Authors:Zongjun Li; Hongtao Wang; Shijie Zheng Abstract: A size-dependent model for bending and free vibration of functionally graded piezoelectric (FGP) microbeam is developed by using modified couple stress theory and a unified higher order beam theory. This model can be specialized to various beam models, such as Euler–Bernoulli, Timoshenko as well as Reddy beam ones and vice versa. The governing equations of motion and associated boundary conditions are derived from Hamilton’s principle. Only one material length scale parameter is introduced to capture the size effect. The analytical solutions of simply supported FGP microbeam are presented by using Navier approach to bring out the effect of the material length scale parameter on the bending and free vibration of microbeam. Numerical simulations are presented to account for the effect of various parameters, such as material length scale parameters, volume fraction indexes, and slenderness ratios on the responses of static bending and free vibration of FGP microbeam. PubDate: 2017-11-08 DOI: 10.1007/s12356-017-0050-0

Authors:Hanane Moulay Abdelali; Khalid El Bikri; Rhali Benamar Abstract: Accurate prediction of the total geometrically non-linear dynamic stress, including both the membrane and bending stresses, is of a crucial importance in the engineering design. A semi-analytical model based on Hamilton’s principle and spectral analysis has been developed recently to study the effects of large vibration amplitudes of fully clamped skew plates. The purpose of the present work was the extension of the model to the analysis of the stresses, including both the non-linear bending and membrane stresses associated to the fundamental non-linear mode shape. It was found that the non-linear frequency increases with increasing the amplitude of vibration, which corresponds to the hardening type effect due to the membrane forces induced by the large vibration amplitudes. The corresponding non-linear bending strains were obtained via the usual strains-displacement relationships, involving partial derivatives of only the transverse displacement function with respect to the space variables. To estimate the non-linear membrane stresses, without having to calculate the in-plane displacements, which would make the model much more laborious and time consuming, a simple practical engineering theory was presented here, which takes into account the contribution of the in-plane displacements u and v in an average sense, along lines parallel to the plate edges. The results show that, at large deflections, higher bending stresses occur near to the clamps, compared with those predicted by the linear theory. Numerical details are presented and comparison of the results obtained here with the ones previously ones treated in the literature shows a satisfactory agreement. PubDate: 2017-10-26 DOI: 10.1007/s12356-017-0049-6

Authors:Michel Frémond Abstract: This article presents a theory of collisions of continua either solid or not. The basic idea which is developed is that the system made of distinct continua is deformable because their relative positions change. The collisions we consider occur while the continua are evolving and the duration of the collisions is small compare to the duration of the whole motion. Thus they are assumed instantaneous. We do not focus on the fast and sophisticated phenomena which occur during collisions. We focus on summing up these phenomena in a coherent theory which gives the elements to pursue the description of the motion. This instantaneity assumption leaves large possibilities to engineers and scientists to develop numerous and useful predictive theories. The basis of the theory is illustrated with the collision of a point with an immobile obstacle. Then the theory is applied to collisions of solids, either rigid or deformable, then to collisions of solids and fluids. The thermal effects of collisions may produce phase change: the example of rain falling on a deeply frozen soil is investigated. Collisions may be so violent that they fracture the bodies: fracturation may also be predicted by the theory. From the theoretical point of view, let us mention that this theory proves that the paradoxes, i.e., illogic results, which are said to result from the equations of mechanics, as the Painlevé–Jellet and Klein paradoxes, may be overcome in a clear and logic manner. Moreover these results are supported by experiments. PubDate: 2017-08-01 DOI: 10.1007/s12356-017-0048-7

Authors:S. Dumont; F. Lebon; M. L. Raffa; R. Rizzoni Abstract: The present paper deals with a general asymptotic theory aimed at deriving some imperfect interface models starting from thin interphases. The novelty of this work consists in taking into account some non-standard constitutive behaviors for the interphase material. In particular, micro-cracks, surface roughness and geometrical nonlinearity are included into the general framework of the matched-asymptotic-expansion theory. The elastic equilibrium problem of a three-composite body comprising two elastic adherents and an adhesive interphase is investigated. Higher order interface models are derived within the cases of soft and hard interphase materials. Simple FEM-based numerical applications are also presented. PubDate: 2017-07-29 DOI: 10.1007/s12356-017-0047-8

Authors:M. H. Yas; S. Kamarian; A. Pourasghar Abstract: In this research work, based on the Euler–Bernoulli theory and by means of Generalized Differential Quadrature (GDQ) method, free vibration characteristics of functionally graded (FG) beams resting on two-parameter foundation are focused. The two-constituent functionally graded beam consists of ceramic and metal grading through the thickness. A generalized power-law distribution is considered for the ceramic volume fraction. A detailed parametric study is carried out to highlight the influences of different profiles of fiber volume fraction, four parameters of power-law distribution and two-parameter elastic foundation modulus on the vibration characteristics of the FG beams. PubDate: 2017-04-22 DOI: 10.1007/s12356-017-0046-9

Authors:Oana-Zenaida Pascan; Yongjun He; Ziad Moumni; Weihong Zhang Abstract: We conduct systematic dynamic experiments on the martensite reorientation in different samples of the single crystal Ni–Mn–Ga Ferromagnetic Shape Memory Alloy (FSMA) driven by a high-frequency magnetic field and a compressive stress. It is found that the output reversible strain strongly depends on the loading frequency, with the maximum output strain up to 6 % at the resonance frequency; and this resonance frequency can be changed by modifying the setting of the compressive stress (the pre-stress level). That provides an alternative way to control/design the system’s optimal working frequency range, besides modifying the spring stiffness and sample geometry. On the other hand, temperature rise accompanies the high-frequency field-induced strain because of the energy dissipation of the martensite twinning and eddy current, which depend on both the frequency and the sample geometry. With these results, some guidelines for improving the FSMA engineering designs are given and some challenging issues for further theoretical study such as the magneto–thermal–mechanical coupling are pointed out. PubDate: 2016-10-21 DOI: 10.1007/s12356-016-0045-2

Authors:Bachar Kabalan; Pierre Argoul; Aissam Jebrane; Gwendal Cumunel; Silvano Erlicher Abstract: One of the main objectives of crowd modeling is to optimize evacuation and improve the design of pedestrian facilities. In this work, a sensitivity analysis is performed to study the effect of the parameters of a 2D discrete crowd movement model on the nature of pedestrian’s collision and on evacuation times. After presenting the proposed model in its full version (three degrees of freedom for each individual), a pedestrian–pedestrian collision is considered. We identified the parameters that govern this type of collision and studied their effects on it. Then an evacuation experiment of a facility with a bottleneck exit is introduced and its configuration is used for numerical simulations. It is shown that without introducing a social repulsive force, the obtained flow rate values are much higher than the experimental ones. For this reason, we introduced the social force as defined by Helbing and performed a parametric study to find the set of optimized values of this force’s parameters that enables us to achieve simulation results close to the experimental ones. Using the values of the parameters obtained from the parametric study, the evacuation simulations give flow rate values that are closer to the experimental ones. The same optimized model is then used to find the density in front and inside the bottleneck and to reproduce the lane formation phenomenon as was observed in the experiment. Finally, the obtained results are analyzed and discussed. PubDate: 2016-03-26 DOI: 10.1007/s12356-016-0044-3

Authors:Giuseppe Rastiello; Jean-Louis Tailhan; Pierre Rossi; Stefano Dal Pont Pages: 1 - 16 Abstract: The article presents a numerical finite element study of fluid leakage in concrete. Concrete cracking is numerically modelled in the framework of a macroscopic probabilistic approach. Material heterogeneity and the related mechanical effects are taken into account by defining the elementary mechanical properties according to spatially uncorrelated random fields. Each finite element is considered as representative of a volume of heterogeneous material, whose mechanical behaviour depends on its own volume. The parameters of the statistical distributions defining the elementary mechanical properties thus vary over the computational mesh element-by-element. A weak hydro-mechanical coupling assumption is introduced to represent the influence of cracking on the variation of transfer properties: it is assumed that the mechanical cracking of a finite element induces a loss of isotropy of its own permeability tensor. At the elementary level, an experimentally enhanced parallel plates model is used to relate the local crack permeability to the elementary crack aperture. A Monte Carlo-like approach allows to statistically validate the numerical method. The self-consistency of the proposed modelling strategy is finally explored through the numerical simulation of the hydro-mechanical splitting test, recently proposed by authors to evaluate the real-time evolution of the transfer properties of a concrete sample under loading. PubDate: 2015-03-21 DOI: 10.1007/s12356-015-0038-6 Issue No:Vol. 7, No. 1-2 (2015)

Authors:G. Blaževičius; J. Atkočiūnas Pages: 17 - 26 Abstract: The paper considers the relationships between the optimization of perfectly elastic–plastic structures under repeated variable load and the valid structural design standards. The physical and geometrical properties of a structure are known in advance. The quasi-static cyclic loading is characterized by time-independent upper and lower bounds. The mathematical model for determining the optimal internal limiting force distribution of a structure at shakedown with strength, stiffness and stability constraints according to EC3 standard is presented. The model takes into account the ultimate and serviceability limit states of EC3 with corresponding reliability levels. The evaluation of the stability of the elements under compression takes into account plastic deformations in the shakedown process. The proposed methodology allows a more precise interpretation of the stability constraints in continuous optimization problems of mathematical programming. The results are valid for the assumption of small displacements. Numerical examples of the optimization of a portal and three storey steel frames are presented. PubDate: 2015-09-16 DOI: 10.1007/s12356-015-0039-5 Issue No:Vol. 7, No. 1-2 (2015)

Authors:Stefano Lenci; Laura Consolini; Francesco Clementi Pages: 27 - 43 Abstract: In this work, we address experimentally the determination of the dynamical properties, in particular natural frequencies and damping factors, of laminated structural glass. Various specimens, coming from different productions and manufactures, are investigated. Damped free vibrations experiments are performed, where the excitation is provided by an instrumented hammer. The boundary conditions are free–free (the specimens lay on a very flexible sponge substrate). The dynamical characteristics are determined by last squares fitting of time histories, a technique that is very simple, fast and provides very good results. Finally, two theoretical models (a two-layer beam model and a 2D finite element model) are employed to interpret the experimental results, and to determine the (dynamical) elastic properties of the interlayer (which in the present case is made of PVB), which are very difficult to be determined directly. PubDate: 2015-09-21 DOI: 10.1007/s12356-015-0040-z Issue No:Vol. 7, No. 1-2 (2015)

Authors:Bo Wang; Xiaolin Chen Pages: 45 - 58 Abstract: A fast multipole boundary element method (FMBEM) is presented for diffusion problems based on a dual reciprocity formulation. In the dual reciprocity formulation, domain integrals that arise from solving the time-dependent boundary value problems are transformed into boundary integrals by constructing particular solutions. The time-derivatives in the governing differential equation are approximated with a first-order finite difference time-stepping scheme. Discontinuous linear elements, which are known to give more accurate results than constant or linear elements, are used in the implementation to discretize the boundary integral equations, in combination with the fast multipole method for speeding up the solution. Three numerical examples of diffusion are presented. The performance of the developed FMBEM is compared with that of a conventional BEM and a commercial finite element program. The results show that the developed FMBEM can be a reliable and efficient tool for solving diffusion problems. PubDate: 2015-11-03 DOI: 10.1007/s12356-015-0041-y Issue No:Vol. 7, No. 1-2 (2015)

Authors:L. Siad Pages: 59 - 69 Abstract: This work addresses an extended version of the well known GTN isotropic hardening model and its numerical integration within a finite element code. The pre-existing yield function of the proposed constitutive model possesses the distinctiveness to be more accurate for arbitrary void volume fraction and especially to explicitly depend upon the third stress invariant. A fully implicit stress integration procedure, based on the return-mapping algorithm, with calculation of the consistent tangent operator is developed for the proposed model. In order to demonstrate the global accuracy and stability of the numerical solution, finite element damage simulations accounting for finite strain and using both the proposed model and, for the purpose of comparison, the GTN isotropic hardening model are performed for the traditional ductile solid problem of necking of a round tensile bar and the two-dimensional simple dynamic shearing problem. The numerical results highlight similarities, good agreement as long as softening initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts, between the proposed model and the GTN model. PubDate: 2015-11-16 DOI: 10.1007/s12356-015-0042-x Issue No:Vol. 7, No. 1-2 (2015)

Authors:Laura Galuppi; Gianni Royer-Carfagni Pages: 71 - 92 Abstract: Approximate methods for calculating laminated glass (LG), a composite where thin polymeric layers are sandwiched by glass plies, are very useful in the design practice. The most common approach relies upon the definition of the effective thickness, i.e., the thickness of a glass monolith that, under the same boundary and load conditions, presents the same maximal stress or deflection of the laminate. Different alternative formulations have been proposed, but for flat glass only. Meeting the increasing interest for curved glazing in modern architecture, here the recent “Enhanced Effective Thickness” method is extended to the case of single-curvature LG panels. Under the assumption that the curvature is moderate, usually met in the practice, simple formulae for the effective thickness are proposed. A practical method is presented to calculate the relevant coefficients, which depend upon the geometry, load and boundary conditions. Comparison with numerical experiments in paradigmatic examples confirms the accuracy of the proposed approach. PubDate: 2015-11-05 DOI: 10.1007/s12356-015-0043-9 Issue No:Vol. 7, No. 1-2 (2015)

Authors:Andrea Trovato; Anil Kumar; Silvano Erlicher Pages: 1 - 16 Abstract: In this article, the entrained response of the modified hybrid Van der Pol/Rayleigh (MHVR) oscillator undergoing a periodic excitation is analyzed. Based on a large experimental database, this self-sustained oscillator was originally proposed by the authors to model the lateral ground force of a pedestrian walking on a rigid floor. In this situation, there is no external excitation on the oscillator (autonomous regime). In a successive development, the authors used the MHVR oscillator in the non-autonomous regime to model the lateral oscillations of a pedestrian walking on a periodically moving floor. In the same work, the MHVR oscillator was analyzed in terms of amplitude of the entrained response, i.e. a solution having constant amplitude and the same frequency as the one of the given periodic excitation. The main goal of the present paper is the stability analysis of entrained responses. Some theoretical results are first discussed. Then, these theoretical notions are applied to the pedestrian modelling problem: the conditions allowing stability of the solution are used to compute the percentage of pedestrians of a given population that can synchronize their walk with a given periodic floor motion. Finally, these model predictions are compared with experimental results concerning pedestrians walking on a periodically moving floor. PubDate: 2014-07-08 DOI: 10.1007/s12356-014-0034-2 Issue No:Vol. 6, No. 1-2 (2014)

Authors:Michaël Peigney Pages: 17 - 28 Abstract: This paper is concerned with the large-time behaviour of shape-memory alloys structures when they are submitted to a given loading history. Extending the approach introduced by Koiter in plasticity, we state sufficient conditions for the energy dissipation to remain bounded in time, independently on the initial state. Such a behavior is classically referred to as shakedown and is associated with the idea that the evolution becomes elastic in the large-time limit. The study of a particular example shows that the large-time behaviour of shape-memory alloys structures exhibit some complex features which are not found in standard plasticity. PubDate: 2014-11-15 DOI: 10.1007/s12356-014-0035-1 Issue No:Vol. 6, No. 1-2 (2014)

Authors:C. Vallée; J. Chaoufi; C. Lerintiu Pages: 29 - 36 Abstract: Generalized Standard Materials are governed by maximal cyclically monotone operators and modelled by convex potentials. Géry de Saxcé’s Implicit Standard Materials are modelled by biconvex bipotentials. Analyzing the intermediate class of n-monotone materials governed by maximal n-monotone operators and modelled by Fitzpatrick’s functions, we find out that n-monotonicity is a relevant criterion for the materials characterisation and classification. Additionally, the Fitzpatrick’s functions allow to describe the thermal or mechanical equilibrium equations of n-monotone materials by primal–dual two-fields variational principles. In doing so, we are led to Dirichlet–Neumann problems that we solve by Uzawa-type algorithms. PubDate: 2014-11-21 DOI: 10.1007/s12356-014-0036-0 Issue No:Vol. 6, No. 1-2 (2014)

Authors:Rupender Bijarnia; Baljeet Singh Pages: 37 - 45 Abstract: In the present paper, the propagation of plane waves in an isotropic two-temperature generalized thermoelastic solid half-space with diffusion is studied. The governing equations are modified with the use of Lord and Shulman theory of generalized thermoelasticity and are solved for plane wave solutions, which show the existence of four plane waves in x–z plane. Reflection phenomenon of these plane waves from thermally insulated stress free surface is also studied to obtain a system of four non-homogeneous equations in reflection coefficients of reflected waves. The expressions for energy ratios of reflected waves are derived. Numerical computations of speed and energy ratios are carried out for a particular material which is modeled as an isotropic generalized thermoelastic solid half-space. The speeds of plane waves are computed against two temperature parameter thermodiffusion constant, measure constants of thermodiffusion effects and diffusive effects to observe the effects of two-temperature and diffusion. Energy ratios of various reflected waves are also computed against the angle of incidence to observe the effects of two-temperature parameter. PubDate: 2014-11-14 DOI: 10.1007/s12356-014-0037-z Issue No:Vol. 6, No. 1-2 (2014)