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Abstract: Optimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters. PubDate: 2022-01-28
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Abstract: Friction rings viscoelastically mounted on the arms of a flywheel to reduce vibration by functioning as friction dynamic vibration absorbers (DVAs) are proposed in this study. A design method is also proposed for the friction ring DVA under different friction models, namely Coulomb friction, tanh friction, and Stribeck friction. An equivalent nonlinear 11-degree-of-freedom (DOF) dynamic model of the flywheel with the friction ring DVA system is established to investigate the vibration reduction performance of the DVA system. A genetic algorithm is employed to determine the optimal parameters for the friction ring DVA. The harmonic balance method and the alternate frequency-/time-domain (AFT) method are used to solve the governing equations of the system and perform forced response analysis and nonlinear modal analysis. In addition, the effects of different parameters on the vibration reduction performance of the friction ring DVA are analysed. The results show that all three types of friction ring DVAs exhibit sufficiently good performance in mitigating the vibration of the flywheel. The friction ring DVAs under Coulomb friction, tanh friction, and Stribeck friction have a broad effective frequency range for vibration reduction. PubDate: 2022-01-25
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Abstract: Due to the discrepancy between slope of deflection curve and rotation due to bending defined in Timoshenko beam theory, the distributed moment proportional to the rotation was extended into the two-parameter foundation, which in essence incorporated the horizontal interface friction produced by the foundation adhesion between the foundation and the beam. Thus, the present foundation can be interpreted by the mutually independent spring to idealize the Winkler foundation, the shear layer to incorporate the foundation cohesion, and the rotation spring to simulate the horizontal interface friction. This foundation was very comprehensive and can be termed as a generalized foundation. Neglecting one of those foundation parameters, the foundation can be degenerated into the classical generalized foundation, two-parameter foundation and Winkler foundation, respectively. Also this foundation provided a mechanical interpretation for understanding the horizontal interface friction produced by the foundation adhesion. Conducting the variational operation, a differential equation of Timoshenko beam on generalized foundation was achieved. To solve the differential equation, an initial parameter solution was deduced to formulate the transfer matrix method. A classical finite element formulation with cubic interpolating functions and a transcendental finite element formulation with the analytical solutions as the shape functions were presented. Four applications were investigated to verify the generalized foundation Timoshenko beam and the related calculating methods. Analytical and numerical results have good agreements with those published in the literature, which demonstrate the accuracy of the present foundation and the related methods. The convergence of the transcendental finite element does not depend on the mesh density of the discrete structures, while the classical finite element fails to achieve such performance. Transfer matrix method and transcendental finite element method provide an efficient and alternative tool for the analysis of elastic foundation beam. Transverse deflections of generalized foundation Timoshenko beam are more sensitive to the compressive stiffness of Winkler foundation than to the stiffness of shear layer and rotation spring of the foundation. Horizontal interface friction due to the foundation adhesion has the coequal influence as the foundation cohesion. It is reasonable to incorporate the horizontal interface friction into the elastic foundation. PubDate: 2022-01-21
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Abstract: The size dependence of central nanovoid embedded in either monocrystalline or polycrystalline high-entropy-alloy (HEA) films under biaxial tension is investigated in this study. Regarding monocrystalline samples, our attention is paid to the proportional increase in the embedded nanovoid with invariant void volume fraction (VVF). The critical stresses in concerned materials at which dislocations start to emit from void under biaxial tension, in an ascending order, are CoCrFeCuNi < CoCrFeMnNi < metal Ni. Lattice distortion appears to facilitate dislocation emission from the void surface in HEAs, which lowers the critical stress compared with the theoretical model. Regarding polycrystalline samples, the size of both the film and embedded nanovoid is kept invariant, whereas grain size of either periodic hexagonal ones or randomly generated ones is allowed to vary. Apart from the random polycrystalline CoCrFeCuNi, the peak stresses of rest polycrystalline samples obey the reverse Hall–Petch effect. Both monocrystalline and polycrystalline CoCrFeMnNi samples fail due to the coalescence with nucleated secondary voids. For the latter, grain boundaries act as primary sites for secondary void nucleation. Unlike HEAs, polycrystalline Ni samples fail due to intergranular cracking instead of void growth and coalescence. PubDate: 2022-01-20
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Abstract: A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods. PubDate: 2022-01-17
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Abstract: In this article, thermally induced vibrations of shallow functionally graded material arches is considered and analyzed. The arch is subjected to sudden thermal loading on one surface while the other surface is kept at a constant temperature. Based on the uncoupled thermoelasticity assumptions, the one-dimensional heat conduction equation is established and numerically solved using the finite difference method and Crank–Nicolson marching scheme. The classical theory of curved beams is used to drive the equations of motion, where the curvature of the beam is assumed to be constant. The strain–displacement relationships are based on the von Kármán nonlinear theory based on the shallow arch theory of Donnell. The governing equations are obtained based on the Hamilton principle and converted to a set of nonlinear algebraic equations via the polynomial Ritz method. The obtained equations are nonlinear and solved using the \(\beta \) -Newmark time marching scheme and the Newton–Raphson method. Comparison of the numerical results is done with other existing results for the case of isotropic homogeneous shallow arches where well agreement is obtained. The effects of different parameters on the numerical results are presented and provided in graphical presentations. PubDate: 2022-01-17
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Abstract: The primary objective of this article is to demonstrate that Rayleigh’s quotient and its variants retain the usual properties of boundedness and stationarity even when the linear vibratory system is non-classically damped, extending previously accepted results that these quotients could attain stationarity when damping was proportional or the modal damping matrix was diagonally dominant. This conclusion is reached by allowing the quotients to be defined in complex space and using complex differentiation. A secondary objective is to show how these quotients and their associated eigenvalue problems can be combined to generate bounds on the system’s eigenvalues, an immediate consequence that follows from establishing boundedness and stationarity in complex space. The reported bounds are simple to compute and appear to be tighter than previous bounds reported in the literature. PubDate: 2022-01-17
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Abstract: In this paper, a recently introduced method has been implemented for the forced vibration analysis of multi-span Timoshenko beams subjected to a wide range of external loads. To this end, the time-weighted residual approach has been developed for the vibration analysis of Timoshenko beams for the first time. Through a simplifying assumption, the governing system of the differential equations is firstly converted to two decoupled equations in terms of the vertical displacement and the rotation of the beam section. Next, the displacement and the rotation fields are considered as a series of exponential basis functions. Storing the information of the solution at each time step on the coefficients of these series plays a vital role in the proposed method. With such a feature, the solution advances in time through a set of recursive relations. The innovative concept of source functions has also been introduced and employed to direct both shear and flexural waves, tailored to the vertical displacement and the rotation of the beam section, toward the beam’s ends. A new dynamic index is also proposed to investigate the validity of Bernoulli assumption for different ranges of the moving object’s velocities. Compared with the results of some available common methods, the accuracy and efficiency of the proposed method have been appraised in the solution of five sample problems of single- and multi-span beams subjected to stationary or moving load/mass, including an overhead crane-suspended payload system. PubDate: 2022-01-15
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Abstract: Strain- and stress-driven two-phase local/nonlocal integral models are applied to study nonlinear post-buckling behaviors of Euler–Bernoulli nanobeam under different boundary conditions. Von Karman nonlinearity is taken into account to obtain the nonlinear governing equations through the principle of minimum potential energy. The relation between nonlinear strain and nonlocal stress components is expressed as an integral forms. Several nominal variables are introduced to simplify mathematical formulation. The integral constitutive relations are transformed unitedly into equivalently differential form with constitutive boundary conditions. Bending deflection and moment are derived explicitly with Laplace transformation for linear buckling, and a nonlinear characteristic equation can be obtained while considering standard and constitutive boundary conditions, from which one can determine the numerical solution for both linear buckling force and buckling mode shape (BMS). The axial displacement and force are derived and expressed explicitly with bending deflection. Local and nonlocal BMSs-based Ritz–Galerkin method and general differential quadrature method combined with Newton’s iterative method are applied to study the post-buckling response of nonlocal nanobeam. Numerical results show that semi-analytical method, nonlocal BMS-based Ritz–Galerkin method and general differential quadrature method would lead to exact same linear buckling force prediction. In addition, nonlocal LBMS-based Ritz–Galerkin method and general differential quadrature method would provide exact same prediction for nonlinear buckling force with respect to beam middle deflection. PubDate: 2022-01-15
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Abstract: In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. https://doi.org/10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented. PubDate: 2022-01-13
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Abstract: The flywheel’s stored energy is usually increased by increasing the thickness of the flywheel rotor due to the limit of radius and speed. However, the flywheel rotor is mostly simplified to a lumped mass point without considering the thickness of the flywheel rotor. This paper proposes a modeling method that considers the thickness of the flywheel rotor. The dynamic characteristics based on the lumped parameter model (LPM), the modeling method proposed in this paper (LFM method) and the finite element method (FEM) are calculated. The first two natural frequencies of the flywheel rotor under different thicknesses are compared with the results of the FEM. The results show that when the rotor thickness is small, the natural frequency results of the LPM are consistent with those calculated using the FEM. However, with the increase of rotor thickness, the error of the results calculated by the LPM increases gradually. The natural frequency results calculated by the LFM are consistent with those calculated by the FEM. The error of the LFM results is small, which verifies the effectiveness of the LFM method. PubDate: 2022-01-12
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Abstract: A new model for electro-elastic Bernoulli–Euler beams of centrosymmetric cubic materials is proposed, which incorporates microstructure and flexoelectric effects. The wave equations and boundary conditions are derived simultaneously through a variational approach based on Hamilton’s principle. The new beam model is then applied to predict elastic wave band gaps in a periodic electro-elastic composite beam structure. Bloch’s theorem and the transfer matrix method for periodic structures are used to solve the wave equations and determine band gaps. The current model reduces to its flexoelectric and classical elastic counterparts as special cases. To illustrate the new model, the effects of microstructure, flexoelectricity, beam thickness, unit cell length and volume fraction on band gaps are investigated through a parametric study. The numerical results show that the microstructure and flexoelectric effects lead to increased band gap frequencies, and these two effects are important when the beam thickness is at the submicron and micron scales. In addition, it is found that the unit cell length and volume fraction can significantly affect the band gap size at all length scales. These findings indicate that band gap frequencies and size can be tailored by adjusting the microstructural and material parameters. PubDate: 2022-01-12
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Abstract: The objectives of this article are to present a mathematical model that uses Eringen’s nonlocal elasticity theory to describe the free vibratory motion of rotating nanoscale beams. The Euler–Bernoulli beam theory, Eringen’s nonlocal elasticity theory, and generalized thermoelasticity with phase-lags are used to derive the system of equations for rotating thermoelastic nanobeams. The studied nanobeam is subjected to ramp-type heating and to a significantly exponentially decaying load. The analytical solution was derived using the Laplace transform method, and the transformation of the converted fields was performed by applying the residue calculus. The numerical results of the physical fields under investigation are collected and displayed graphically. The impacts of nonlocal parameters, different types of loads, and ramping-time parameters in addition to rotation were studied and analyzed. PubDate: 2022-01-11
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Abstract: In this paper, we consider a conformal mapping function with complex constants coefficients to solve the problem of infinite plate weakened by a curvilinear hole. The conformal mapped is used outside the unit circle \(\varpi \) in the presence of an initial heat flowing perpendicular to the plate. All previous works, in this field, considered this problem without time and most of them regarded the conformal mapping with real constants. Here, we use complex variable method by new rational mapping to give convenient expression of Gaursat functions in applications with time effect. The hole takes different shapes that make this study applicable to many cases, such as caves, tunnels, excavations in soils or rocks. Stress components are obtained and plotted to investigate their physical meaning. Using maple 18, the different forms a hole are received and distribution of stresses in 3-D are obtained. PubDate: 2022-01-10
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Abstract: This paper proposes an interval prediction approach of ultimate strength for laminated structures. For the response prediction of complex structures, the presented method can ensure the necessary accuracy and greatly reduce the cost of computation. The method is different from the other traditional methods of prediction, which overcomes the limitation of perturbation methods in solving nonlinear problems, such as the Taylor series expansion, and avoids the enormous computation of the Monte Carlo simulation (MCS). In this paper, the output can be calculated by the finite element technology and mechanics of composite materials, and then the neural network (NN) is introduced to approximate the relation between the input and output, and finally the surrogate model is constructed. Subsequently, the issue of uncertainty propagation can be translated to optimal problem for extremum value. In addition, although the explicit expression of the established mapping relationship is unknown, the best fitness and worst fitness can be searched in the given bound of uncertain variables based on genetic algorithm (GA), and then achieve the upper bound and lower bound of the structural response depending on the capability of global search. After proposed technologies are given in detail, the engineering example of composite structure is presented and the results are discussed with common methods of uncertain propagation based on Taylor series expansion method and MCS, which demonstrates the validity and reasonability of the developed methodology. PubDate: 2022-01-10
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Abstract: The main failure mode of a wheel–axle assembly, which is an important moving part of rail vehicles, in the interference fit zone is partial fatigue. Given that neither the plane analytical method nor the axisymmetric finite element method can reveal the local and stochastic contact stress concentration at the end of the wheel seat, this study analyzed various factors influencing a machined mating surface and found that the cylindricity error is a key factor in transforming the plane contact into a 3D contact. In addition, the experimental data of the pressing force applied to 60 groups of wheel–axle assemblies were analyzed, and the circumferential contour of the mating surface was found to conform to a beta distribution. Accordingly, a method for obtaining random interpolation points on the circumferential contour was proposed. To ensure the continuity of the mating surface, the circumferential Hermite interpolation method and the axial cubic interpolation method were employed, and the contact surface with random characteristics was modeled. Based on the random ergodicity of the mating surface, a small-sample 3D finite element model of a wheel–axle assembly was established using the random cylindricity error, and a calculation method for the 3D contact stress was proposed. Taking the RE2B axle of railway locomotive as an example, compared with the axisymmetric method, the inhomogeneity analysis of the contact stress of the small-sample model proposed in this paper could help explain the problem of local stress concentration at the end of the wheel seat. The analysis results showed that the maximum stress of the 3D model based on the cylindricity is greater than that of the axisymmetric model, enabling strength evaluation in the design of wheel–axle assemblies. PubDate: 2022-01-06
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Abstract: Open circular holes are an important design feature, for instance in bolted joint connections. However, stress concentrations arise whose magnitude depends on the material anisotropy and on the defect size relative to the outer finite plate dimensions. To design both safe and light-weight optimal structures, precise means for the assessment are crucial. These can be based on analytical methods providing efficient computation. For this purpose, the focus of the present paper is to provide a comprehensive stress and failure analysis framework based on analytical methods, which is also suitable for use in industry contexts. The stress field for the orthotropic finite-width open-hole problem under uniform tension is derived using the complex potential method. The results are eventually validated against Finite-Element analyses revealing excellent agreement. Then, a failure analysis to predict brittle crack initiation is conducted by means of the Theory of Critical Distances and Finite Fracture Mechanics. These failure concepts of different modelling complexity are compared to each other and validated against experimental data. The size effect is captured, and in this context, the influence of finite width on the effective failure load reduction is investigated. PubDate: 2022-01-05
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Abstract: Design/optimization of the tuned mass damper (TMD) system may not always lead toward robust performance if uncertainties exist. In view of this, a stochastic design of multiple TMD (MTMD) systems has been proposed in the present study taking into account various uncertainties. Taylor-expansion is used to perturb the objective function facilitating stochastic design/optimization. An interval-extension is used to observe the effect of uncertainties of different levels. The Lyapunov equation is used in the design of TMD systems by minimizing the dispersion of displacement of the primary system. The present work takes into account a model of generalized MTMD system. Seismic excitation is considered as a random process in the form of both: (a) stationary Kanai–Tajimi (KT) filter and (b) stationary Gaussian white noise directly applied to the base of structure. A numerical investigation is carried out to observe the consequences of uncertainties on the optimum design of MTMD parameters for both the excitation models (with and without incorporating Kanai–Tajimi filter). Efficiency of the MTMD systems (with variation of number of MTMD mass-units) is compared under various levels of uncertainties. Finally, some significant earthquake records are utilized toward more realistic understanding on the performance of stochastic design of TMD/MTMD systems under seismic excitation with various levels of uncertainties. PubDate: 2022-01-01
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Abstract: This paper presents steady axisymmetric creeping motion of a conducting, incompressible viscous fluid past a weakly permeable slightly deformed sphere in the presence of transverse magnetic field. The Stokes approximation of momentum equation and Darcy’s law together with Lorentz force are used for the flow outside and within the semi-permeable particle. The governing equations are changed into dimensionless form, and resulting equations are solved using separation of variables method. We have determined the resistance force exerted on the oblate spheroid in the presence of magnetic field as a particular case of an approximate sphere. The impact of Hartmann numbers, permeability and deformation parameter on the coefficient of drag and the streamline pattern is exhibited graphically. Some special cases are deduced from the current study and compared with some previous results. The outcome clarifies that the Hartmann numbers enhance the drag on the oblate spheroid in comparison with prolate spheroid. PubDate: 2022-01-01
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