An equilibrium-based formulation with nonlinear configuration dependent interpolation for geometrically exact 3D beams

This article describes a novel equilibrium-based geometrically exact beam finite element formulation. First, the spatial position and rotation fields are interpolated by nonlinear configuration-dependent functions that enforce constant strains along the element axis, completely eliminating locking phenomena. Then, the resulting kinematic fields are used to interpolate the spatial sections force and moment fields in order to fulfill equilibrium exactly in the deformed configuration. The internal variables are explicitly solved at the element level and closed-form expressions for the internal force vector and tangent stiffness matrix are obtained, allowing for explicit computation, without numerical integration. The objectivity and absence of locking are verified and some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. The proposed formulation is successfully tested in several numerical application examples.     

Size dependent buckling analysis of nano sandwich beams by two schemes

Abstract

Within the framework of Timoshenko beam theory, the buckling of nano sandwich beams is developed. The material properties are assumed to vary arbitrarily in both axial and thickness directions. These types of beams are referred to as bi-directional functionally graded (BDFG) beams. Two types of nano sandwich beams with different material distribution patterns and immovable supports are considered. Since the size effects play a significant role in mechanical behavior of nanostructures, the small-scale effects are captured by Eringen’s nonlocal theory of elasticity. The governing equations are derived using the variational formulation. Symmetric smoothed particle hydrodynamics (SSPH) and the Galerkin method are adopted as numerical solution approaches. As a truly meshless method, the convergence of the SSPH technique mainly depends on the smoothing length value and distribution of particles in the compact support domain of the kernel function. The Revised Super Gauss Function is used as the kernel function and an optimum value for the smoothing length that bears the fastest convergence rate is obtained. The solution methods are verified through benchmark problems found in the literature. Numerical and illustrative results show that various parameters, including the aspect ratio, nonlocal parameter, gradient indexes, and cross-sectional types have significant effects on the buckling responses of BDFG nano sandwich beams.     

Polarization separation of light beams at the interface of two mesophases

The features of reflection of the linearly polarized light beams at the interface between two regions of a nematic liquid crystal (LC) with the orthogonal director orientation have been analyzed. The relationship between light beam propagation in a LC material and polarization of laser radiation has been established. Rotation of the polarization plane of a light beam has been found for the radiation introduced through the free surface “LC—air” deformed due to the capillarity effect. The total internal reflection effect has been demonstrated experimentally together with the possibility for special separation of the orthogonally polarized light beams at the interface of two mesophases.     

Interpolation of rotational variables in nonlinear dynamics of 3D beams

The formulation of dynamic procedures for three-dimensional (3-D) beams requires extensive use of the algebra pertaining to the non-linear character of the rotation group in space. The corresponding extraction procedure to obtain the rotations that span a time step has certain limitations, which can have a detrimental effect on the overall stability of a time-integration scheme. The paper describes two algorithms for the dynamics of 3-D beams, which differ in their manifestation of the above limitation. The first has already been described in the literature and involves the interpolation of iterative rotations, while an alternative formulation, which eliminates the above effect by design, requires interpolation of incremental rotations. Theoretical arguments are backed by numerical results. Similarities between the conventional and new formulation are pointed out and are shown to be big enough to enable easy transformation of the conventional formulation into the new one. © 1998 John Wiley & Sons, Ltd.     

On the interaction between two circular voids in a nonlinear elastic solid

Summary We study finite plane strain deformations of an infinite body containing two circular voids and made of a Blatz-Ko material. The body is subjected to either uniform tensile tractions at infinity or a uniform pressure on the void surfaces. In each case, the effect of varying the distance between the void centers on the deformations of the body is analyzed. When the voids are located close to each other, a uniform pressure on the void surfaces results in noncircular deformed voids, and for a fixed value of the pressure, the deformation induced increases as the voids get closer to each other. When the body is subjected to uniform tensile tractions at infinity, say along thex-axis, the voids are deformed into ellipsoids with major axes aligned along thex-axis.     

Charged polaron-enhanced circular dichroism of optically nonlinear 3-nitroaniline crystal

The circular dichroism (CD) spectra in visible range of the 3-nitroaniline (m-NA) single crystal, of its solution in chloroform, and in the KBr pellet were recorded. Neither the molecular (m or C_s) nor the crystal (mm2 or C_2v) point groups belong to the chiral groups. The DFT calculation of CD spectrum of the m-NA isolated neutral molecule confirmed its chirality. The red shifted bands in the calculated CD spectrum of m-NA radical anion (charged polaron), as compared with the neutral molecule, resemble better the spectra of solids than that of the solution. It seems that these facts corroborate qualitatively the “hop and turn” model explaining the m-NA optical nonlinearity and electric conductivity proposed in Szostak et al. [M.M. Szostak, H. Chojnacki, E. Staryga, M. D?u?niewski, G. B?k, Chem. Phys. 365 (2009) 44-52].     

Torsional vibrations of quartz crystal beams

An exact solution of a partial differential equation including elastic compliance constant s'₅₆, with respect to stress function ψ has been found for torsional modes of vibration of an arbitrary (singly, doubly, triply) rotated beam with a pair of parallel free edges. The solution is obtained by relaxing the condition that the edge planes are perpendicular to the main faces of the beam. That is, the edges are off perpendicular by the angle Θ=arctan(-s'₅₆ /8'₅₅). The exact solution can reduce the difference of the calculated and measured values for a thickness-to-width ratio which gives the first-order temperature coefficient α=0. Also, a comparatively large inclination of the edge cuts is required to reduce the unwanted complicated mode shapes to simple ones     

Generation of propagation-invariant light beams from semiconductor light sources

We have studied the possibility of generating propagation-invariant (nondiffracting) light beams using various semiconductor sources of radiation. The propagation-invariant (Bessel) beams have been generated using cone-shaped lenses (axicones) with an apical angle of 178° and 170°, which provided beams with a central spot diameter of 100 and 10 μm, respectively. The radiation sources were represented by various types of light-emitting diodes, quasi-single-mode semiconductor vertical-cavity surface-emitting lasers and broad-stripe (100 μm) edge-emitting laser diodes. It is demonstrated that these semiconductor light sources offer a promising basis for the generation of propagation-invariant light beams in various devices (including optical tweezers) intended for manipulating micro- and nanodimensional objects.     

共聚焦非线性声场的研究

1引言 聚焦换能器可在焦点附近产生很强的非线性并且能有效地提高分辨率,从而被广泛应用于超声医学诊断及非线性超声显微镜中.章东、龚秀芬等基于近轴及准线性近似下的KZK非线性方程[1],利用高斯函数叠加法[2]来近似表示活塞聚焦声源的源分布函数,研究了生物组织样品插入后聚焦换能器的非线性声场,得到二次谐波分量的解析解[3].本文在此基础上进一步研究了在聚焦声场中用另一聚焦换能器接收到的二次谐波分量,并对生物组织样品(猪的肝组织、脂肪组织)插入到焦区后接收到的二次谐波分量与两换能器间距离的关系进行了数值模拟.     

Determination of light output function and angle dependent correction for a stilbene crystal scintillation neutron spectrometer

In addition to liquid NE213 scintillators also stilbene solid crystals are applied traditionally for fast neutron spectrometry. A proper evaluation of experimental data provides a precise determination of the nonlinear light output function for the given scintillator/photomultiplier combination, and for stilbene additionally an adequate correction of the anisotropy effect. Calibration experiments with monoenergetic neutrons (1.2, 2.5, 5.0, 13.95, 14.8, 19.0 MeV) and various neutron incidence angles were carried out at the accelerator facility of the PTB Braunschweig for two cylindrical scintillators (∅30 mm×25 mm, ∅10 mm×10 mm). An improved analytic light output function as well as an adequate angle dependent correction function were derived.     

Quadratic nonlinear optical parameters of 7% MgO-doped LiNbO3 crystal

Pure and 7% MgO-doped lithium niobate (LiNbO₃) single crystals were grown by the Czochralski technique. The shift of optical absorption edge in 7% MgO-doped crystal in direction of shorter wavelength compared to undoped crystal was observed. The second harmonic generation measurements of 7% MgO-doped LiNbO₃ crystal were performed at room temperature by means of the rotational Maker fringe technique using Nd:YAG laser generating at 1064 nm in picoseconds regime. Experimentally obtained value of nonlinear optical coefficient d₃₃ for 7% MgO-doped LiNbO₃ was found to be less than for undoped crystal but higher than for 5% MgO-doped. I-type phase-matched second harmonic generation was achieved and the value of phase-matched angle was calculated. High quadratic nonlinearity together with tolerance to intensive laser irradiation makes 7% MgO-doped LiNbO₃ crystal interesting for application in optoelectronics.     

Generation of long-range nondiffracting narrow light beams

A type of nondiffracting narrow light beam that propagates across a long range with a narrow beamwidth is presented. This beam is formed by a distorted concave spherical wave front that can be generated by a Galilean transmitting telescope with an eyepiece that has a spherical aberration. We observed an unusual image with a striped pattern in the laser beam's atmospheric backscatter that provided an opportunity to examine this effect. We demonstrate the mechanism of the generation and the characteristics of the long-range nondiffracting beam. The results show that a nondiffracting core beam with a width of the order of millimeters with a propagation distance of the order of a kilometer is generated by a 10-cm-diameter laser beam.     

Rotation of multimode Gauss-Laguerre light beams in free space

An iterative algorithm is presented for calculating diffractive phase optical elements that form light beams which are an effective superposition of a small number of nonradially symmetric Gauss-Laguerre modes with a prescribed energy contribution from each mode. Pis’ma Zh. Tekh. Fiz. 23, 1–6 (September 12, 1997)     

Approximation of minimal maximal deflection of nonlinear beams

A geometrically nonlinear beam of fixed volume is subjected to both bending and stretching. A method is presented for approximating the distribution of mass of the beam so as to get the smallest maximum displacement for a given load. The method allows for easy error estimates.     

空间微重力条件下生长LiIO3、GaAs晶体的研究进展

综述了空间微重力环境下生长GaAs、α-LiIO3晶体的研究进展,展望了其应用前景.     

Characteristics of cleavage fracture during interaction of nonlinear waves with the free surface of a copper single crystal

A molecular dynamics method was used to study the interaction of isolated compression pulses with the (100) and (110) free surface in a copper monocrystallite. It is shown that this may be accompanied by cleavage fracture. Parameters of compression pulses which lead to cleavage processes are determined. Pis’ma Zh. Tekh. Fiz. 25, 22–27 (December 12, 1999)     

Temperature-dependent Sellmeier equations of nonlinear optical crystal Na3La9O3(BO3)8

The principal refractive indices of Na₃La₉O₃(BO₃)₈ (NLBO) crystal in the wavelength range of 0.363–2.325 μm were accurately measured by using the minimum deviation method within the temperature range from 23.5 °C to 160 °C. We derived the expressions of thermal refractive index coefficient as a function of wavelength that could be used to calculate the principal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also derived and used to calculate the phase-matching (PM) angles for a frequency conversion device based on NLBO crystal at different temperatures. We found that the thermal refractive index coefficients of NLBO crystal changed from positive to negative values with the increase of wavelength. In addition, the phase matching conditions for third harmonic generation (THG) at different temperatures were also investigated.