Rivulet dynamics at isothermal film flow

Averaged fields of thickness of an isothermal vertically flowing liquid film, obtained by the laserinduced fluorescence method, have been analyzed. The chosen minimum averaging time interval, at which the wave motion is completely averaged, allows one to observe rivulet dynamics in a transverse direction. It is found that short-lived rivulets, which are chains of no less than five to eight waves with similar transverse coordinates, are dominant structures on the film surface at Reynolds number Re > 50.     

Orthonormal polynomials in wavefront analysis: analytical solution

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. In recent papers, we derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror. We extend our work to elliptical, rectangular, and square pupils. Using the circle polynomials as the basis functions for their orthogonalization over such pupils, we derive closed-form polynomials that are orthonormal over them. These polynomials are unique in that they are not only orthogonal across such pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects for circular pupils. The polynomials are given in terms of the circle polynomials as well as in polar and Cartesian coordinates. Relationships between the orthonormal coefficients and the corresponding Zernike coefficients for a given pupil are also obtained. The orthonormal polynomials for a one-dimensional slit pupil are obtained as a limiting case of a rectangular pupil.     

A truly mesh-distortion-enabled implementation of cell-based smoothed finite element method for incompressible fluid flows with fixed and moving boundaries

Mesh-free properties are part of the superiority of cell-based smoothed finite element method (CS-FEM), but have yet to be fully exploited for computational fluid dynamics. A novel implementation of CS-FEM for incompressible viscous fluid flows in stationary and deforming domains discretized by severely distorted bilinear four-node quadrilateral (Q4) elements is presented in this article. The negative determinant of the Jacobian transformation from the Cartesian coordinates to the natural coordinates is intentionally stipulated for the corresponding mesh over which FEM inevitably fails in practice. It is found that, without ad hoc modifications, CS-FEM incurs unsatisfactory results and even a failure on fixed meshes. To cater for general computations on either a uniform or nonuniform mesh represented by these badly degenerated elements, four smoothing cells (SCs) are deployed in convex Q4 element whereas one SC in concave Q4 element. A simple hourglass control is introduced into those under-integrated quadrilaterals for stabilizing the one-SC quadrature in smoothed Galerkin weak form. Thanks to the adoption of characteristic-based split (CBS) scheme for the fluid solution, a byproduct is the unfolded equivalence of the CBS stabilization and balancing tensor diffusivity under the incompressibility constraint. Several benchmark problems involving incompressible fluid flow and fluid-structure interaction are solved. Numerical results show the good accuracy and robustness of the proposed approach that raises a seductive idea for resolving moving-mesh problems.     

Coordinate Transformations with Multiple Computer-generated Optical Elements

Abstract

An afocal system for coherent optical coordinate transformation using computer-generated holograms is presented. The afocal geometry allows cascading of transformations and simple incorporation into optical systems. A two-element afocal transformation system from Cartesian to log-polar coordinates, and a three-element cascaded afocal transformation system from polar to Cartesian coordinates, are presented for simple objects.     

Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency

A rigorous computational framework for the dimensional reduction of discrete, high‐fidelity, nonlinear, finite element structural dynamics models is presented. It is based on the pre‐computation of solution snapshots, their compression into a reduced‐order basis, and the Galerkin projection of the given discrete high‐dimensional model onto this basis. To this effect, this framework distinguishes between vector‐valued displacements and manifold‐valued finite rotations. To minimize computational complexity, it also differentiates between the cases of constant and configuration‐dependent mass matrices. Like most projection‐based nonlinear model reduction methods, however, its computational efficiency hinges not only on the ability of the constructed reduced‐order basis to capture the dominant features of the solution of interest but also on the ability of this framework to compute fast and accurate approximations of the projection onto a subspace of tangent matrices and/or force vectors. The computation of the latter approximations is often referred to in the literature as hyper reduction. Hence, this paper also presents the energy‐conserving sampling and weighting (ECSW) hyper reduction method for discrete (or semi‐discrete), nonlinear, finite element structural dynamics models. Based on mesh sampling and the principle of virtual work, ECSW is natural for finite element computations and preserves an important energetic aspect of the high‐dimensional finite element model to be reduced. Equipped with this hyper reduction procedure, the aforementioned Galerkin projection framework is first demonstrated for several academic but challenging problems. Then, its potential for the effective solution of real problems is highlighted with the realistic simulation of the transient response of a vehicle to an underbody blast event. For this problem, the proposed nonlinear model reduction framework reduces the CPU time required by a typical high‐dimensional model by up to four orders of magnitude while maintaining a good level of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Removing ring artifacts in CBCT images via smoothing

Ring artifacts often appear in cone‐beam computed tomography (CBCT) images due to the inconsistent response of detector pixels. How to remove ring artifacts without impairing the image quality is still a hard problem. This article proposes a novel method to remove ring artifacts from CBCT images. First, the reconstructed CBCT image is transformed from Cartesian coordinates into polar coordinates, such that ring artifacts in Cartesian coordinates are transformed as stripe artifacts in polar coordinates that are easier to be removed. Second, a minimization model based on smoothing is introduced to smooth the transformed image such that the major edges of the image are reserved while the artifacts are eliminated as special low‐amplitude structures. Finally, the obtained artifacts are transformed back into Cartesian coordinates and are subtracted from the original CBCT image. Thus, the CBCT image without ring artifacts is obtained. The experiments based on different CBCT images show that the proposed method is more effective compared with other algorithms. © 2016 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 26, 284–294, 2016     

Complex variable moving least‐squares method: a meshless approximation technique

Based on the moving least‐squares (MLS) approximation, we propose a new approximation method—the complex variable moving least‐squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two‐dimensional problem is formed with a one‐dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two‐dimensional elasticity problems—the complex variable meshless method (CVMM)—and the formulae of the CVMM for two‐dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM. Copyright © 2006 John Wiley & Sons, Ltd.     

FATIGUE CRACK GROWTH SIMULATIONS BASED ON FREE FRONT SHAPE DEVELOPMENT

Abstract— A single-crack evolution model with eight degrees of freedom and an isotropic Paris law constant was used to simulate fatigue crack growth at the surface of a plate, and from the toe of a transverse non-load-bearing fillet weld in a T-joint. A planar crack was assumed. In the simulated cases fatigue cracks usually propagate through the plate thickness under the dominant effect of the mode I stress system. The crack front shape was modelled as a broken line. The straight sided crack tip elements were tangential to the direction of an initial elliptical crack front. It was found that the simple eight degrees of freedom model performed well and the predicted aspect ratio development was in good agreement with experimental data.     

两类鞍形线圈产生磁场均匀性效能的研究

以毕奥-萨伐尔定律在笛卡尔直角坐标下对两种鞍形匀场线圈进行数学建模,通过对两种轴对称线圈单组的数值分析得出线圈系统在径向磁场分布的一般特征,在理论计算获得线圈最佳结构下利用Matlab优化结构参数。对比了这两类鞍形线圈在轴上和空间立方体的磁场均匀区大小及与中心磁场的相对偏差。并给出了这两种线圈磁场相对偏差ε≤1%的有效匀场空间区域,为主动屏蔽系统的线圈类型选择提供了参考依据。     

Improvements on winding flux models for a slotless self-bearing motor

For a large-scale slotless permanent-magnet self-bearing motor actuator, finite-element analysis (FEA) indicates a significant difference from the previous simple winding flux model. In this paper, we first derive a general winding current distribution. We use and compare three analytical methods to calculate the air gap field produced by the windings when only torque is required. Each of the first two solves one homogeneous Laplace's equation with the current source incorporated into a harmonic boundary condition, in polar and Cartesian coordinates, respectively. The good agreement between these two allows the third method to treat the current source separately and solve one nonhomogeneous and one homogeneous Laplace's equations simultaneously in two subregions, simply using the unwrapped geometry in Cartesian coordinates. The result from the two-layer model matches the FEA prediction for this particular actuator very well and it is thus more accurate to model the thick windings as a separate source layer. We propose a simple approach to include the interference of the magnetic fields due to the segment currents whenever a bearing force is required, which was completely neglected in all the previous models. The approach is quite accurate, as shown by the corresponding FEA result.     

Free asymmetric transverse vibration of polar orthotropic annular sector plate with thickness varying parabolically in radial direction

In the present paper, free asymmetric transverse vibrations of a non-uniform polar orthotropic annular sector plate, with parabolically varying thickness in the radial direction, have been studied on the basis of classical plate theory. The circular edges of the plate are elastically restrained against translation and rotation while the straight (radial) edges are simply-supported. Fourth-order linear differential equations with variable coefficients governing the motion have been solved by using the collocation interpolation technique with Chebyshev points as the interpolating nodes. Frequency parameters of the plate with flexible boundary conditions at the circular edges for some typical values of the taper parameters, the rigidity ratios and the radii ratio have been presented.     

A variational principle for nonlinear water waves

Summary This paper is concerned with a variational formulation of non-axisymmetric water waves and of two-dimensional surface waves in a running stream of finite depth. The full set of equations of motions for the non-axisymmetric water wave problem in cylindrical polar coordinates and for the two-dimensional surface waves in the running stream in Cartesian coordinates is obtained from a Lagrangian function which is equal to the pressure.With 1 Figure     

Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems

The boundary integral equation method in conjunction with the degenerate kernel, the direct searching technique (singular value decomposition), and the only two-trials technique (2 × 2 matrix eigenvalue problem) are analytically and numerically used to find the degenerate scales, respectively. In the continuous system of boundary integral equation, the degenerate kernel for the 2D Kelvin solution in the polar coordinates is reviewed and the degenerate kernel in the elliptical coordinates is derived. Using the degenerate kernel, an analytical solution of the degenerate scales for the elasticity problem of circular and elliptical cases is obtained and compared with the numerical result. Further, the triangular case and square case were also numerically demonstrated.     

Comparison of high‐order curved finite elements

Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two‐dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS‐enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p‐FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

圆弧齿锥齿轮接触动力学分析

运用三角网格方法重构了三维离散的圆弧齿啮合齿面模型。基于多体动力学理论和迟滞接触动力学方法,提出了考虑全齿面动态接触关系的螺旋锥齿轮三维接触动力学模型和动力学分析方法。运用三角网格单元接触的包围盒搜索技术和微分代数方程求解方法,仿真分析了单侧齿面接触、双侧齿面接触、负载扭矩和齿侧侧隙等因素对齿轮啮合传动特性的影响,获得了圆弧齿啮合全齿面接触冲击力,力矩和角速度等齿轮啮合传动的动态响应特性。研究表明：新方法和动力学模型较好地模拟了圆弧齿锥齿轮的承载特性和啮合接触动力学特性,对以动力学特性为目标的圆弧齿锥齿轮设计和齿轮系统动力学研究提供了理论参考。     

Unitary transformation between Cartesian- and polar-pixellated screens

A unitary transformation between Cartesian and polar pixellations of finite two-dimensional images is obtained from the su(2) model for discrete and finite signals. This transformation analyzes the original image into its finite Cartesian "Laguerre-Kravchuk" modes (involving Wigner little-d functions) and synthesizes it back using a polar mode basis with the same set of mode coefficients. The polar basis is derived from the quantum angular momentum theory, and its modes are given by Clebsch-Gordan coefficients.     

Conjugated Effect of Joule Heating and Magnetohydrodynamic on Laminar Convective Heat Transfer of Nanofluids Inside a Concentric Annulus in the Presence of Slip Condition

In the current study, the conjugated effect of Joule heating and magnetohydrodynamics (MHD) on the forced convective heat transfer of fully developed laminar nanofluid flows inside annular pipes, under the influence of MHD field, has been investigated. The temperature and nanoparticle distributions at both the inner and outer walls are assumed to vary in the direction of the fluid. Furthermore, owing to the nanoparticle migrations in the fluid, a slip condition becomes far more important than the no-slip condition of the fluid–solid interface, which appropriately represents the non-equilibrium region near the interface. The governing equations—obtained by employing the Buongiorno’s model for nanofluid in cylindrical coordinates—are converted into two-point ordinary boundary value differential equations and solved numerically. The effects of various controlling parameters on the flow characteristics, the average Nusselt number and the average Sherwood number have been assessed in detail. Additionally, the effect of the inner to outer diameter ratio on the heat and mass transfer rate has been studied. The results obtained indicate that, in the presence of a magnetic field when the fluid is electrically conductive, heat transfer will be reduced significantly due to the influences of Joule heating, while the average mass transfer rate experiences an opposite trend. Moreover, the increase in the slip velocity on both the walls causes the average heat transfer to rise and the average mass transfer to decrease.     

On the null and nonzero fields for true and spurious eigenvalues of annular and confocal elliptical membranes

In this paper, the dual boundary element method (BEM) and the null-field boundary integral equation method (BIEM) are both employed to solve two-dimensional eigenproblems. The positions of true and spurious eigenvalues for circular, elliptical, annular and confocal elliptical membranes are analytically examined in the continuous system and numerically studied in the discrete system. To analytically study eigenproblems, the polar and elliptical coordinates in conjunction with the Bessel functions, the Mathieu functions, the Fourier series and eigenfunction expansions are adopted. The fundamental solution is expanded into the degenerate kernel while the boundary densities of circular and elliptical boundaries are expanded by using the Fourier series and eigenfunction expansion, respectively. Dirichlet and Neumann eigenproblems are both considered as well as simply and doubly-connected domains are both addressed. By employing the singular value decomposition (SVD) technique in the discrete system, the common right unitary vectors corresponding to the true eigenvalues for the singular and hypersingular formulations are found while the common left unitary vectors corresponding to the spurious eigenvalues are obtained for the singular formulation or hypersingular formulation. True eigenvalues depend on the boundary condition while spurious eigenvalues depend on the approach, the singular formulation or hypersingular formulation of BEM/BIEM. Nonzero field in the domain are analytically derived and are numerically verified in case of the true eigenvalue while the interior null field and nonzero field for the complementary domain are obtained in case of the spurious eigenvalue. Four examples, circular, elliptical, annular and confocal elliptical membranes, are considered to demonstrate the finding of the present paper. After comparing with the analytical and numerical results, good agreements are made. The dual BEM displays the dual structure in the unitary vector and the null field.