Elastic wave propagation energy dissipation characteristics analysis on the viscoelastic damping material structures embedded with acoustic black hole based on semi-analytical homogeneous asymptotic method

Elastic wave energy dissipation and absorption properties of viscoelastic damping material (VDM) composite plates embedded with acoustic black hole (ABH) are analyzed in this paper. Considering the periodic distribution of the ABH-embedded VDM structure in the composite plate, semi-analytical homogeneous asymptotic theory is applied, which transforms the macroscopic to a microscopic problem. In-plane variables of the composite structure are defined and generated by the third-order shear deformation theory of Reddy, and the equilibrium equations are derived by extended Hamilton's principle and the internal balance is consequently determined by representative volume element theory. Determining the constitutive equations of the composite laminate structure allow the equivalent shear and strain equilibrium equations to be achieved. Subsequently, the complex equivalent stiffness is defined according to the general Hooke's law, and the dimensionless equivalent loss tangent tanδ of the composite sandwich plate is finally evaluated from the equivalent loss and storage modulus. The ABH and VDM layer factors which affect tanδ are thoroughly analyzed and discussed. The investigation can supply a new efficient method to dissipate and absorb propagation wave energy with a wide bandwidth at low frequency. Additionally, the analysis is validated by numerical simulation and Galerkin methods.     

Molecular conformation of n-alkanes using terrain/funneling methods

Understanding molecular conformation is a first step in understanding the waxing (or formation of crystals) of petroleum fuels. In this work, we study the molecular conformation of typical fuel oils modeled as pure n-alkanes. A multi-scale global optimization methodology based on terrain methods and funneling algorithms is used to find minimum energy molecular conformations of united atom n-alkane models for diesel, home heating, and residual fuel oils. The terrain method is used to gather average gradient and average Hessian matrix information at the small length scale while funneling is used to generate conformational changes at the large length scale that drive iterates to a global minimum on the potential energy surface. In addition, the funneling method uses a mixture of average and point-wise derivative information to produce a monotonically decreasing sequence of objective function values and to avoid getting trapped at local minima on the potential energy surface. Computational results clearly show that the calculated united atom molecular conformations are comprised of zigzag structure with considerable wrapping at the ends of the molecule and that planar zigzag conformations usually correspond to saddle points. Furthermore, the numerical results clearly demonstrate that our terrain/funneling approach is robust and fast.     

Fractional calculus in viscoelasticity: An experimental study

Viscoelastic properties of soft biological tissues provide information that may be useful in medical diagnosis. Noninvasive elasticity imaging techniques, such as Magnetic Resonance Elastography (MRE), reconstruct viscoelastic material properties from dynamic displacement images. The reconstruction algorithms employed in these techniques assume a certain viscoelastic material model and the results are sensitive to the model chosen. Developing a better model for the viscoelasticity of soft tissue-like materials could improve the diagnostic capability of MRE. The well known “integer derivative” viscoelastic models of Voigt and Kelvin, and variations of them, cannot represent the more complicated rate dependency of material behavior of biological tissues over a broad spectral range. Recently the “fractional derivative” models have been investigated by a number of researchers. Fractional order models approximate the viscoelastic material behavior of materials through the corresponding fractional differential equations. This paper focuses on the tissue mimicking materials CF-11 and gelatin, and compares fractional and integer order models to describe their behavior under harmonic mechanical loading. Specifically, Rayleigh (surface) waves on CF-11 and gelatin phantoms are studied, experimentally and theoretically, in order to develop an independent test bed for assessing viscoelastic material models that will ultimately be used in MRE reconstruction algorithms.     

Modeling the asymmetry in traffic flow (b): Macroscopic approach

In [H. Xu, H. Liu, H. Gong, Modeling the asymmetry in traffic flow (a): microscopic approach, J. Appl. Math. Model. (submitted for publication)], the asymmetric characteristic of traffic flow has been studied from a microscopic approach through the modeling of car-following behavior. This paper further discusses the asymmetric traffic flow modeling at the macroscopic scale. The microscopic asymmetric full velocity difference model is extended to a continuum traffic flow model to study the anisotropic characteristic and diffusive influence under various traffic conditions. In order to accurately solve the mathematical problem, a weighted essentially no-oscillatory (WENO) approach is applied. The performance of the model is then demonstrated through thorough evaluation against select classic models and field data. The macroscopic model is the first of its kind that is directly developed from an asymmetric car-following approach. The results show that the model is able to present many complex traffic phenomena observed in the field such as shock waves, rarefaction waves, stop-and-go waves and local cluster effects at a better level of accuracy than most of the existing models.     

Applications of Artificial Neural Networks to combat simulations

As a result of reduced budgets and personnel levels, the Department of Defense has increased reliance on combat simulations for such diverse areas as training, testing, planning, and analysis. Each area has its own set of needs, goals, and objectives for designing future generations of combat simulation models. However, budget constraints alone mandate the development of multipleuse combat models. The bottom line is that future generations of combat models need to be faster, have higher fidelity and larger scale than current models. Research into emerging technologies for approaches to make computer simulations more effective and efficient is an essential ingredient to developing successful future generations of combat models. One emerging technology that has such potential is Artificial Neural Networks (ANN). Potential applications of ANN to combat simulation modeling are discussed. The main results of the author's dissertation Artificial Neural Network Metamodels of Stochastic Computer Simulations [1] are discussed along with the ramifications on combat modeling and recommendations for future research.     

Stochastic multi-scale finite element based reliability analysis for laminated composite structures

This paper proposes a novel multi-scale approach for the reliability analysis of composite structures that accounts for both microscopic and macroscopic uncertainties, such as constituent material properties and ply angle. The stochastic structural responses, which establish the relationship between structural responses and random variables, are achieved using a stochastic multi-scale finite element method, which integrates computational homogenisation with the stochastic finite element method. This is further combined with the first- and second-order reliability methods to create a unique reliability analysis framework. To assess this approach, the deterministic computational homogenisation method is combined with the Monte Carlo method as an alternative reliability method. Numerical examples are used to demonstrate the capability of the proposed method in measuring the safety of composite structures. The paper shows that it provides estimates very close to those from Monte Carlo method, but is significantly more efficient in terms of computational time. It is advocated that this new method can be a fundamental element in the development of stochastic multi-scale design methods for composite structures.     

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型北大核心CSCD

基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式.基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应.证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化.以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异.结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大.     

Estimation of a non-negative location parameter with unknown scale

For a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide conditions for estimators to dominate the benchmark minimax MRE estimator, and thus be minimax under scale invariant loss. These minimax estimators include the generalized Bayes estimator with respect to the truncation of the common non-informative prior onto the restricted parameter space for normal models under general convex symmetric loss, as well as non-normal models under scale invariant \(L^p\) loss with \(p>0\) . We cover many other situations when the loss is asymmetric, and where other generalized Bayes estimators, obtained with different powers of the scale parameter in the prior measure, are proven to be minimax. We rely on various novel representations, sharp sign change analyses, as well as capitalize on Kubokawa’s integral expression for risk difference technique. Several properties such as robustness of the generalized Bayes estimators under various loss functions are obtained.     

Multiscale modelling of skeletal muscle tissue by incorporating microstructural effects

The macroscopic mechanical response of skeletal muscle tissue is mainly influenced by the properties and arrangement of microstructural elements, such as, for example, sarcomeres and connective tissue. Like for many biological materials, the mechanical properties of skeletal muscle tissue can vary quite significantly between different specimens like, for example, different persons or muscle types. Current state-of-the-art continuum-mechanical muscle models often lack the ability to take into account such variations in a natural way. Further, phenomenological constitutive laws face the challenge that appropriate material parameter sets need to be found for each tissue variation. Thus, the present work aims to identify the microstructural features and parameters governing the overall mechanical response and to incorporate them into a macroscopic material model by applying suitable homogenisation methods. The motivation hereby is that the estimation of material parameters for microstructures, such as collagen fibres, can be done in a more reliable and general way and that fluctuations between specimens are included by, for example, adapting the alignment of the collagen fibres inside the muscle. Moreover, instead of computationally expensive homogenisation methods like FE², this work proceeds from well-founded analytical homogenisation techniques in order to keep the model as simple as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic characteristics of ferrocement reinforced with woven meshes

Applying structural mechanics methods for composite materials, we have worked out a procedure for predicting the elasticity modulus, the shear modulus, and Poisson's ratio for ferrocement taking into account the elastic properties of the components, the wire diameter, the mesh size, and the distance between the meshes. The results make it possible to exploit the potential of such reinforcement to the fullest.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 526–530, July–August, 1994.     

Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.     

Vers des lois de parois multi-échelle implicites

The purpose of this Note is to present a unifying approach of boundary layer approximations for the Laplace operator in domains with periodic rugous boundaries. We show a negative result for an averaged second-order like wall-law. To circumvent this difficulty, we propose new multi-scale wall-laws that include microscopic oscillations on the fictitious boundary. In a first step they are explicit non-homogeneous Dirichlet conditions, afterwards an implicit multi-scale Saffman–Joseph-like wall-law is derived. We establish theoretical orders of convergence and provide their numerical assessment, as well as a counter-example that demonstrates the impossibility of a real averaged second order wall-law. To cite this article: D. Bresch, V. Milisic, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Determination of in-plane shear characteristics of composite materials with [±45°] layup

The shear characteristics of a composite with a [±45°] layer layup are measured experimentally by different methods. Investigations were conducted on flat and tubular specimens. The strength and shear modulus were determined by the rail method, the losipescu method, and by applying torsion to thin-wall tubes; only the shear modulus was determined by applying torsion to square plates. Determination of the shear modulus yields quantitatively comparable results, and, at the same time, the scatter of the shear-strength values of the specimens is significant. Maximum strength is achieved on the tubular specimens. The cause of the lower strength values of the flat specimens can be explained by secondary stresses and strains in their effective sections. The influence exerted by the geometry of the specimens on their strength is investigated for specimens tested by the rail and losipescu methods. It is shown that it is possible to increase the strength appreciably by varying the specimen's geometry.Institute of Polymer Mechanics. Latvian Academy of Sciences, Riga, Latvia. AERPAC Company. Netherlands. Translated from Mekhanika Kompozitmykh Materialov, Vol. 32, No. 2, pp. 256–264, March–April, 1996.     

A three-dimensional quasicontinuum approach for predicting biomechanical properties of malaria-infected red blood cell membrane

This paper presents the first attempt to comprehensively estimate the elastic properties and mechanical responses of malaria-infected red blood cell (iRBC) membrane when subjected to uniaxial, shear and isotropic area-dilation loading conditions. With the three-dimensional (3D) quasicontinuum approach, we predicted the biomechanical properties of the iRBC membrane for all infection stages. Effect of temperature on the membrane elastic properties during the trophozoite stage was also examined. It is found that a multifold increase in the elastic properties of the iRBC membrane occurs as infection progresses. The axial, shear and area stiffnesses of the iRBC membrane increase exponentially, resulting in semi-logarithmic stress–strain relationship curves. In addition, the rigidity of the iRBC membrane in the trophozoite stage increases as temperature rise. It is concluded that Plasmodium falciparum parasites significantly affect the biomechanical properties of the RBC membrane due to the structural remodeling of the iRBC membrane microstructure.     

Game and decision theory in mathematics education: epistemological, cognitive and didactical perspectives

In the 1950s, game and decision theoretic modeling emerged—based on applications in the social sciences—both as a domain of mathematics and interdisciplinary fields. Mathematics educators, such as Hans Georg Steiner, utilized game theoretical modeling to demonstrate processes of mathematization of real world situations that required only elementary intuitive understanding of sets and operations. When dealing with n-person games or voting bodies, even students of the 11th and 12th grade became involved in what Steiner called the evolution of mathematics from situations, building of mathematical models of given realities, mathematization, local organization and axiomatization. Thus, the students could participate in processes of epistemological evolutions in the small scale. This paper introduces and discusses the epistemological, cognitive and didactical aspects of the process and the roles these activities can play in the learning and understanding of mathematics and mathematical modeling. It is suggested that a project oriented study of game and decision theory can develop situational literacy, which can be of interest for both mathematics education and general education.     

MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

In this paper,we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon(MOS) capactior,First,the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problems is presented .Some matrix analysis tools are applied to explore the parameters‘ sensitivities,And thired,the parameters are extracted using Levenberg-Marquardt optimization method.The essential difficulty arises from the effect of multi-scale physical differeence of the parameters.We explore the relationship between the parameters‘ sensitivitites and the sequencs for optimization,which can seriously affect the final inverse modeling results.An optimal sequence can efficiently overcome the multip-scale problem of these parameters,Numerical experiments show the efficiency of the proposed methods.     

The most intensive fluctuation in chaotic time series and relativity principle

Relativity principle in mechanics and principle of invariant speed of light lead to Einstein theory. The exponent of p-order momentum, derived from a piece of multi-scale chaotic time series, varies with the order p and cannot exceeds a maximum, so there exists the principle of scale relativity. Its special case is the same one as Lorenz transformation from Einstein theory.