Abstract: 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: 2019-09-14

Abstract: The series expansions in Eq. (16) of [1] for trigonometric functions depending on a small evolution parameter shall be corrected. PubDate: 2019-08-26

Abstract: 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: 2019-08-12

Abstract: Abstract In this work, an historical overview concerning the theory of shell structures is presented. Early conjectures proposed by, among others, French, German, and Russian authors are discussed. Moreover, considering a recent approach in the field of structural analysis, based on the static–kinematic duality concept, static and kinematic matrix operator equations are formulated in the case of shells of revolution, emphasizing how these operators are one the adjoint of the other. In this way, any possible inaccuracy provided by the previous approaches can be overcome. PubDate: 2019-08-12

Abstract: Abstract A dynamic model of the rotor-bearing system with bolted joint structure is set up based on the Lagrange’s equations, which considers the bearing clearance, the gyroscopic effect and the initial deformation due to the non-uniform preload. The nonlinear dynamic responses of the system were obtained by using the Runge–Kutta–Fehlberg method, and then the influence of the radial bearing clearance on the nonlinear dynamic behaviors of the rotor system is studied by means of bifurcation diagram, frequency spectrum, shaft orbits and Poincaré maps. The results indicate that the larger bearing clearance will make the system enter into chaotic motion at a lower rotating speed. In addition, with the increase in bearing clearance, the duration of the chaotic motion becomes longer. Furthermore, the influence of initial deformation on the stability of the bolted joint rotor system with bearing clearance is studied. The results show that when the bearing clearance is present, the instability speed of the rotor system will gradually rise with the increase in initial deformation. Meanwhile, as the bearing clearance continuously increases, the regions of the chaotic motion become less and smaller, and the motion state should be completely changed under certain initial deformation. The related results can provide guidance for the optimization and design of the bolted joint rotor-bearing system. PubDate: 2019-08-08

Abstract: Abstract This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic columns with preexisted longitudinal cracks and finite adhesion between the cracked sections. Consequently, the analytical solution for the buckling loads is derived for the first time. The critical buckling loads are calculated for two different types of connections between the cracked sections, namely for slipping only and simultaneous slipping and uplifting between them. The parametric study is performed to analyze the effect of the crack length on the critical buckling loads. It is shown that the critical buckling load can be greatly affected by the crack length and type of the connection between the cracked sections. Finally, the presented results obtained can be used as a benchmark solution. PubDate: 2019-08-01

Abstract: Abstract In this article, the transient response of a cylinder, with a piezoelectric coating, weakened by multiple radial cracks is investigated. The problem is under torsional transient loading. First, the solution of the problem, weakened by a Volterra-type screw dislocation, is achieved by using Laplace and the finite Fourier sine transform. The solution is obtained for displacement and stress fields in the bar with a piezoelectric layer. At the next step, the dislocation solution is used to derive a set of Cauchy singular integral equations for analysis of bars with a circular cross section containing some radial cracks. The solution of the singular integral equations is used to determine the torsional rigidity of the cross section and also the stress intensity factors of the crack tips. In addition, several examples are presented to show the effect of the piezoelectric coating and torsional transient loading on the stress intensity factors and torsional rigidity of the system. PubDate: 2019-08-01

Abstract: Abstract This paper presents an analytic solution method to evaluate transient response of the joints in the truss-type structural networks. The analytic method models the wave propagation along the elastic members connected to the joints and derives the functions for the reflection and transmission coefficients for the structural joints. The coefficients of wave reflection and transmission across the joints are functions of material properties and geometrical parameters of the elements connected to the joint. The present analytic solution considers the effects of abrupt change in material properties as well as the alignment of connected elements on the transmission and reflection coefficients of the joints. The analytic solution method derives the functions for the transmission and reflection coefficients at the connection point of two different coaxial elements as well as the joints in planar and space frame structures. PubDate: 2019-08-01

Abstract: Abstract The main objective of the present paper is to study the temperature and thermal stress analysis of a functionally graded rectangular plate with temperature-dependent thermophysical characteristics of materials under convective heating. The nonlinear heat conduction equation is reduced to linear form using Kirchhoff’s variable transformation. Analytic solution of the heat conduction equation is obtained in the transform domain by developing an integral transform technique for convective-type boundary conditions. Goodier’s displacement function and Boussinesq harmonic functions are used to obtain the displacement profile and its associated thermal stresses. A mathematical model is prepared for functionally graded ceramic–metal-based material. The results are illustrated numerically and depicted graphically for both thermosensitive and nonthermosensitive functionally graded plate. During this study, one observed that notable variations are seen in the temperature and stress profile, due to the variation in the material parameters. PubDate: 2019-08-01

Abstract: Abstract The paper concerns an analysis of equilibrium problems for elastic bodies with elastic Timoshenko inclusion in the presence of defects. Defects are characterized by a positive damage parameter. This parameter is responsible for a connection between defect faces. Asymptotic properties of solutions are investigated with respect to the damage parameters as well as with respect to a rigidity parameter of the inclusions. Limit models are investigated; in particular, different equivalent problem formulations are proposed. PubDate: 2019-08-01

Abstract: Abstract The problem of multiple adhesive contact is considered for an elastic substrate modeled as a transversely isotropic elastic half-space. It is assumed that a large number of the Kendall-type microcontacts are formed between the substrate and circular rigid (i.e., nondeformable) and frictionless micropads, which are interconnected between themselves, thereby establishing a load sharing. The effect of microcontacts interaction is accounted for in the formulation of the detachment criterion for each individual microcontact. A number of different asymptotic models are presented for the case of dilute clusters of microcontacts with their accuracy tested against a special case of two-spot contact, for which an analytical solution is available. The pull-off force has been estimated and the effects of the array size and the microcontact spacing are studied. It is shown that the flexibility of the micropads fixation, which is similar to that observed in mushroom-shaped fibrils, significantly increases the pull-off force. The novelty of the presented approach is its ability to separate different effects in the multi-scale contact problem, which allows one to distinguish between different mathematical models developed for bioinspired fibrillar adhesives. PubDate: 2019-08-01

Abstract: Abstract This paper presents a theoretical and experimental analysis of buckling load of the square wooden beams. The buckling tests were conducted on the wooden beams with three different lengths, and the critical buckling load was determined on the basis of the measured relation between the axial displacement and axial load. Analytical solutions for the critical buckling load of the beams were derived using the Euler–Bernoulli beam theory and Timoshenko beam theory. When deriving the models, both small and large deformation theories were considered. Moreover, the effect of a grain orientation was included in the models. The results show that the selected solution was in agreement with the values measured from the experiment. The paper provides a review of mathematical models and gives us a comparison between the theories and experiments with subsequent recommendations for practice. PubDate: 2019-08-01

Abstract: Abstract In this paper, the stability of an elastic column, one end of the column fixed and the other end supported by a spring, is studied under the Euler critical load with Koiter stability theory. The potential energy of the system is written as a functional of tangent angle, and the disturbance quantity is expanded into the Fourier series. The quadratic matrix of second-order variation of potential energy is obtained, and all order principal minor determinants are transformed into elementary expressions. The second-order variation is semi-positive definite. And the stability of the critical point depends on the higher-order variations of potential energy. The results show that the stability of the critical state of the flexible restrained column is related to the relative stiffness of the constraint. The post-buckling behavior is analyzed according to Koiter’s initial post-buckling theory. The post-buckling path is upward or downward corresponding to stable or unstable equilibrium, respectively. The critical loads of stability and instability under different relative stiffness values are solved accurately. PubDate: 2019-08-01

Abstract: Abstract In this paper, a closed-chain multibody model of a pantograph/catenary system is developed and used for the optimal design of a nonlinear controller based on an open-loop control architecture. The goal of the nonlinear controller is the reduction of the contact force arising from the pantograph/catenary interaction and, at the same time, the suppression of the mechanical vibrations of the pantograph mechanism. The analytical formulation employed in this paper for describing the nonlinear dynamics of the pantograph/catenary multibody system considers a Lagrangian approach and is based on a redundant set of generalized coordinates. The contact forces generated by the pantograph/catenary interaction are modeled in this work employing an elastic force element collocated between the pantograph pan-head and a moving support. The external support follows a prescribed motion law that simulates the periodic deployment of the catenary system. On the other hand, in this investigation, the algebraic constraints arising from the closed-loop topology of the pantograph multibody system are enforced employing a method based on the Udwadia–Kalaba equations recently developed in the field of analytical dynamics. Furthermore, the problem of the determination of an effective feedforward controller for reducing the pantograph/catenary contact force is formulated in this work as a nonlinear optimal control problem. For this purpose, the solution of the control optimization problem is carried out by using an adjoint-based computational procedure. Numerical simulations demonstrate the effectiveness of the nonlinear controller obtained in this investigation for the pantograph/catenary multibody system. PubDate: 2019-08-01

Abstract: Abstract The present paper proposes an interphase model for the simulation of damage propagation in masonry walls in the framework of a mesoscopic approach. The model is thermodynamically consistent, with constitutive relations derived from a Helmholtz free potential energy. With respect to classic interface elements, the internal stress contribute is added to the contact stresses. It is considered that damage, in the form of loss of adhesion or cohesion, can potentially take place at each of the two blocks–mortar physical interfaces. Flow rules are obtained in the framework of the Theory of Plasticity, considering bilinear domains of ‘Coulomb with tension cut-off’ type. The model aims to be a first research step to solve the inverse problem of damage propagation in masonry generated by vertical ground movements, in order to ex-post identify the cause of a visible damage. The constitutive model is written in a discrete form for its implementation in a research-oriented finite element program. The response at the quadrature point is analyzed first. Then, the model is validated through comparisons with experimental results and finally employed to simulate the failure occurred in a wall of an ancient masonry building, where an arched collapse took place due to a lowering of the ground level under part of its foundation. PubDate: 2019-08-01

Abstract: Abstract In the present investigation, a new equivalent micromechanics method is proposed, and then, an analysis model has been developed to estimate the nonlinear coefficients of thermal expansion (CTEs) of three-phase composites. As Compared with previous analytical models, the innovative point of this paper is that the influence of the debonding surface thickness is investigated. It is noted that the parameters of thickness of debonding surface have a significant effect on both the longitudinal CTEs and transverse CTEs. The CTEs of composites are also very sensitive to the different inclusion aspect ratios. The constitutive equation curves for different variable parameters can describe the influence of debonding damage on thermal expansion coefficients (CTEs) of the composites. The new model provides a direct prediction of CTEs and can account for the effects of inclusion aspect ratio, volume fractions and thickness of debonding surface. PubDate: 2019-08-01

Abstract: Abstract A unified solution procedure applicable for analyzing the free transverse vibration of both rectangular and annular sectorial plates is presented in this study. For the annular sectorial plate, the basic theory is simplified by a variable transformation in the radial direction. The analogies of coordinate system, geometry and potential energy between the two different shapes are drawn and then unified in one framework by introducing the shape parameter. A generalized solving procedure for the two shapes becomes feasible under the unified framework. The solution adopts the spectro-geometric form that has the advantage of describing the geometry of structure by mathematical or design parameters. The assumed displacement field and its derivatives are continuous and smooth in the entire domain, thereby accelerating the convergence. In this study, the admissible functions are formulated in simple trigonometric forms of the mass and stiffness matrices for both rectangular and annular sectorial plates can be obtained, thereby making the method computationally effective, especially for analyzing annular sectorial plates. The generality, accuracy and efficiency of the unified approach for both shapes are fully demonstrated and verified through benchmark examples involving classical and elastic boundary conditions. PubDate: 2019-08-01

Abstract: Abstract This paper addresses the problem of characterizing the mechanical behaviour and collapse of symmetric circular and pointed masonry arches subject to their own weight. The influence on the arch’s collapse features of its shape and thickness, as well as the friction between the arch’s voussoirs, is analysed. The safety level of arches is then investigated by suitably reworking in semi-analytical form the graphical method of the stability area proposed by the renowned nineteenth century French scholar, Durand-Claye. According to Durand-Claye’s method, the arch is safe if along any given joint both the bending moment and shear force do not exceed the values determined by some given limit condition. The equilibrium conditions corresponding to all possible symmetric collapse modes are individuated. As was expected, pointed and circular arches exhibit different collapse behaviours, in terms of both collapse modes and safe domain. The limit values of arch thickness and friction coefficient are determined and the results obtained consistently compared with those published by Michon in 1857. PubDate: 2019-08-01

Abstract: Abstract Force finding of cable–strut structures is to identify self-equilibrated pre-stress states for structures with given shape, which is a crucial step in the structural design of flexible structures since pre-stresses significantly affect their mechanical behaviors. Utilizing symmetry properties of structures is generally considered as a practical way to facilitate the force finding process. To indicate the symmetric feature of structures, an algebraic indicator is proposed in the context of the equilibrium matrix theory. Furthermore, it is found that the orthogonal projection onto the null space of the equilibrium matrix could show the symmetry properties of structures geometrically. Then, a symmetry-based method of computing feasible pre-stress states is developed in the light of the above orthogonal projection. Finally, the proposed method is applied on three examples to confirm its validity and accuracy. PubDate: 2019-08-01

Abstract: Abstract We consider a coated rigid inclusion inserted into an elastic matrix subjected to uniform remote anti-plane shear stresses and examine whether the inclusion can be made neutral (meaning that its introduction will not disturb the original uniform stress field in the surrounding uncut matrix) despite the presence of partial debonding along the inclusion–coating interface. Our analysis involves the introduction of a conformal mapping function (expressed in terms of a Laurent series) for the (thick) coating, a Laurent series expansion for the corresponding Plemelj function and simple matrix algebra. Our method demonstrates that coated neutral inclusions continue to be available under these challenging yet more realistic physical conditions. Numerical results are presented to demonstrate the feasibility of the solution method. PubDate: 2019-08-01