Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure

Elastic analysis of a functionally graded thick-walled cylindrical pressure vessel is analytically studied in the present research. Gradation is considered for all mechanical properties along the thickness direction based on a power function. The constitutive relations are developed in the general cylindrical coordinate system for an axisymmetric pressurized cylinder. For simulation of these two deformation components, first order shear deformation theory is considered. The FG cylinder is subjected to longitudinally non-uniform pressure along the length of the cylinder. The present problem is applicable for simulation of non-uniform pressurized cylinder by fluids or gases.     

Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

A new level‐dependent coarse grid correction scheme for indefinite Helmholtz problems

In this paper, we construct and analyze a level‐dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid‐dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two‐grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state‐of‐the‐art MG‐preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES. Copyright © 2013 John Wiley & Sons, Ltd.     

Orientation-dependent deformation mechanisms of bcc niobium nanoparticles

Nanoparticles usually exhibit pronounced anisotropic properties, and a close insight into the atomic-scale deformation mechanisms is of great interest. In present study, atomic simulations are conducted to analyse the compression of bcc nanoparticles, and orientation-dependent features are addressed. It is revealed that surface morphology under indenter predominantly governs the initial elastic response. The loading curve follows the flat punch contact model in [1 1 0] compression, while it obeys the Hertzian contact model in [1 1 1] and [0 0 1] compressions. In plastic deformation regime, full dislocation gliding is dominated in [1 1 0] compression, while deformation twinning is prominent in [1 1 1] compression, and these two mechanisms coexist in [0 0 1] compression. Such deformation mechanisms are distinct from those in bulk crystals under nanoindentation and nanopillars under compression, and the major differences are also illuminated. Our results provide an atomic perspective on the mechanical behaviours of bcc nanoparticles and are helpful for the design of nanoparticle-based components and systems.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点，从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同，层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭，并在层间结合面处发生强不连续，呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用，不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出，现有各种考虑剪切变形影响的计算模型虽然有了很大的发展，但在全面和准确性上仍然存在一定的不足，难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型，同时可适用于各种薄板与厚板的分析，对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化，与三维弹性理论的标准解高度吻合。数值算例进一步表明，随着层间纤维走向的变化，板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此，本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

Toward deformation densities for intramolecular interactions without radical reference states using the fragment,atom, localized,delocalized, and interatomic (FALDI) charge density decomposition scheme

A novel approach for calculating deformation densities is presented, which enables to calculate the deformation density resulting from a change between two chemical states, typically conformers, without the need for radical fragments. The Fragment, Atom, Localized, Delocalized, and Interatomic (FALDI) charge density decomposition scheme is introduced, which is applicable to static electron densities (FALDI‐ED), conformational deformation densities (FALDI‐DD) as well as orthodox fragment‐based deformation densities. The formation of an intramolecular NH⋅⋅⋅N interaction in protonated ethylene diamine is used as a case study where the FALDI‐based conformational deformation densities (with atomic or fragment resolution) are compared with an orthodox EDA‐based approach. Atomic and fragment deformation densities revealed in real‐space details that (i) pointed at the origin of density changes associated with the intramolecular H‐bond formation and (ii) fully support the IUPAC H‐bond representation. The FALDI scheme is equally applicable to intra‐ and intermolecular interactions. © 2017 Wiley Periodicals, Inc.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rot...