Abstract: Abstract A high-order theory is developed for the analysis of beams with general mono-symmetric cross-sections. The theory represents the nonlinear distribution of the longitudinal normal stress across the section depth by a polynomial series expansion up to any order as specified by the analyst. The corresponding shear and transverse normal stresses are obtained by satisfying the 2D infinitesimal stress-flow equilibrium conditions. The resulting statically admissible stress fields are then used in conjunction with the principle of stationary complementary strain energy to formulate the governing compatibility equations and boundary conditions. Closed form solutions are then developed for general loading and boundary conditions. Comparisons with the theory of elasticity and 3D finite element analysis predictions showcase the ability of the present theory to naturally capture shear deformation effects, transverse normal stress effects, nonlinear longitudinal normal stress distributions in deep beams, as well as the effect of support height. Unlike conventional beam solutions that are based on postulated kinematic assumptions, which tend to converge to the displacement response from below, the present theory avoids introducing any kinematic assumptions and is shown to converge to the solution from above. The theory is applicable to beams with doubly symmetric or mono-symmetric cross-sections, with isotropic or orthotropic materials, and subjected to general loading and boundary conditions. The theory is shown to offer advantages compared to other theories when modelling deep beams and/or beams with supports that are offset from the centroidal axis. PubDate: 2019-12-18

Abstract: Abstract A formulation is presented for the 2D dynamic analysis and earthquake response simulation of base isolation systems. The approach is force-based and consists of casting the computation in each time increment as a convex optimization problem. Interaction between the two horizontal components of response is considered in an elegant and simple way through yield functions appearing as constraints of the optimization problem. Numerical examples are carried out to illustrate the approach. These comprise bidirectional shearing of a high damping rubber bearing and earthquake simulations of a real-world base isolation system. PubDate: 2019-10-23

Authors:Michele Serpilli Abstract: Abstract The paper deals with the derivation of non classical interface conditions in linear poroelasticity in the framework of the quasi-static diphasic Biot’s model. More precisely, we analyze the mechanical behavior of two linear isotropic poroelastic solids, bonded together by a thin layer, constituted by a linear isotropic poroelastic material, by means of an asymptotic analysis. After defining a small parameter \(\varepsilon\) , which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems, the so-called soft, hard and rigid poroelastic interface models, respectively. First and higher order interface models are derived. Moreover, we identify the non classical transmission conditions at the interface between the two three-dimensional bodies in terms of the jump of the stresses, specific discharge, pressure and displacements. PubDate: 2019-02-12 DOI: 10.1007/s12356-019-00052-5

Authors:M. H. Yas; S. Kamarian; A. Pourasghar Pages: 1 - 11 Abstract: 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: 2017-12-01 DOI: 10.1007/s12356-017-0046-9 Issue No:Vol. 9, No. 1-2 (2017)

Authors:S. Dumont; F. Lebon; M. L. Raffa; R. Rizzoni Pages: 13 - 27 Abstract: 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: 2017-12-01 DOI: 10.1007/s12356-017-0047-8 Issue No:Vol. 9, No. 1-2 (2017)

Authors:Michel Frémond Pages: 29 - 56 Abstract: 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: 2017-12-01 DOI: 10.1007/s12356-017-0048-7 Issue No:Vol. 9, No. 1-2 (2017)

Authors:Hanane Moulay Abdelali; Khalid El Bikri; Rhali Benamar Pages: 57 - 67 Abstract: 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: 2017-12-01 DOI: 10.1007/s12356-017-0049-6 Issue No:Vol. 9, No. 1-2 (2017)

Authors:Fabrizio Greco; Raimondo Luciano; Giorgio Serino; Nicolò Vaiana Abstract: Abstract The paper investigates the accuracy, the stability and the computational efficiency of a mixed explicit–implicit time integration approach proposed for predicting the nonlinear response of base-isolated structures subjected to earthquake excitation. Adopting the central difference method for evaluating the response of the nonlinear base isolation system and the Newmark’s constant average acceleration method for estimating the superstructure linear response, the proposed partitioned solution approach is used to analyze a 3D seismically isolated structure subjected to a bidirectional earthquake excitation. Both isolation systems adopting lead rubber and friction pendulum bearings are considered. Numerical results show that the computational time required by the proposed method, in spite of its conditional stability arising from the use of the central difference method in the explicit integration substep, is clearly reduced in comparison to the widely used implicit time integration method adopted in conjunction with the pseudo-force approach (i.e., pseudo-force method). As a matter of fact, the typical low stiffness of the isolation system leads to a critical time step larger than the one used to define the ground acceleration accurately and the proposed method preserves its computational efficiency even in the case of isolators with very high initial stiffness (i.e., friction pendulum bearings) for which the critical time step size could become smaller. PubDate: 2017-12-02 DOI: 10.1007/s12356-017-0051-z

Authors:Zongjun Li; Hongtao Wang; Shijie Zheng Abstract: 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:Bachar Kabalan; Pierre Argoul; Aissam Jebrane; Gwendal Cumunel; Silvano Erlicher Pages: 1 - 15 Abstract: 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: 2016-12-01 DOI: 10.1007/s12356-016-0044-3 Issue No:Vol. 8, No. 1-2 (2016)

Authors:Oana-Zenaida Pascan; Yongjun He; Ziad Moumni; Weihong Zhang Pages: 17 - 25 Abstract: 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: 2016-12-01 DOI: 10.1007/s12356-016-0045-2 Issue No:Vol. 8, No. 1-2 (2016)