Authors:H. Yazdani Sarvestani; A. H. Akbarzadeh Pages: 927 - 947 Abstract: While the structural analysis of straight beams is straightforward, the behavior of curved beams is more complex to predict. In the present work, a displacement approach of toroidal elasticity is used to analyze thick isotropic curved tubes subjected to axial load, torque, and bending moment. The governing equations are developed in a toroidal coordinate. The method of successive approximation is used to obtain the general solution. The accuracy of the present methodology is tested comparing the numerical results with those obtained by finite element method (FEM) and stress-based toroidal elasticity (SBTE). The proposed methodology is computationally cost-effective, and its results reveal good agreements with FEM and SBTE results. Finally, several numerical examples of stress distributions in thick isotropic curved tubes under axial load, torque, and bending moment are presented. By using the present methodology, displacements as well as stresses are obtained which are important information for fracture analysis. PubDate: 2017-06-01 DOI: 10.1007/s00419-016-1223-8 Issue No:Vol. 87, No. 6 (2017)

Authors:Stanislav Kotšmíd; Chang-Hung Kuo; Pavel Beňo Pages: 949 - 960 Abstract: This paper presents a theoretical and experimental analysis of buckling load of the circular tube with flattened ends. The buckling tests were conducted on the steel tubes with different length and diameter, and the critical buckling force was determined from the measured relation between the lateral displacement and axial force. Analytical solutions for the critical buckling force of the circular tubes were derived in the series form, and a numerical procedure based on the finite difference method and quasi-Newton method was developed to determine the critical buckling load. The results show that both analytical and numerical solutions were in agreement with those measured from the experiment. Moreover, the effect of flattened part length on the value of the critical buckling force was investigated there. The paper provides a mathematical model of mentioned case and gives us some simplifications calculating the critical buckling force. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1224-2 Issue No:Vol. 87, No. 6 (2017)

Authors:Yunke Zhao; Dongyan Shi; Huan Meng Pages: 961 - 988 Abstract: In the present article, a spectro-geometric-Ritz solution for free vibration analysis of conical–cylindrical–spherical shell combinations with arbitrary boundary conditions is presented. The classical theory of small displacements of thin shells is employed to formulate the theoretical model. The admissible functions of each shell components are described as a combination of a two-dimensional (2-D) Fourier cosine series and auxiliary functions. As an innovative point of this work, the auxiliary functions are introduced to accelerate the convergence of the series representations and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and the junction between the shell components. The artificial spring technique is adopted here to model the boundary condition and coupling condition, respectively. All the expansion coefficients are considered as the generalized coordinates and determined by Ritz procedure. Convergence and comparison studies for both open and closed conical–cylindrical–spherical shells with arbitrary boundary conditions are carried out to verify the reliability and accuracy of the present solutions. Some selected mode shapes are illustrated to enhance the understanding of the research topic. It is found the present method exhibits stable and rapid convergence characteristics, and the present results, including the natural frequencies and the mode shapes, agree closely with those solutions obtained from the finite element analyses and results in the literature. The effects of the geometrical dimensions of the shell combinations on the natural frequencies are also investigated. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1225-1 Issue No:Vol. 87, No. 6 (2017)

Authors:Tieding Guo; Houjun Kang; Lianhua Wang; Yueyu Zhao Pages: 989 - 1006 Abstract: Cables’ in-plane nonlinear vibrations under multiple support motions with a phase lag are investigated in this paper, which is a continuation of our previous work (Guo et al. in Arch Appl Mech 1647–1663, 2016). The main results are twofold. Firstly, asymptotically reduced models for the cable’s in-plane nonlinear vibrations, with or without internal resonance, excited by multiple support motions, are established using a boundary modulation approach. Two in-plane boundary dynamic coefficients are derived for characterizing moving supports’ effects, which depend closely on the cable’s initial sag, distinct from the out-of-plane ones Guo et al. (2016), and are also found to be equal for symmetric in-plane dynamics while opposite for antisymmetric dynamics. Secondly, cable’s in-plane nonlinear responses due to multiple support motions are calculated and phase lag’s dynamic effects are fully investigated. Two important factors associated with phase lags, i.e., the excitation-reduced and excitation-amplified factors, are both derived analytically, indicating theoretically that the phase lags would weaken the cable’s single-mode symmetric dynamics but amplify the antisymmetric dynamics. Furthermore, through constructing frequency response diagrams, the phase lag is found to change the characteristics of cables’ two-to-one modal resonant dynamics, both qualitatively and quantitatively. All these semi-analytical results obtained from the reduced models are also verified by applying the finite difference method to the cable’s full model, i.e., the continuous partial differential equation. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1226-0 Issue No:Vol. 87, No. 6 (2017)

Authors:Hulun Guo; Bin Liu; Yangyang Yu; Shuqian Cao; Yushu Chen Pages: 1007 - 1018 Abstract: In this paper, an adaptive and passive galloping suppression of a suspended linear cable is investigated. The limit cycle oscillation (LCO) of cable due to nonlinear wind loading is effectively eliminated by a lightweight, easy-to-make attachment: nonlinear energy sink (NES). Analytical mechanism of LCO is explored by using harmonic balance method, implying that NES is valid for LCO suppression under any wind speed. Finally, the influences of mass ratio, damping, stiffness and location of NES on vibration suppression are highlighted in detail. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1227-z Issue No:Vol. 87, No. 6 (2017)

Authors:Ekaterina V. Shishkina; Serge N. Gavrilov Pages: 1019 - 1036 Abstract: We deal with a new phase nucleation in a phase-transforming bar caused by a collision of two non-stationary waves. We consider an initial stage of dynamical process in the finite bar before the moment of time when the waves emerged due to new phase nucleation reach the ends of the bar. The model of a phase-transforming bar with trilinear stress–strain relation is used. The problem is formulated as a scale-invariant initial value problem with additional restrictions in the form of several inequalities involving the problem parameters. We consider the particular limiting case where the stiffness of a new phase inclusion is much greater than the stiffness of the initial phase and obtain the asymptotic solution in the explicit form. In particular, the domains of existence of the solution in the parameter space are constructed. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1228-y Issue No:Vol. 87, No. 6 (2017)

Authors:V. Rizov Pages: 1037 - 1048 Abstract: The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress–strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1229-x Issue No:Vol. 87, No. 6 (2017)

Authors:Guowei Zhao; Jianming Du; Zhigang Wu Pages: 1049 - 1059 Abstract: In this study, we reconstructed a dynamic model of a rotating cantilever beam for which the geometric stiffening term was obtained by accounting for the longitudinal shrinkage caused by the transverse deflection of the beam. Previous investigations focused on kinetic energy but neglected strain energy. For this study, we retained these strain energy coupling terms. We used Hamilton’s principle to derive the complete coupling model. Taking the effect of steady-state axial deformation into account, we obtained the transverse equation of motion and the coupling general characteristic equation. Unlike previous models, this model incorporates not only the geometric stiffening effect but also the geometric softening effect. In relevant numerical examples, as the angular velocity increases, the bending frequency gives rise to geometric stiffening in line with the results obtained in previous studies. When the angular velocity reaches and exceeds a critical value, the bending frequency produces a geometric softening phenomenon. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1231-3 Issue No:Vol. 87, No. 6 (2017)

Authors:Huan Li; Chun Li; Huang Yuan Pages: 1061 - 1075 Abstract: Cohesive zone modeling of fatigue crack growth retardation in aerospace titanium alloy Ti–6Al–4V subjected to a single overload during constant amplitude is presented in this work. The cyclic softening behavior of the bulk material is simulated according to the Ohno–Wang’s cyclic plasticity theory. The fracture process zone is represented by an irreversible cohesive law which governs the material separation of fatigue crack. The material degradation mechanism is described by the gradual reduction of the unloading cohesive stiffness after each loading cycle. The fatigue crack growth behaviors are examined using the proposed cohesive model under both constant and variable amplitude loadings. The computational results are verified according to the experimental data, which confirm that the present model can be applied to predict the transient retardation in fatigue crack growth rate of the Ti–6Al–4V alloy accurately. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1232-2 Issue No:Vol. 87, No. 6 (2017)

Authors:Ivan Jeník; Petr Kubík; František Šebek; Jiří Hůlka; Jindřich Petruška Pages: 1077 - 1093 Abstract: Two alternative methods for the stress–strain curve determination in the large strains region are proposed. Only standard force–elongation response is needed as an input into the identification procedure. Both methods are applied to eight various materials, covering a broad spectre of possible ductile behaviour. The first method is based on the iterative procedure of sequential simulation of piecewise stress–strain curve using the parallel finite element modelling. Error between the computed and experimental force–elongation response is low, while the convergence rate is high. The second method uses the neural network for the stress–strain curve identification. Large database of force–elongation responses is computed by the finite element method. Then, the database is processed and reduced in order to get the input for neural network training procedure. Training process and response of network is fast compared to sequential simulation. When the desired accuracy is not reached, results can be used as a starting point for the following optimization task. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1234-0 Issue No:Vol. 87, No. 6 (2017)

Authors:Aristophanes J. Yiotis; John T. Katsikadelis Abstract: The meshless analog equation method, a purely meshless method, is applied to the buckling analysis of moderately thick plates described by Mindlin’s theory and resting on two-parameter elastic foundation (Pasternak type). The method is based on the concept of the analog equation, which converts the three governing second-order partial differential equations (PDEs) in terms of the three plate displacements (transverse displacement and two rotations) into three substitute equations, the analog equations. The analog equations constitute a set of three uncoupled Poisson’s equations under fictitious sources, which are approximated by multi-quadric radial basis functions (MQ-RBFs) series. This enables the direct integration of the analog equations and allows the representation of the sought solution by new RBFs series. These RBFs approximate accurately not only the displacements but also their derivatives involved in the governing equations. Then, inserting the approximate solution in the original PDEs and in the associated boundary conditions (BCs) and collocating at mesh-free nodal points, a generalized eigenvalue problem is obtained, which allows the evaluation of the buckling load and the buckling modes. The studied examples demonstrate the efficiency of the presented method that is its ability to solve accurately and in a straightforward way difficult engineering problems. PubDate: 2017-06-16 DOI: 10.1007/s00419-017-1269-2

Authors:Shaowei Hu; Jiang Yu; Congjie Wei; Zhaoguang Zhang Abstract: Due to non-uniform distribution of structural deformation along its transverse width direction, shear lag behavior widely exists in composite structure with multi-box and leads to structural instability and destruction. To in-depth explore its mechanical mechanism, a type of steel–concrete composite structure with double-box (the DBSCCS model) is proposed, and its longitudinal warping shape functions are set up. Based on the minimum potential energy principle, governing differential equations of the DBSCCS model and its boundary conditions are deduced by means of the variational method. And then, its strain functions and shear lag coefficients are also obtained under concentrated loading and symmetrical loading, respectively. What is more, experimental verification and its related parametric sensitivity analysis are launched based on deduced longitudinal strain functions and shear lag coefficients. Through this analysis, it shows that this method can be used to illustrate and predict shear lag characteristics for this type of the DBSCCS model. That further suggests that it provides a more reference value for engineering design and structure optimization in some extent for the composite structures. PubDate: 2017-06-14 DOI: 10.1007/s00419-017-1268-3

Authors:B. Emek Abali; Wolfgang H. Müller; Francesco dell’Isola Abstract: In continuum mechanics, there exists a unique theory for elasticity, which includes the first gradient of displacement. The corresponding generalization of elasticity is referred to as strain gradient elasticity or higher gradient theories, where the second and higher gradients of displacement are involved. Unfortunately, there is a lack of consensus among scientists how to achieve the generalization. Various suggestions were made, in order to compare or even verify these, we need a generic computational tool. In this paper, we follow an unusual but quite convenient way of formulation based on action principles. First, in order to present its benefits, we start with the action principle leading to the well-known form of elasticity theory and present a variational formulation in order to obtain a weak form. Second, we generalize elasticity and point out, in which term the suggested formalism differs. By using the same approach, we obtain a weak form for strain gradient elasticity. The weak forms for elasticity and for strain gradient elasticity are solved numerically by using open-source packages—by using the finite element method in space and finite difference method in time. We present some applications from elasticity as well as strain gradient elasticity and simulate the so-called size effect. PubDate: 2017-06-05 DOI: 10.1007/s00419-017-1266-5

Authors:S. H. Mirtalaie; M. A. Hajabasi Abstract: The nonlinear axial-lateral-torsional free vibration of the rotating shaft is analyzed by employing the Rayleigh beam theory. The effects of lateral, axial and torsional deformations, gyroscopic forces and rotary inertia are taken into account, but the shear deformations are neglected. In the new developed dynamic model, the nonlinearities are originated from the stretching of beam centerline, nonlinear curvature and twist and inertial terms which leads to the coupling between the axial, lateral and torsional deformations. The deformed configuration of the cross section of the beam is represented by the axial and lateral deformations, also the geometry of the beam in the deformed configuration is represented by Euler angles. A system of coupled nonlinear differential equations is obtained which is examined by the method of multiple scales and the nonlinear natural frequencies are determined. The accuracy of the solutions is inspected by comparing the free vibration response of the system with the numerical integration of the governing equations. The effect of the spin speed and radius-to-length ratio of the rotating shaft on the free vibrational behavior of the system is inspected. The study demonstrates the effect of axial-lateral-torsional coupling on the nonlinear free vibrations of the rotating shaft. PubDate: 2017-06-05 DOI: 10.1007/s00419-017-1265-6

Authors:Christos D. Sofianos; Vlasis K. Koumousis Abstract: This work presents the development of a hysteretic beam element in the context of the finite element method, that is suitable for the inelastic dynamic analysis of framed structures. The formulation proposed is able to capture the main characteristics of hysteresis in structural systems and mainly accounts for stiffness degradation, strength deterioration and pinching phenomena, as well as for non-symmetrical yielding that often characterizes their behavior. The proposed formulation is based on the decoupling of deformations into elastic and hysteretic parts by considering additional hysteretic degrees of freedom, i.e., the hysteretic curvatures and hysteretic axial deformations. The direct stiffness method is employed to establish global matrices and determine the mass and viscous damping, as well as the elastic stiffness and the hysteretic matrix of the structure that corresponds to the newly added hysteretic degrees of freedom. All the governing equations of the structure, namely the linear global equations of motion and the nonlinear evolution equations at elemental level that account for degradations and pinching, are solved simultaneously. This is accomplished by converting the system of equations into state space form and implementing a variable-order solver based on numerical differentiation formulas (NDFs) to determine the solution. Furthermore, hysteretic loops and degradation phenomena are easily controlled by modifying the model parameters at the element level enabling simulations of a more realistic response. Numerical results are presented and compared against experimental results and other finite element codes to validate the proposed formulation and verify its ability to simulate complex hysteretic behavior exhibiting cyclic degradations. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1263-8

Authors:Jialin Tian; Yinglin Yang; Lin Yang Abstract: For the nonlinear vibration of the drill string in the drilling process, vibration characteristics analysis and experimental study of the drill string are conducted, which are to analyze the drill string dynamic characteristics with wellbore random friction force on the basis of the horizontal well. Firstly, considering the wellbore random friction force, the analysis models of the drill string vibration and the drilling efficiency of the horizontal well are established. Then, the establishment method of the random wellbore friction field is also obtained. With the combination of solution expressions of each force in the vibration equation, the discrete method of the dynamic model is established. According to the experimental test, the key input parameters are determined, and then, the example analysis of the vibration model is conducted. With the comparison of the experimental test and theoretical calculation, the influences of key parameters on the dynamic characteristics of the drill string are analyzed to verify the accuracy of the analysis model. The results can provide a new insight to the researches of the drill string dynamics, especially for the complex well, such as ultra-deep well, branch well and directional well, in which the wellbore friction has a significant influence on the result of the drill string kinetics. Moreover, the results can offer an important guidance for the design and application of new downhole tools. PubDate: 2017-06-01 DOI: 10.1007/s00419-017-1262-9

Authors:Xuhui Liao; Shunming Li; Lianying Liao; Haodong Meng Abstract: An important procedure in transfer path analysis (TPA) is to measure the frequency response functions (FRFs) of the decoupled passive subsystem. The classical TPA method obtains the passive subsystem’s FRFs by direct measuring when the system is disassembled. The main shortcoming of the classical method to measure the FRFs is that it is time-consuming due to the necessity to dismount the active part. In this paper, a novel method is proposed to estimate the passive subsystem’ FRF matrix without disassembling the coupled mechanical structure. The key idea of this method is that the effect of a coupled subsystem will be canceled out if the links which connect this subsystem with the other one have no deformation, since the coupled systems influence each other only through the links which can be regarded as combinations of connecting springs and dampers. Following this idea, the expression of the passive subsystem’s FRF matrix can be deduced from the entire system’s FRF matrix directly. The proposed method in this paper is called the virtual decoupling method, since the decoupling is not ‘real’ but ‘virtual’. Obviously, the actual decoupling procedure is avoided so that the shortcoming mentioned above is overcome. The method is validated by a numerical model and a finite element model. PubDate: 2017-05-29 DOI: 10.1007/s00419-017-1264-7

Authors:Guoqi Zhao; Wenfeng Hao; Xixuan Sheng; Yin Luo; Guangping Guo Abstract: In this study, the interactions of matrix crack with inclusions of different shapes were investigated using the method of caustic. First, the specimens with inclusions of different shapes were prepared, where glass was used as inclusion and epoxy was used as matrix. Then, caustic experiments were conducted, and the typical caustic spots at the crack tip with varied distances from three different shapes of inclusions were obtained. Ultimately, the stress intensity factors of the cracks shielded by different shapes of inclusions were extracted from the caustic spots, and finite element simulations were conducted to verify the experimental results using the ABAQUS software. The results show that the stress intensity factors measured by the caustic method are in good agreement with the finite element simulation results. PubDate: 2017-05-25 DOI: 10.1007/s00419-017-1261-x

Authors:Jinyu Zhou; Wujun Chen; Bing Zhao; Shilin Dong Abstract: For a structure with given shape, to acquire feasible pre-stress states without changing its predefined shape is the main purpose of force finding as a crucial step in structural designs, since mechanical behaviors of cable-strut structures are highly sensitive to their pre-tensioning levels. One of practical ways to initial force designs is double singular value decomposition (DSVD), the essence of which is visual inspections of symmetry properties that could be arbitrary and time consuming due to its manual grouping. To reduce the iteration times of finding a proper group division, a grouping scheme was developed by utilizing the distributed static indeterminacy as a symmetry indicator that represents both geometric and stiffness symmetry. The existing DSVD method was subsequently modified using the proposed scheme that could provide an initial group classification being helpful to decrease the undesirable numbers of pre-stress states. Finally, two examples were investigated to verify the validity and accuracy of the modified method, and then it was applied in an enormous stadium with saddle-shaped roof structure showing good agreement with results obtained by a conventional approach. PubDate: 2017-05-15 DOI: 10.1007/s00419-017-1257-6

Authors:Mostafa Mohammadian; Mehdi Akbarzade Abstract: In the current paper, a powerful approximate analytical approach namely the global residue harmonic balance method (GRHBM) is proposed for obtaining higher-order approximate frequency and periodic solution of nonlinear conservative oscillatory systems arising in engineering problems. The proposed method has a main difference with other traditional harmonic balance methods such that the residual errors obtained in pervious order approximation are used in the present one. Comparison of the obtained results with the exact and numerical solution as well as well-known analytical methods such as Hamiltonian approach, Max–Min approach, variational approach, and He’s amplitude–frequency formulation reveals the correctness and usefulness of the GRHBM. It is shown that the results are valid for different values of system parameters and both small and large amplitudes. Hence, the method can be easily applied to other strongly nonlinear conservative oscillatory systems. Furthermore, using the obtained analytical expressions, the effect of amplitude and system parameters on nonlinear frequency is studied. PubDate: 2017-05-10 DOI: 10.1007/s00419-017-1252-y