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 Archive of Applied MechanicsJournal Prestige (SJR): 0.79 Citation Impact (citeScore): 2Number of Followers: 6      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0939-1533 - ISSN (Online) 1432-0681 Published by Springer-Verlag  [2574 journals]
• Micromechanical modeling of unidirectional composites with random fiber
and interphase thickness distributions
• Abstract: Unidirectional composites having random fiber and interphase thickness distributions are considered, and the corresponding transverse effective mechanical properties are determined by the computational homogenization method developed based on linear elastic equilibrium relationship in multi-phase composite. The micromechanical unit cell model including random coated fibers is generated by a simple and efficient algorithm, and the periodic displacement constraints are applied on the cell boundary to keep the cell edges straight after deformation. Then, the effective transverse elastic properties of composites are determined numerically by the present computational model, which is validated through a comparison against available experimental and analytical/numerical results. Finally, the influences of micromechanical parameters on composites are investigated. It is observed that the nonuniformity of interphase thickness has little influence to the overall material properties of composites, which are significantly affected by the interphase thickness and elastic modulus, especially for the case of high fiber volume content.
PubDate: 2019-12-01

• Convergence of the Rayleigh–Ritz Method for buckling analysis of
arbitrarily configured I-section beam–columns
• Abstract: Design of the slender members requires calculation of buckling loads in addition to stress and deflection demand/capacity ratios. The Rayleigh–Ritz Method, which allows one to present approximate closed-form solutions for certain cases, is one of the simplest methods for this purpose. This study evaluates the buckling analysis of the I-section prismatic beam–columns with the Rayleigh–Ritz Method in detail. First, algebraic, trigonometric, and exponential trial functions for various restraint configurations are derived carefully in finite series form. Then, an iterative procedure to calculate buckling loads and modes is described. Finally, a software is developed with Mathematica and the sensitivity of the results and performance to trial function type and the number of terms is investigated over 1000 computer-generated numerical examples, which include doubly and singly symmetric sections, simply supported and cantilever members, intermediate torsional and lateral restraints, transversal concentrated and distributed loads acting above/below the shear center, and axial loads.
PubDate: 2019-12-01

• Effective conductivity and the effect of electric current on thermal
stress around an arbitrarily shaped inhomogeneity
• Abstract: We consider the electric, thermal and elastic fields in an infinite conductor or semiconductor plate containing an arbitrarily shaped inhomogeneity. Complex variable and numerical methods are used to discuss effective conductivities and the effect of electric current on the thermal stress distribution. Our results show that the effective electric and thermal conductivities depend strongly on the shape and size of the inhomogeneity. In addition, the electric current generates considerable thermal stress in the vicinity of the inhomogeneity allowing for the possibility of enhancing or neutralizing any thermal stress induced by heat flux. Detailed analyses indicate that the remote electric current suppresses the maximum normal stress while either suppressing or enhancing the maximum shear and hoop stresses around an arbitrarily shaped inhomogeneity depending on the material parameters and shape of the inhomogeneity. Our findings also allow us to conclude that the electric current suppresses maximum normal and shear stresses on the interface in the case of a triangular inhomogeneity, which, of course, dramatically reduces the threat of interface debonding which is known to be one of the main causes of failure in composites. This research provides a theoretical basis for the prediction of the effective performance as well as for the control of thermal stress in composites.
PubDate: 2019-12-01

• Study of reflection and transmission of axially symmetric body waves
incident on a base of semi-infinite poroelastic solid cylinder
• Abstract: This paper deals with the study of the reflection and transmission phenomena when axial symmetric body waves incident on the base of a poroelastic semi-infinite solid cylinder, surrounded by another medium. Cylinder is assumed to be isotropic so that Biot’s theory of poroelasticity can be employed. Reflection and transmission coefficients are computed as a function of angle of incidence in the case of permeable base. In addition, square root of energy ratio is computed for the body waves. Numerical results are presented graphically for two types of poroelastic solids, namely sandstone saturated with kerosene and sandstone saturated with water.
PubDate: 2019-12-01

• Mesh bias and shear band inclination in standard and non-standard continua
• Abstract: A severe, spurious dependence of numerical simulations on the mesh size and orientation can be observed in elasto-plastic models with a non-associated flow rule. This is due to the loss of ellipticity and may also cause a divergence in the incremental-iterative solution procedure. This paper first analyses the dependence of the shear band inclination in a biaxial test on the mesh size as well as on the mesh orientation. Next, a Cosserat continuum model, which has been employed successfully for strain-softening plasticity, is proposed to prevent loss of ellipticity. Now, numerical solutions result for shear band formation which are independent of the size and the orientation of the discretisation.
PubDate: 2019-12-01

• An inconsistent phase selection assessment for harmonic peaks elimination
in operational modal testing
• Abstract: An improvement on modal analysis technique is always exacerbated by the limitation on both operational modal analysis (OMA) and experimental modal analysis (EMA). In a recent year, a novel method was introduced named impact-synchronous modal analysis (ISMA) which represents a magnificent achievement in this field. The efficiency of this method as a viable option for EMA and OMA is proven in previous research. However, a quick and straightforward real-time ISMA method is desired as the current procedure is labour-intensive and time-consuming due to the lack of control on the impact timing with respect to phase angle of the disturbances. Thus, the aim of this paper is to identify the significance of phase difference information between acceleration response and cyclic load component in eliminating the disturbances through impact-synchronous time averaging. The paper presented a phase selection assessment, and the results showed that a few averages, (i.e. four averages) are sufficient to filter out the disturbances by 72–80% of dominant periodic response due to cyclic load and over 50% reduction for second harmonic, when the phase angles with respect to the impact are inconsistent for each impact applied. A better modal identification result is obtained through a straightforward way of eliminating the periodic response. Thus, the estimated frequency response function is strongly enhanced and good correlation is observed between modal extraction data and benchmark EMA result.
PubDate: 2019-12-01

• Three-dimensional elasticity analysis of sandwich panels with functionally
• Abstract: In this paper, three-dimensional elastic deformation of rectangular sandwich panels with functionally graded transversely isotropic core subjected to transverse loading is investigated. An exponential variation of Young’s and shear moduli through the thickness is assumed. The approach uses displacement potential functions for transversely isotropic graded media and a three-dimensional elasticity solution for a transversely isotropic graded plate developed by the authors. The effects of transverse shear modulus, loading localisation, panel thickness and anisotropy on the stresses and displacements in the panel are examined and discussed.
PubDate: 2019-12-01

• Fracture and mode mixity analysis of shear deformable composite beams
• Abstract: To analyse delaminated composite beams with high accuracy under mixed-mode I/II fracture conditions first-, second-, third- and Reddy’s third-order shear deformable theories are discussed in this paper. The developed models are based on the concept of two equivalent single layers and the system of exact kinematic conditions. To deduce the equilibrium equations of the linearly elastic system, the principle of virtual work is utilised. As an example, a built-in configuration with different delamination position and external loads are investigated. The mechanical fields at the delamination tip are provided and compared to finite element results. To carry out the fracture mechanical investigation, the J-integral with zero-area path is introduced. Moreover, by taking the advantage of the J-integral, a partitioning method is proposed to determine the ratio of mode-I and mode-II in-plane fracture modes. Finally, in terms of the mode mixity, the results of the presented evaluation techniques are compared to numerical solutions and previously published models in the literature.
PubDate: 2019-12-01

• Dynamic analysis of the in-plane free vibration of a multi-cable-stayed
beam with transfer matrix method
• Abstract: Cable-stayed bridge is one of the most popular bridges in the world and is always the focus in engineering field. In this work, the in-plane free vibration of a multi-cable-stayed beam, which exists in cable-stayed bridge, has been studied. The general expressions are conducted for the multi-cable-stayed beam based on basic principle of the transfer matrix method. A double-cable-stayed beam is taken as an example and solved according to governing differential equations considering axial and transverse vibrations of cables and beam. Then, numerical analyses are implemented based on carbon fiber-reinforced polymer cables. The dynamic characteristics including natural frequencies and mode shapes are investigated and compared with those obtained by finite element model. Meanwhile, parametric analyses are carried out in detail aiming to explore the effects of parameters on natural frequencies of a two-cable-stayed beam. Finally, some interesting phenomena are revealed and a few interesting conclusions are also drawn.
PubDate: 2019-12-01

• Conventional and star-shaped auxetic materials for the creation of band
gaps
• Abstract: A band gap region, or simply a band gap, is a range of frequencies where vibrations of certain frequency ranges are isolated. In the present paper, such ranges are sought through the study of different cases for the shape of the unit cells of a lattice, i.e., of an assembly of classical structural elements, such as beams and plates. A lattice with a specific, special designed microstructure is considered in the present investigation. Each particular cell of the examined lattice is studied as a classical composite material consisting of a matrix and the reinforcing core (e.g., matrix-fiber composite), and it is discretized by using two-dimensional plane stress finite elements. The form of the core of the unit cells can be of several shapes, e.g., quadratic, circular, and star. Some of these shapes provide the whole lattice with auxetic behavior, with negative Poisson’s ratio at the homogenized properties. The shape and the microstructure of the lattice is optimized in order to achieve isolation of the desired frequencies. A first attempt on the optimization of star-shaped microstructures is also presented. The optimization is carried out using powerful global optimization methods, such as the genetic algorithms. Results indicate that band gaps may appear in both conventional and auxetic microstructures. Moreover, the appearance and the size of the band gaps depend on the selected microstructure.
PubDate: 2019-12-01

• An analytical solution for buckling of plates with circular cutout
• Abstract: This paper investigates the buckling of isotropic plates with circular cutout subjected to non-uniform in-plane loading. The buckling load is calculated in two steps. In the first step, the prebuckling stress distribution is computed. The existence of cutout causes the solution of stress distribution to be nontrivial. In this paper, a novel analytical method is presented for calculating the stress distribution. This method is based on expansion of the stress function in polar coordinates and using a boundary integral to satisfy the boundary conditions at plate edges. In the second step, the obtained stress distribution is used to calculate the buckling load from the Ritz method. In this method, The displacement field is defined according to the first order shear deformation theory and the characteristic beam functions are used for approximation. The effect of cutout size, plate’s aspect ratio, different uniaxial and biaxial loading profiles, i.e. constant, parabolic and cosine loading and different boundary conditions on the buckling load is studied.
PubDate: 2019-12-01

• Saint-Venant torsion of non-homogeneous orthotropic circular cylinder
• Abstract: The object of this paper is the Saint-Venant torsion of a radially non-homogeneous, hollow and solid circular cylinder made of orthotropic piezoelectric material. The elastic stiffness coefficients, piezoelectric constants and dielectric constants have only radial dependence. This paper gives the solution of the Saint-Venant torsion problem for torsion function, electric potential function, Prandtl’s stress function and electric displacement potential function.
PubDate: 2019-11-20

• Bone remodeling: an improved spatiotemporal mathematical model
• Abstract: Bone remodeling is a key process in vertebrate organisms, since it is responsible for maintaining skeleton’s integrity. However, in some pathological conditions, such as osteoporosis or Paget’s disease, bone’s function becomes compromised. To gain a better understanding about these conditions, bone remodeling has become a determinant subject of research. Remodeling implies resorption of bone by osteoclasts followed by formation of new tissue by osteoblasts. The interaction between these two bone cells is reproduced in this work by extending the bone remodeling model of Ayati et al. (Biol Direct 5:28, 2010. https://doi.org/10.1186/1745-6150-5-28). Also, for the first time, a discrete numerical method—finite element method (FEM)—is applied to solve the remodeling equations and analyze the results. A single cycle of remodeling is simulated using a two-dimensional bone patch. Results show that the developed mathematical model is able to correlate bone cell dynamics with different phases of the remodeling process, allowing to obtain the transient spatial distribution of bone’s apparent density along time. Thus, the presented model reveals itself as a successful approach, producing an accurate temporal-spatial evolution of bone cells during an event of bone remodeling.
PubDate: 2019-11-19

• Nonlocal strain gradient torsion of elastic beams: variational formulation
and constitutive boundary conditions
• Abstract: Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional-free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviors of structures involved in modern nano-electro-mechanical systems.
PubDate: 2019-11-19

• Suggestion of the DLV dimensionless number system to represent the scaled
behavior of structures under impact loads
• Abstract: A group of dimensionless numbers, termed density–length–velocity (DLV) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham $$\Pi$$ theorem with an essential basis. The distinct features of this group of dimensionless numbers are that it relates physical quantities of the impacted structures to essential basis of the density, the length and the velocity, and thus it can represent the scaled influence of material property, geometry characteristic and velocity on the behavior of structure. The newly 15 proposed dimensionless numbers reflect three advantages: (1) the intuitively clear physical significance of these dimensionless numbers, such as the ratios of force intensity, force, moment of inertia to the corresponding dynamic quantities, the Johnson’s damage number $$D_{n}$$ and Zhao’s response number $$R_{n}$$, are naturally included; (2) the property of directly matching the dimensionless expression of response equations of dynamic problems with these dimensionless numbers through simple equation analysis; (3) the addressing ability of non-scaling problems for different materials and strain-rate-sensitive materials through adjusting impact velocity of the scaled model or adjusting density of the scaled model, as well as the VSG (initial impact velocity–dynamic flow stress–impact mass G) system. Four classical impact models are used to verify the directly matching property and the non-scaling addressing ability of the DLV system by equation analysis. The results show that the proposed dimensionless number system is simple, clear and efficient, and we suggest using it to represent the scaled behavior of structures under impact loads.
PubDate: 2019-11-18

• A vehicle–track beam matching index in EMS maglev transportation
system
• Abstract: In order to study the stability and bifurcation of the EMS maglev transportation system, an index that can evaluate the matching degree between the EMS vehicle and track beam is proposed. The coupling system is simplified reasonably and the ordinary differential equations model of EMS basic levitation unit and track beam coupling system is established based on the interaction principle between vehicle and track beam. The bifurcation characteristics of the model equilibrium point with two key parameters of the track beam are calculated by theoretical analysis and numerical simulation. The Lyapunov coefficient of the bifurcation points is calculated to determine which Hopf bifurcation occurred. The Hopf bifurcation diagram of the coupling system with two key parameters of the track beam is drawn, respectively, and the stability of the model equilibrium point under different parameters and the size of its convergence range are determined. An index of matching degree between the parameters of EMS maglev vehicle and track beam is defined by the ratio between the size of the stability region and the static deflection of the track beam.
PubDate: 2019-11-18

• On dynamic behavior of composite plates using a higher-order Zig-Zag
theory and exponential basis functions
• Abstract: In this paper, a boundary node method is presented to study wave propagation in laminated composite plates. The Zig-Zag theory of Cho and Parmerter is used for deriving the governing equations of laminated plates. To the best of the authors’ knowledge, this study is the first one employing the theory in non-stationary dynamic plate problems addressing wave propagation issues. For this theory, there is no information about the Green’s functions and thus the presented method can be considered as an alternative to the boundary integral method. With the use of exponential basis functions (EBFs), the response of the structure is first found in the frequency domain and finally the time-domain response is obtained using inverse Fourier transformation. The EBFs are found so that they satisfy the governing equations in the frequency domain. For the first time, in this paper, we shall present explicit relations for the EBFs in the frequency domain for Cho and Parmerter’s Zig-Zag theory. The coefficients of the EBFs are found through the collocation of the boundary conditions. The dynamic analysis of some composite laminated plates is presented, and the results are compared to those obtained from the dynamic analysis of two-/three-dimensional finite element method (FEM). We shall discuss the capabilities and limitations of the theory and the solution method. The capability of the method, in the analysis of problems excited by high-frequency loads, is shown in the solution of wave propagation problems for which the FEM needs excessive number of elements and thus it is practically impossible to be applied.
PubDate: 2019-11-18

• Exact closed-form static solutions for parabolic arches with concentrated
damage
• Abstract: The statics of fully deformable parabolic arches affected by a small crack at opposite sides of a damaged cross section is studied. The finite governing equations are linearized; the mechanical response for ‘small’ displacements and rotation is assumed. The effect of the crack is modelled by springs with stiffnesses calculated through linear elastic fracture mechanics. Closed-form exact static solutions are found under suitable boundary and continuity conditions. The effects of the crack position along the arch axis, its depth, and location on the cross section for different loading and boundary conditions are investigated and commented. The possibility of using these solutions in structural identification is discussed.
PubDate: 2019-11-16

• A novel family of composite sub-step algorithms with desired numerical
dissipations for structural dynamics
• Abstract: A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in structural dynamics. The new scheme is a self-starting, unconditionally stable and second-order-accurate two-sub-step algorithm with the same computational cost as the Bathe algorithm. The new algorithm can control continuously numerical dissipations in the high-frequency range in an intuitive way, and the ability of numerical dissipations can range from the non-dissipative trapezoidal rule to the asymptotic annihilating Bathe algorithm. Besides, the new algorithm only involves one free parameter and always achieves the identical effective stiffness matrices inside two sub-steps, which is not always achieved in three Bathe-type algorithms, to reduce the computational cost in the analysis of linear systems. Some numerical examples are given to show the superiority of the new algorithm over the Bathe algorithm and the CH-$$\alpha$$ algorithm.
PubDate: 2019-11-15

• Nonlinear analysis of piezoelectric wind energy harvesters with different
geometrical shapes
• Abstract: Piezoelectric wind energy harvesters consisting a bluff body and a piezoelectric cantilever beam have great potential for powering small-sized wireless devices. To achieve a higher energy output, the beam is designed for large deformation. This results in the nonlinear nature of the energy harvesters. In this paper, a nonlinear model of a piezoelectric wind harvester with different geometrical parameters is developed. A comparison of the energy harvesting performance of these energy harvesters with different geometrical parameters is provided. Results show that the onset speeds of galloping for trapezoidal and exponential piezoelectric energy harvesters are significantly lower than those of rectangular beam. The average power output density of the beam with exponential shape is larger than trapezoidal and rectangular beams. Therefore, designing a beam with exponentially varying shape can obtain the largest power density and therefore can reduce the cost of piezoelectric wind energy harvester.
PubDate: 2019-11-15

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