipating connection for steel frames has drawn considerable attention because of its good seismic performance. Friction mechanisms, such as friction damped post-tensioned (FDPT) steel connections, are typically used to improve energy dissipating capacity. Many researchers have investigated the seismic behavior of FDPT through numerical or experimental method. Prior studies have indicated that the analysis by elaborate FE models is very time-consuming. To overcome this disadvantage, a friction element was first proposed based on general FE code and then incorporated into a simplified numerical model of PT connection to consider the effects of friction. The accuracy of results derived by this model was validated against prior experimental investigations. The effects of friction force value and initial PT force seismic behavior of FDPT connection was investigated. The geometric and material nonlinearities and strands can be considered in the modeling. A planar steel frame structure was established, and hysteretic analysis was conducted in the end. Results indicated the computational cost can be reduced significantly by this model. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1449-8 Issue No:Vol. 88, No. 12 (2018)

Authors:Manish Kumar Dubey; Satyajit Panda Pages: 2261 - 2281 Abstract: An extension mode piezoelectric fiber composite (PFC) actuator with cylindrically periodic microstructure is presented in this work especially for directional actuation of plane structures of revolution. The PFC actuator is designed in the form of a thin annular disk where the continuous piezoelectric fibers are periodically distributed along the circumferential direction to yield the directional actuation along the radial direction in the cylindrical principal material coordinate system. This kind of microstructure of the annular PFC actuator yields its radially varying electromechanical properties that are determined through the asymptotic segmentation of its (PFC) volume into a large number of microvolumes of different fiber volume fractions. The closed-form expressions for the effective electromechanical coefficients of the microvolumes are derived, and the corresponding verification is carried out through the numerical homogenization using finite element procedure. The results reveal the indicative magnitude of an effective piezoelectric coefficient ( \(e_{31})\) that quantifies the directional actuation along the radial direction. But, the magnitude of this coefficient ( \(e_{31})\) decreases indicatively with the increasing radius, and thus the annular PFC actuator is redesigned in a special manner for the improved magnitude of the coefficient ( \(e_{31})\) at any radius. With these improved properties of the annular PFC actuator, its indicative actuation capability in control of vibration of an annular plate is observed, and thus this annular PFC actuator may be recommended for active control of plane structures of revolution specifically where the actuation along the radial direction is the major requirement. PubDate: 2018-12-01 DOI: 10.1007/s00419-018-1451-1 Issue No:Vol. 88, No. 12 (2018)

Authors:Xuejuan Niu; Wenfeng Pan; Yang Li Pages: 2283 - 2292 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: 2018-12-01 DOI: 10.1007/s00419-018-1454-y Issue No:Vol. 88, No. 12 (2018)

Authors:B. Shekastehband Pages: 2293 - 2316 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: 2018-12-01 DOI: 10.1007/s00419-018-1455-x Issue No:Vol. 88, No. 12 (2018)

Authors:Marina Bošković; Radovan R. Bulatović; Slaviša Šalinić; Goran R. Miodragović; Gordana M. Bogdanović Pages: 2317 - 2338 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: 2018-12-01 DOI: 10.1007/s00419-018-1457-8 Issue No:Vol. 88, No. 12 (2018)

Authors:Michael Grinfeld; Pavel Grinfeld Abstract: For centuries, statics and dynamics of two-phase heterogeneous systems were and remain to be in the focus of multiple academic and engineering disciplines. Phase transformations phenomena include both strong reversible and irreversible effects. Many of the irreversible effects, such as friction, viscosity, heat conduction, etc., are the same as in the single-phase systems. In addition to those, the two-phase systems are known for one more irreversible effect. It is the effect entailed by finite rate of kinetics of phase transformation. Below, we explore this irreversible phenomenon for two two-phase heterogeneous systems: (i) the layered system of incompressible phases in the external gravity field and (ii) the two-phase, two-layered self-gravitating planet. PubDate: 2018-12-10 DOI: 10.1007/s00419-018-1488-1

Authors:E. Džindo; S. A. Sedmak; A. Grbović; N. Milovanović; B. Đođrević Abstract: The numerical analysis of the behaviour of a pressure vessel with a reinforcement ring subjected to both static and dynamic load is presented in this paper. This research was based on a previous analysis which involved different reinforcement ring dimensions, and their influence on the stress distribution within the pressure vessel, assuming the presence of a crack (Sedmak et al., in: International Conference on Structural Integrity and Durability, 2017). The aim was to compare the numerical results for two models, one of which was a 2D model simulated with classic FEM, whereas the other included a 3D fatigue crack, and was simulated with extended finite element method, using Morfeo software. The numerical simulation was based on a pressure vessel which is typically used as a part of hydropower plants, containing a manhole which is supported by the reinforcement ring. The analysis focused on a crack that was located in the welded joint between the reinforcement ring and the pressure vessel mantle. The results obtained by the simulations have shown the differences in the stress magnitudes and in the consequences resulting from the crack growth in both cases, depending on the type of the load, wherein the second (fatigue) load case was noticeably more extreme. PubDate: 2018-12-07 DOI: 10.1007/s00419-018-1435-1

Authors:Philip Schreiber; Christian Mittelstedt Abstract: The present paper deals with a new holistic closed-form analytical model for the local buckling load of thin-walled composite beams with I-, Z-, C-, L- and T-cross sections under axial compressive load. The beam is simply supported at both ends (Euler case II), and the plate behaviour of web and flanges is described by the Classical Laminated Plate Theory. Furthermore, symmetric and orthotropic laminates are considered. In previous investigations on composite beams under compression, the web and flange plates are considered as separate composite plates. The present analysis is performed using the Ritz method in which an approach for the entire cross section is realized. The individual webs and flanges of the beam are assembled by suitable continuity conditions into one system. In order to achieve that, new displacement shape functions for web and flange that fulfil all boundary conditions have been developed. The present closed-form analytical method enables the explicit representation of the buckling load for the entire composite beam under axial compression. The comparison between the present approach and comparative finite element simulations shows a very satisfactory agreement. The present method is ideal for pre-designing such structures, highly efficient in terms of computational effort and very suitable for practical engineering work. PubDate: 2018-11-29 DOI: 10.1007/s00419-018-1496-1

Authors:Zhiqiang Yang; Tianyu Guan; Yi Sun Abstract: A novel second-order multiscale asymptotic expansion is developed in this work to analyze chemo-mechanical properties of composites with periodic microstructure. The chemo-mechanical coupling model which considers mutual interaction between the displacement and concentration fields of composites is introduced at first. Then, the second-order multiscale formulas based on homogenization methods and multiscale asymptotic expansion for evaluating the chemo-mechanical coupling problems are proposed, including the microscale cell functions, homogenized coefficients and homogenized equations. Further, the related numerical algorithms on the basis of the proposed multiscale models are brought forward. Finally, by some representative examples, the efficiency and accuracy of the presented algorithms are verified. The numerical results clearly illustrate that the second-order multiscale methods proposed in this work are effective and valid to predict the chemo-mechanical coupling properties, and can capture the microscale behavior of the composites accurately. PubDate: 2018-11-28 DOI: 10.1007/s00419-018-1497-0

Authors:D. Čakmak; Z. Tomičević; H. Wolf; Ž. Božić Abstract: This paper presents an optimization and numerical analysis of vibration-induced fatigue in a two degree-of-freedom inerter-based vibration isolation system. The system is comprised of a primary, e.g. source body, and a secondary, e.g. receiving body, mutually connected through an isolator. The isolator includes a spring, a dashpot and an inerter. Inerter is a mechanical device which produces a force proportional to relative acceleration between its terminals. A broadband frequency force excitation of the primary body is imposed throughout the study. The goal of the proposed optimization is to prolong the fatigue life of the ground connecting helical spring of the secondary body. The optimization is based on minimizing separately the displacement and velocity amplitudes. Both optimization criteria are compared with regard to spring fatigue life improvement for fair benchmark comparison. The inerter-based optimized systems, in which the \({\mathcal {H}}_{2}\) index of the receiving body is minimized, are also compared with the optimized systems without inerter. Notable improvements are observed in inerter-based systems due to the inclusion of an optimally tuned inerter in the isolator. The proposed analytical vibration fatigue method optimization results are compared with the finite element method results, and a very good agreement is observed. Most accurate helical spring deflection and stress correction factors are discussed and determined. Furthermore, the inerter concept is successfully implemented into finite element-based dynamic solution. PubDate: 2018-11-28 DOI: 10.1007/s00419-018-1495-2

Authors:Y. L. Pei; P. S. Geng; L. X. Li Abstract: Though the higher-order beam theory is variationally consistent, the lower-order beam theory has more definite engineering significance in practical applications. This paper begins with the modified uncoupled higher-order theory of functionally graded (FG) beams. After evaluating the three rigidity coefficients, contribution of the two higher-order generalized stresses to the virtual work is ignored and therefore a modified uncoupled lower-order theory is established for FG beams, including the basic equations and the shear correction factor, so that the lower-order beam theory is theoretically correlated with the high-order beam theory. The cases of pure shearing, pure bending and pure tension are solved, compared and discussed for a FG beam. The analytical solutions validate the accuracy and applicability of the present uncoupled lower-order theory. PubDate: 2018-11-26 DOI: 10.1007/s00419-018-1494-3

Authors:Jiong Zhang; Zhan Qu; Weidong Liu; Li Zhou; Liankun Wang Abstract: This paper presents an automatic fatigue crack propagation solution for particulate-reinforced composites. In this solution, the Eshelby’s equivalent inclusion method is used to solve the elastic fields of a two-dimensional plane containing multiple elliptical inclusions. Then the continuous distributed dislocations in an infinite plane are adopted to model the multiple cracks in the plane containing multiple elliptical inclusions. By combining the two methods, a system of singular integral equations can be formulated based on the stress condition of the cracks. The stress intensity factor of each crack can be obtained by solving the singular integral equations. The propagation of the cracks is studied based on the maximum circumferential stress criterion. Numerical examples are presented to show the complicated changes in the stress intensity factors and crack growth behaviors of the cracks affected by the inclusions. PubDate: 2018-11-21 DOI: 10.1007/s00419-018-1490-7