An improved return‐map stress update algorithm for finite deformation analysis of general isotropic elastoplastic geomaterials

This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd.     

Boussinesq水波方程新型数值解法

为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。     

海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究

浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。     

带阻尼项的欧拉-泊松方程组的爆破解

研究了N维空间中带阻尼项的欧拉-泊松方程组的径向对称解的爆破.当方程组非奇异的经典解（ρ,u）在[0,R]上有紧支集（R>0是正常数）,且初始速度u满足一定的初值条件,借助积分法,其径向对称解会在有限时间内爆破.     

基于飞机场特殊高边坡填筑施工放样

填筑的高边坡不平行于飞机杨跑道纵轴线,由于有两个坡比,给施工放样样找点带来困难.建立空间平面方程,计算坡顶线的法向线坡比,编程计算施工放样,这种方法的效果是较明显的,工作简单、便捷、高效,放样数据计数准确、可靠.     

A two-grid method for coupled free flow with porous media flow

This paper presents a two-grid method for solving systems of partial differential equations modelling incompressible free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numerical errors and convergence rates for solutions obtained from the two-grid method are presented. CPU times for the two-grid algorithm are shown to be significantly less than those obtained by solving the fully coupled problem.     

正交曲线坐标系二维浅水方程ELADI有限差分方法

N-S方程数值模拟的精度和效率一直是计算流体力学的重要研究课题.结合欧拉-拉格朗日方法(ELM)和交替方向隐式方法( ADI)建立正交曲线坐标系二维浅水方程的ELADI (Eulerian-Lagrangian alternating direction implicit method)有限差分方法,详细阐述了基本原理...     

A 3-D time-domain coupled model for nonlinear waves acting on a box-shaped ship fixed in a harbor

A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.     

Frictional contact of laminated elastic half‐spaces allowing interface cavities. Part 2: Numerical results

The paper presents some numerical results of the problem on contact of stratified elastic half‐spaces possessing unevenness of their surface layers. The approach of the Jacobi polynomials is used to reduce the singular integral equation of the problem to a system of linear algebraic equations. On the basis of the system's solution the dependence of gaps' geometric characteristics on external load and friction is investigated for two types of initial boundary disturbances, namely a local symmetric recess and a periodic set of recesses at a flat boundary. Numerical results are presented in figures for a few elastic and geometric parameters of joint components. The analysis shows that elastic properties and geometric structure of a laminated half‐space have a significant influence on the shape of interface gaps and their location. Copyright © 2001 John Wiley & Sons, Ltd.