Implicit equations for thermoelastic bodies

In this paper we generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play. The implicit constitutive relations for thermoelastic response presented here provide a very natural way to overcome a serious problem associated with the celebrated model due to Fourier, namely infinite speed of the propagation of temperature. We also study some boundary value problems within the context of the implicit equations that we have developed. We carry out a linearization based on the classical assumption that the displacement gradient is small and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature.     

Homogenization of kinetic laminates in linearized elasticity

The homogenization of kinetic laminates in the framework of time‐dependent linearized elasticity is studied from a variational point of view through the Γ‐convergence of the associated energies. The characterization of the effective coefficients is achieved by means of a finite dimensional minimization problem.     

Korn inequalities for shells with zero Gaussian curvature

We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero principal longitudinal curvature and positive circumferential curvature, including, for example, cylindrical and conical shells with arbitrary convex cross sections. We prove that the best constant in the first Korn inequality scales like thickness to the power 3/2 for a wide range of boundary conditions at the thin edges of the shell. Our methodology is to prove, for each of the three mutually orthogonal two-dimensional cross-sections of the shell, a “first-and-a-half Korn inequality”—a hybrid between the classical first and second Korn inequalities. These three two-dimensional inequalities assemble into a three-dimensional one, which, in turn, implies the asymptotically sharp first Korn inequality for the shell. This work is a part of mathematically rigorous analysis of extreme sensitivity of the buckling load of axially compressed cylindrical shells to shape imperfections.     

复合材料中矩形夹杂角端部力学行为分析

提出了一种分析矩形夹杂角端部奇异应力场的新型杂交有限元方法,该方法在分析矩形夹杂角端部奇异应力场时,需要在夹杂端部构造一个超级单元。超级单元的刚度矩阵可以通过夹杂端部特征问题数值解建立。我们用这种方法计算了单向载荷作用下无限大均质板中单个矩形夹杂角端部奇异应力场,并与现有的数值解进行了比较。比较结果表明:本文提出的方法是可行的、有效的,而且数值结果精度高。为说明本文方法适用范围更广,文章最后讨论了各向异性弹性材料和横观各向同性压电材料中矩形夹杂角端部电弹性场行为。     

三维弹性问题高次有限元方程的代数多层网格法

有限元法是数值求解三维弹性问题的一类重要的离散化方法,高次有限元又是其中的一类常用有限元。由于高次元对问题具有更好的逼近效果及具有某些特殊的优点,如能解决弹性问题的闭锁现象(Poisson’s ratio locking),使得它们在实际计算中被广泛使用。但与线性元相比,它具有更高的计算复杂性。通过分析高次有限元空间与线性有限元空间之间的关系,提出了一种求解三维弹性问题高次有限元方程的两水平方法,然后,通过调用现有的代数多层网格法求解粗水平方程,建立了求解高次有限元方程的AMG法。数值实验表明,本文设计的AMG法对求解三维弹性问题高次有限元方程具有很好的计算效率和鲁棒性。     

Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors

A nonlocal continuum-based model is derived to simulate the dynamic behavior of bridged carbon nanotube-based nano-scale mass detectors. The carbon nanotube (CNT) is modeled as an elastic Euler-Bernoulli beam considering von-Kármán type geometric nonlinearity. In order to achieve better accuracy in characterization of the CNTs, the geometrical properties of an attached nano-scale particle are introduced into the model by its moment of inertia with respect to the central axis of the beam. The inter-atomic long-range interactions within the structure of the CNT are incorporated into the model using Eringen's nonlocal elastic field theory. In this model, the mass can be deposited along an arbitrary length of the CNT. After deriving the full nonlinear equations of motion, the natural frequencies and corresponding mode shapes are extracted based on a linear eigenvalue problem analysis. The results show that the geometry of the attached particle has a significant impact on the dynamic behavior of the CNT-based mechanical resonator, especially, for those with small aspect ratios. The developed model and analysis are beneficial for nano-scale mass identification when a CNT-based mechanical resonator is utilized as a small-scale bio-mass sensor and the deposited particles are those, such as proteins, enzymes, cancer cells, DNA and other nano-scale biological objects with different and complex shapes.     

三取代直链烷基苯磺酸钠的界面扩张性质

利用悬挂滴方法研究了五种表面活性剂3,4-二己基苯磺酸钠(66)、3,4-二庚基苯磺酸钠(77)、2-乙基-4,5-二己基苯磺酸钠(266)、2-丙基-4,5-二己基苯磺酸钠(366)和2-丁基-4,5-二己基苯磺酸钠(466)在空气-水和癸烷-水界面上的扩张流变性质,考察了烷基取代在苯环不同位置对分子界面行为的影响.研究发现,苯环不同位置的取代烷基链长变化对扩张弹性模量和扩张粘性模量影响不同.随着烷基链长增长,表面扩张弹性模量均增加,而扩张粘性模量表现则不同:邻位短链烷基碳数从2变化到4,对粘性模量贡献不大;而间位长链烷基增长对表面弛豫过程影响较大,粘性模量明显增大.油分子的插入能大大削弱间位长链烷基间的强相互作用,一方面导致界面弹性模量和粘性模量远低于表面,同时使得同分异构分子77和266的界面扩张粘性模量数值接近.     

Valuing American options under the CEV model by Laplace-Carson transforms

This paper investigates American option pricing under the constant elasticity of variance (CEV) model. Taking the Laplace-Carson transform (LCT) to the corresponding free-boundary problem enables the determination of the optimal early exercise boundary to be separated from the valuation procedure. Specifically, a functional equation for the LCT of the early exercise boundary is obtained. By applying Gaussian quadrature formulas, an efficient method is developed to compute the early exercise boundary, American option price and Greeks under the CEV model.     

Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field

Based on nonlocal theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. The present model treats each of the nested tubes as an individual column interacting with adjacent nanotubes through the intertube van der Waals forces. The thermal effect is incorporated in the formulation. In particular, an explicit expression is derived for the critical axial strain of a double-walled carbon nanotube which clearly demonstrates that small scale effects contribute significantly to the thermo-mechanical behavior of multiwalled carbon nanotubes and cannot be ignored.