Applied Mathematics and Mechanics (English Edition)

Shape gradient and classical gradient of curvatures: driving forces on micro/nano curved surfaces

殷雅俊陈超吕存景郑泉水

2011, 32(5): 533-550. doi:10.1007/s10483-011-1436-6

摘要 ( 380 )

PDF (287KB) ( 1212 )

相关文章 | 多维度评价

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a general theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived: (a) Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. (b) On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. (c) Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradients form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. (d) The direction of the driving force induced by the hard curved surface is independent of the hydrophilicity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.

Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification

马杭郭钊秦庆华

2011, 32(5): 551-562. doi:10.1007/s10483-011-1437-x

摘要 ( 574 )

PDF (454KB) ( 967 )

相关文章 | 多维度评价

The low-order polynomial-distributed eigenstrain formulation of the boundary integral equation (BIE) and the corresponding definition of the Eshelby tensors are proposed for the elliptical inhomogeneities in two-dimensional elastic media. Taking the results of the traditional subdomain boundary element method (BEM) as the control, the effectiveness of the present algorithm is verified for the elastic media with a single elliptical inhomogeneity. With the present computational model and algorithm, significant improvements are achieved in terms of the efficiency as compared with the traditional BEM and the accuracy as compared with the constant eigenstrain formulation of the BIE.

General solutions of plane problem for power function curved cracks

郭俊宏袁泽帅卢子兴

2011, 32(5): 563-570. doi:10.1007/s10483-011-1438-9

摘要 ( 539 )

PDF (281KB) ( 956 )

相关文章 | 多维度评价

A new exact and universal conformal mapping is proposed. Using Muskhelishvili’s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors (SIFs) for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

A. CHATTOPADHYAY S. GUPTA S. A. SAHU A. K. SINGH

2011, 32(5): 571-586. doi:10.1007/s10483-011-1439-7

摘要 ( 567 )

PDF (447KB) ( 1830 )

相关文章 | 多维度评价

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.

Analysis of cavitation problem of heated elastic composite ball

尚新春张锐任会兰

2011, 32(5): 587-594. doi:10.1007/s10483-011-1440-9

摘要 ( 545 )

PDF (274KB) ( 783 )

相关文章 | 多维度评价

The cavitation problem of a composite ball under a uniform temperature is investigated, and the ball is composed of two elastic solid materials. The nonlinear mathematical model of the problem is established with the finite logarithmic strain measure for a large geometric deformation and by the Hooke law for elastic materials. The analytic solutions in a parametric form are derived for the thermal dilatation of the composite ball with a large elastic deformation. Solution curves are given to describe the variations of the critical temperature in the cavitation with the geometric and material parameters. The bifurcation curve is also given to reveal the cavity growth after void nucleation. The numerical results for a computational example indicate that the radius of the cavity will rapidly grow above the critical temperature, and the loop stress will become infinite when void nucleation. This means that the materials near the cavity will produce a plastic deformation leading to local failure and fracture if the material of the internal ball is elastoplastic. In addition, the cavitation of the composite ball appears at a low temperature if the elastic property of the material of the internal ball is nearly uncompressible.

Influence of magnetic field on wave propagation at liquid-microstretch solid interface

B. SINGH

2011, 32(5): 595-602. doi:10.1007/s10483-011-1441-6

摘要 ( 632 )

PDF (216KB) ( 1024 )

相关文章 | 多维度评价

The reflection and refraction of a longitudinal wave at an interface between a perfectly conducting nonviscous liquid half-space and a perfectly conducting microstretch elastic solid half-space are studied. The appropriate solutions to the governing equations are obtained in both the half-spaces satisfying the required boundary conditions at the interface to obtain a system of five non-homogeneous equations in the amplitude ratios of various reflected and transmitted waves. The system is solved by a Fortran program of the Gauss elimination method for a particular example of an interface between water and aluminum-epoxy composite. Numerical values of the amplitude ratios are computed for a certain range of the incidence angle both in the presence and absence of an impressed transverse magnetic field. The effects of the presence of the transverse magnetic field on the amplitude ratios of various reflected and transmitted waves are shown graphically.

Stability analysis of helical rod based on exact Cosserat model

刘延柱薛纭

2011, 32(5): 603-612. doi:10.1007/s10483-011-1442-8

摘要 ( 590 )

PDF (237KB) ( 1172 )

相关文章 | 多维度评价

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff’s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff’s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler’s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov’s stability of the helical equilibrium is discussed in static category. Euler’s critical values of axial force and torque are obtained. Lyapunov’s and Euler’s stability conditions in the space domain are the necessary conditions of Lyapunov’s stability of the helical rod in the time domain.

Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil

相倩吴颂平李椿萱曹宁

2011, 32(5): 613-620. doi:10.1007/s10483-011-1443-8

摘要 ( 414 )

PDF (401KB) ( 1099 )

相关文章 | 多维度评价

The preconditioning technique can address the stiffness of a low Mach number flow, while its stability is poor. Based on the conventional preconditioning method of Roe’s scheme, a low-diffusion scheme is proposed. An adjustable parameter is introduced to control numerical dissipation, especially over the dissipation in the boundary layer and extremely in a low speed region. Numerical simulations of the low Mach number and low Reynolds number flows past a cylinder and the low Mach number and high Reynolds number flows past NACA0012 and S809 airfoils are performed to validate the new scheme. Results of the three tests well agree with experimental data, showing the applicability of the proposed scheme to low Mach number flow simulations.

Study on application of random walk method to calculate water exchange in large-scale bay

李小宝袁德奎陶建华

2011, 32(5): 621-634. doi:10.1007/s10483-011-1444-x

摘要 ( 435 )

PDF (318KB) ( 972 )

相关文章 | 多维度评价

The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.

Scattering of water waves by thin vertical plate submerged below ice-cover surface

P. MAITI P.RAKSHIT S. BANERJEA

2011, 32(5): 635-644. doi:10.1007/s10483-011-1445-7

摘要 ( 468 )

PDF (312KB) ( 897 )

相关文章 | 多维度评价

The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green’s integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.

Turbulent flow in converging nozzles, part one:boundary layer solution

R. MADDAHIAN B. FARHANIEH B. FIROOZABADI

2011, 32(5): 645-662. doi:10.1007/s10483-011-1446-6

摘要 ( 1162 )

PDF (543KB) ( 2556 )

相关文章 | 多维度评价

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.

Solution and stability of mixed type functional equation in non-Archimedean random normed spaces

张石生 R. SAADATI G. SADEGHI

2011, 32(5): 663-676. doi:10.1007/s10483-011-1447-6

摘要 ( 478 )

PDF (201KB) ( 1014 )

相关文章 | 多维度评价

The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.

当期目录