根部柔性梁的不确定性建模与确认

首先导出了包含根部挠性参数的悬臂梁动力学方程近似解,将平动和转动柔性参数作为不确定性源,根据若干预紧力矩下的模态实验结果完成了柔性参数识别,并假定其服从正态随机分布,识别了均值与标准差,进而通过回归分析建立了不确定参数随预紧力矩变化的数学模型.最后通过新的模态实验结果对所建模型进行了确认,通过确认结果,明确了该模型的使用范围.     

The Blasius and Sakiadis flow with variable fluid properties

A theoretical study of the effect of variable fluid properties on the classical Blasius and Sakiadis flow is presented in this paper. The investigation concerns engine oil, water and air taking into account the variation of their physical properties with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented, as well as values of wall shear stress and wall heat transfer, for a variety of temperatures between the plate and the ambient fluid. It is found that the variation of fluid properties and especially viscosity have a strong influence on the results. The results of oil and water are, in general, similar and are generalized to liquids whereas air results are different and are generalized to gases. Except of the new results found in the present work some inaccurate results existing in the literature have been identified.     

An exact multiphase Riemann solver for compressible cavitating flows

This paper presents a new one-fluid method for simulating formation and the collapse of cavitation regions in water during an isothermal process. In this method, the fluid phase changes are included into the wave pattern of an exact Riemann solver. The model behavior is assessed by comparing the numerical results with the other numerical models for several 1D Riemann problems. One-dimensional water hammer problems with vast creation and collapsing of cavitation zones are simulated as well—and the numerical results are compared to experimental results. The new model results are in very good agreement with accepted results reported in the literature. The presented results clearly show that the new model is able to capture the various behaviors of water during the phase change in the saturation dome and the vapor state, which was neglected in previous studies. Finally, the new model is adopted to an ALE method on an adaptive triangular grid to simulate an underwater explosion phenomenon inside a rigid cylinder—and the results are compared with other simulations.     

Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces

The stability of clamped stepped and stiffened rectangular plate subjected to in-plane forces is examined. The plate is divided into 900 rectangular meshes and the partial derivatives are approximated using central difference formula. Altogether 841 equations of equilibrium and 248 equations representing boundary conditions are formed, finally leading to the solution of eigenvalue problem. The buckling coefficients are calculated for various types of stepped plates and the results are presented in tables for ready use by designers. The results are compared with the published results and they are in close agreement.     

悬索非线性动力学中的直接法与离散法

以悬索为例对结构非线性动力学中直接法与离散法的应用进行了研究. 针对悬索面内运动的第$n$阶模态的主共振，分别利用这两种方法对悬索的非线性响应进行求解，得到悬索非线性响应的二次近似解以及相应的幅频响应曲线，并比较和讨论了这两种方法得到的结果及其差异. 通过分析得知：离散法在用于非对称结构非线性动力学的求解时可能导致错误的结果.     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Height of burst explosions: a comparative study of numerical and experimental results

In the current work, we use the Constant Volume model and the numerical method, Regularized Smoothed Particle Hydrodynamics (RSPH) to study propagation and reflection of blast waves from detonations of the high explosives C-4 and TNT. The results from simulations of free-field TNT explosions are compared to previously published data, and good agreement is found. Measurements from height of burst tests performed by the Norwegian Defence Estates Agency are used to compare against numerical simulations. The results for shock time of arrival and the pressure levels are well represented by the numerical results. The results are also found to be in good agreement with results from a commercially available code. The effect of allowing different ratios of specific heat capacities in the explosive products are studied. We also evaluate the effect of changing the charge shape and height of burst on the triple point trajectory.      

Newtonian heating in stagnation point flow of Burgers fluid

The Newtonian heating effects in the stagnation point flow of a Burgers fluid are addressed in this paper. The boundary layer flow problems are stated in the spatial domain from zero to infinity. The solution expressions for the velocity and the temperature are obtained and examined for the influential variables. The tabulated values show comparison with the previous results. It is observed that the obtained results are in good agreement with the existing results in limiting sense.     

金属靶板侵彻数值模拟对比研究

数值模拟是研究靶板侵彻问题的重要手段。为对相关软件的选取提供参考,采用当前广泛使用的3种有限元软件（LS-DYNA、ABAQUS、PAM-CRASH）对同一个靶板侵彻实验进行了数值模拟,并比较了各模拟软件的优缺点。研究结果表明:3种软件的模拟结果与实验结果均基本一致;对平头形弹体侵彻的模拟效果普遍优于对半球形弹体的模拟效果;在弹体剩余速度、冲塞块速度2个方面,3种有限元软件的数值模拟结果与实验结果大致吻合。其中,ABAQUS和PAM-CRASH对上述特征量的模拟结果更接近实验结果,平均相对误差普遍小于15%,且PAM-CRASH多数模拟结果误差都小于10%;而在弹体变形量上,3种软件的模拟结果均与实验结果相差较大。此外,LS-DYNA在模拟时的鲁棒性较好,模拟结果较稳定,PAM-CRASH对参数设置最敏感,ABAQUS在计算时间和效果上较平衡。     

三维显式有限元程序及炸药冲击起爆应用

冲击和爆炸数值模拟在军事工程和民用领域都应用广泛。基于显式有限元理论,本文介绍了自主研发的三维冲击和起爆流体动力学程序。该程序的功能包含了材料本构、状态方程、炸药反应速率方程和接触碰撞算法,能够模拟复杂条件下结构冲击和炸药起爆问题。由于采用面向对象的编程方法,程序结构相对简单并且容易修改。首先,进行了Taylor杆碰撞数值模拟,并将计算结果与实验结果以及DYNA2D结果进行了比较;接着,基于Lee-Tarver点火增长模型,模拟了冲击加载下裸炸药和带壳炸药的冲击起爆问题。计算结果表明,三维程序计算结果与实验值和商业软件结果都非常吻合,该程序能够较准确地模拟三维结构的冲击和炸药起爆问题。同时,基于面向对象开发的三维计算程序实现了模块化功能,易于后续开发,为冲击和爆炸计算程序的开发提供了参考。     

Stresses around elliptic holes in circular cylindrical shells

The stress state around an elliptic hole in a circular cylindrical shell under axial loads is measured. The test cylinders which are made of aluminum are loaded both in tension and compression. Stress-concentration factors around the hole for different eccentricities of the ellipse and different curvature parameters are evaluated. Stress-concentration factors away from the edge of the hole are also determined. The results obtained are compared with theoretical results available in the literature. The effect of bending on the stress concentration as related to the eccentricity of the elliptic hole and to the curvature parameters of the shell is discussed. The results from tension test and those from compression test are also compared, and the sensitivity of the shell to any imperfection and possible local buckling at the hole in the case of compression test are demonstrated.     

Subgrid modeling of flow processes in an anisotropic fractal medium

Equations are derived for the effective coefficients of random conductivity fields in the stationary problem of flow in an anisotropic medium. For the fields, lognormal statistics is assumed. The problem is solved using the subgrid modeling method. The results of theoretical calculations are compared with the results of direct three-dimensional numerical modeling. The results of numerical and theoretical calculations are shown to be in good agreement with each other.     

局部削弱压杆的稳定性实验研究

因为缺乏相关的理论和实验研究,局部削弱压杆的临界载荷通常按无削弱压杆处理.工程中,局部削弱压杆的使用极为普遍.对局部削弱压杆的稳定性的定量研究结果,无论是工程中,还是材料力学教学中都是迫切需要的.本文在前人理论研究的基础上,对局部削弱压杆的临界载荷作了定量的实验研究.试验结果表明,对细长压杆,即使削弱部分的刚度下降达到38.9%,对失稳临界载荷的影响仍可忽略;试验结果与黄玉珊提出的对局部削弱压杆稳定性的定量计算方法也比较接近.研究结果对部分工程问题和材料力学教学都具有一定的指导意义.     

Dynamic extension and twist of a non-linear elastic tube

The propagation of waves in a non-linear cylindrical elastic membrane is considered when one end is fixed and the other is subjected to a dynamic extension and twist. The governing equations are derived for a hyperelastic material with a general strain energy function. In order to obtain specific results the equations are specialised to deal with neo-Hookian materials and in this case we show that there are three real wave speeds in each direction along the cylinder. Numerical results are given and a limiting case considered which provides a check on these results.     

考虑横向剪切变形的扁球壳在集中力作用下的分析

采用适于夹层壳的直线假设扁壳理论，应用三角级数法，导出了扁球壳齐次方程的解析解。进而分析了在顶点作用法向集中力和在偏心集中力作用下的解。计算了在偏心集中力作用下带孔球壳的位移和应力，并将结果与经典理论的结果进行了比较分析，结果表明，在集中力作用处和孔边处两种理论结果明显不同。     

Thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying temperature

The present work is concerned with the thermally induced vibration in a homogeneous and isotropic unbounded body with a spherical cavity. The Green and Nagdhi model of thermoelasticity without energy dissipation is employed. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed.     

Comments to the paper “An application of a damage constitutive model to concrete at high temperature and prediction of spalling” by Rosen Tenchev and Phil Purnell [Int. J. Solids Struct. 42 (26) (2005) 6550–6565]

The assumption that pressures of water and gas in concrete at high temperature are equal one to another and its theoretical consequences are discussed. The results of hygro-thermal simulations performed by Tenchev and Purnell are analysed and compared to the Authors’ results based on the assumption about local thermodynamic equilibrium.     

Non-linear vibration of bimaterial magneto-elastic cantilever beam with thermal loading

Formulas and numerical results are studied for the transient vibration and dynamic instability of a bimaterial magneto-elastic cantilever beam which is subjected to alternating magnetic field and thermal loading. Materials are assumed isotropic, and the physical properties are assumed to have unique values in each layer. The governing equation of motion is derived by the extended Hamilton's principle, in which the damping factor, the electromagnetic force, the electromagnetic torque, and the thermal load are considered. The solution of thermal effect is obtained by superposing certain fundamental linear elastic stress states which are compatible with the Euler–Bernoulli beam theory. The axial stresses results are found to be in good agreement with some known numerical solutions. Using Galerkin's method, the equation of motion is reduced to a time-dependent Mathieu equation. The numerical results of the regions of dynamic instability are determined by the incremental harmonic balance (IHB) method, and the transient vibratory behaviors are presented by the fourth-order Runge–Kutta method. The results show that the responses of the transient vibration and dynamic instability of the system are influenced by the magnetic field, the thickness ratio, the excitation frequency, but not by the temperature increase in this study.     

Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.