Dynamic analysis of single and cyclic indentation of an elastic-plastic multi-layered medium by a rigid fractal surface

Dynamic indentation of an elastic-plastic multi-layered medium by a rigid rough surface that exhibits fractal behavior was analyzed with the finite element method. A sufficiently large mesh was used to avoid the effects of the faster propagating dilatation waves after they were reflected from the artificial mesh boundaries. Single-indentation results illustrate the significance of the thickness of the surface layer and the indentation speed on the contact pressure distribution and subsurface stresses and strains. The initiation of yielding and the development of plasticity are interpreted in the context of results for the von Mises equivalent stress and equivalent plastic strain obtained during the loading and unloading phases of an indentation cycle. Cumulative plasticity and elastic shakedown are discussed in light of results revealing the evolution of deformation in the multi-layered medium due to cyclic indentation. The analysis provides insight into the importance of indentation speed, layer thickness, surface topography, and indentation cycle on the mechanical response of a multi-layered medium in dynamic contact with a rough surface exhibiting multi-scale (fractal) roughness.     

表面轮廓分形维数计算方法的研究

阐述了表面轮廓分形和分形曲线的基本概念，对目前常用于表面轮廓分形维数的４种计算方法的基本思路作了评介，指出这些方法的计算结果都存在一定的偏差，对选择不同计算尺度得到的分形维数表现出较大的不稳定性，致使分形维数难以准确地反映表面轮廓的真实复杂特征．根据表面轮廓的均方差与区间尺度成比例的性质，提出了表面轮廓分形维数计算的协方差加权法．通过与Ｗｅｉｅｒｓｔｒａｓｓ－Ｍａｎｄｅｌｂｒｏｔ分形函数曲线的分形维数计算的比较，协方差加权法所得表面轮廓分形维数的稳定性良好，计算结果的准确性也明显提高，可以简化表面形貌的识别过程，为摩擦学研究中更准确地描述粗糙表面的复杂特征提供了一种简便适用的新方法．     

A comparative study of destructive effects resulting from road profile acting on off-road towed vehicles

The more extreme conditions the vehicle is exposed to, the sooner it wears out and deteriorates. In order to determine the forces affecting the lifespan of vehicles we need to know the environmental conditions eliciting these forces.This research aims at elaborating and testing a method which can help to conduct a comparative analysis of forces acting on towed vehicles used in different terrain conditions. Excitation forces acting on a vehicle being towed across terrain cause vibrations which lead to wear and structural deterioration. The rate of deterioration depends on the activating forces resulting from the road profile geometry and the dynamic properties of the vehicle. A knowledge of the relationship between the towed vehicle and the terrain profile will enable the design of an artificial road profile for fatigue testing with which similar stresses arise as during normal use. With the developed comparative method, a connection can be established between stochastic road profiles and road profiles containing artificially built obstacles.     

大跨桥梁参数识别响应面方法中的近似函数及样本选取

以某大跨斜拉桥实验室物理模型设计参数与动力特性之间复杂的隐式关系为对象,分析响应面模型中近似函数和试验样本对回归模型精度的影响。首先推导多项式和径向基函数响应面模型的建模方法,然后基于斜拉桥三维空间模型的有限元动力分析,比较分析完全二阶多项式与几种径向基函数模型在设计域和扩展设计域内以及噪声污染情况下的回归精度。最后对几种少量样本的试验设计方法和响应面试验设计方法进行了分析。结果表明,径向基函数模型各方面性能优于多项式模型,响应面实验设计方法优于其他方法,少量样本可采用D优化设计,较多样本情况下以中心复合设计较佳。     

Finite element analysis of flow and heat transfer with moving free surface using fixed grid system

A numerical study was performed on flow and heat transfer involving moving free surfaces that occurs in mold filling processes such as casting and injection molding. In these problems, the calculation domain changes continuously and the numerical treatment of the moving interface tends to cause artificial diffusion. Among the solution algorithms based on the Eulerian method, the volume-of-fluid (VOF) method was used because the method is simple and efficient in handling the complex flow patterns inside the cavity. To solve the transport equation of free surface without artificial smearing of the interface the baby-cell method was employed in the geometric reconstruction of the free surface. Furthermore, a predictor–corrector method was adopted in the time integration of volume-of-fluid (VOF) transport equation to increase the accuracy. The proposed scheme was verified through several benchmark problems. In order to show the capability of the proposed method, several three-dimensional mold filling processes were solved. The current algorithm was applied to the floating body problem. Three-dimensional floating body problems were tested.     

Regular wave integral approach to numerical simulation of radiation and diffraction of surface waves

A regular wave integral method is developed in the discretisation of a linear hydrodynamic problem on radiation and diffraction of surface waves by a floating or submerged body. The velocity potential of the problem is expressed as a solution of a body boundary integral equation involving the pulsating free surface Green function or pulsating free surface sources distributed on the body surface. With the use of a discretisation on the regular wave integral rather than discretisations on the singular wave integral of the Green function as in earlier investigations, the singular wave integral is approximated as an expansion of regular (or nonirregular) wave potentials. Influence coefficients between pulsating free surface source points are computed by the approximate expansion together with Hess–Smith panel integral formulas. Thus the velocity potential solution is evaluated by a boundary element algorithm. The numerical results produced from the proposed method agree well with semi-analytic solution results.     

焊接节点半椭圆表面裂纹应力强度因子的权函数计算

本文采用一种改进的权函数法来计算焊接节点半椭圆表面裂纹应力强度因子ＫＩ值，并给出了相应的数值处理方法，就Ｔ型板节点进行了数值验算。     

A numerical method for the evaluation of hydrodynamic forces of translating bodies under a free surface

This paper presents a numerical method to evaluate the hydrodynamic forces of translating bodies under a free surface. Both steady and unsteady problems are considered. Analytical and numerical studies are carried out based on the Havelock wave‐source function and the integral equation method. Two main problems arising inherently in the proposed solution method are overcome in order to facilitate the numerical implementation. The first lies in evaluating the Havelock function, which involves integrals with highly oscillatory kernels. Particular integration contours leading to non‐oscillatory integrands are derived a priori so that the integrals can be evaluated efficiently. The second problem lies in evaluating singular kernels in the boundary integral equation. The corresponding non‐singular formulation is derived using some theorems of potential theory, including the Gauss flux theorem and the property related to the equipotential body. The subsequent formulation is amenable to the solution by directly using the standard quadrature formulas without taking another special treatment. This paper also attempts to enhance the computational efficiency by presenting an interpolation method used to evaluate matrix elements, which are ascribed to a discretization procedure. In addition to the steady case, numerical examples consist of cases involving a submerged prolate spheroid, which is originally idle and then suddenly moves with a constant speed and a constant acceleration. Also systematically studied is the variation of hydrodynamic forces acting on the spheroid for various Froude numbers and submergence depths. Copyright © 2000 John Wiley & Sons, Ltd.     

Multiscale reliability of physical systems based on the principle of least variance

Multiscale reliability places priority on the shifting of space-time scale while dual-scale reliability concentrates on time limits. Both can be ranked by applying the principle of least variance, although the prevailing criteria for assessment may differ. The elements measuring reliability can be ideally assumed to be non-interactive or interactive as a rule. Different formulations of the latter can be adopted to yield weak, strong, and mixed reliability depending on the application. Variance can also be referred to the average based on the linear sum, the root mean square, or otherwise. Preference will again depend on the physical system under consideration. Different space-time scale ranges can be chosen for the appropriate time span to failure. Up to now, only partial validation can be made due to the lack of lower scale data that are generated theoretically.A set of R-integrals is defined to account for the evolution effects by way of the root functions from Ideomechanics. The approach calls for a “pulsating mass” model that can connect the physical laws for the small and large bodies, including energy dissipation at all scale level. Non-linearity is no longer an issue when characterization of matter is made by the multiscaling of space-time. Ordinary functions can also be treated with minor modifications.The key objective is not to derive new theories, but to explain the underlying physics of existing test data, and the reliability of diversified propositions for predicting the time span to failure. Present and past investigations have remained at the micro-macro or mi-ma scale range for several decades due to the inability to quantify lower scale data. To this end, the available mi-ma fatigue crack growth data are used to generate those at the na-mi and pi-na scale ranges. Reliability variances are computed for the three different scale ranges, covering effects from the atomic to the macroscopic scale. They include the initial crack or defect length and velocities. Specimen with large initial defects are found to be more reliable. This trend also holds for each of the na-mi and pi-na scale range. Also, large specimen data had smaller reliability variances than the smaller specimens making them more reliable. Variances for the nano- and pico-scale range had much more scatter and were diversified. Uncertainties and un-reliabilities at the atomic and sub-atomic scale are no doubt related, although their connections remain to be found.Reliability with high order precisions are also defined for multi-component systems that can involve trillions of elements at the different scale ranges. Such large scale computations are now within reach by the advent of super-speed computers, especially when reliability, risk, and among other factors may have to be considered simultaneously.     

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress,the modified couple stress theory(MCST),and the nonlocal elasticity theories using the differential quadrature method(DQM)is presented.Main advantages of the MCST over the classical theory(CT)are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter.Based on the nonlinear von K′arm′an assumption,the governing equations of equilibrium for the micro-classical plate considering midplane displacements are derived based on the minimum principle of potential energy.Using the DQM,the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained.Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature.A parametric study is conducted to show the effects of the aspect ratio,the side-to-thickness ratio,Eringen’s nonlocal parameter,the material length scale parameter,Young’s modulus of the surface layer,the surface residual stress,the polymer matrix coefficients,and various boundary conditions on the dimensionless uniaxial,biaxial,and shear critical buckling loads.The results indicate that the critical buckling loads are strongly sensitive to Eringen’s nonlocal parameter,the material length scale parameter,and the surface residual stress effects,while the effect of Young’s modulus of the surface layer on the critical buckling load is negligible.Also,considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate.The results show that the critical biaxial buckling load increases with an increase in G12/E2and vice versa for E1/E2.It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude.Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios,it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.