考虑岩体破坏分区的岩石爆破爆炸荷载历程研究

针对岩石爆破爆炸荷载历程中未联合考虑岩石爆破动态过程和炮孔周围岩体破坏分区的不足,开展了考虑岩体破坏分区的岩石爆破爆炸荷载历程及其适用性研究。联合岩石爆破动态过程和岩体破坏分区的理论解,推导了考虑岩体破坏分区的岩石爆破爆炸荷载理论公式,比较了考虑岩体破坏分区的岩石爆破爆炸荷载历程与实测炮孔爆炸压力曲线,开展了单孔爆破现场试验和相应条件下3种爆炸荷载工况的数值模拟,并对爆破振动现场实测和数值模拟结果进行了对比。研究结果表明：考虑岩体破坏分区的爆炸荷载历程包括上升段和衰减段Ⅰ、Ⅱ、Ⅲ,上升段持续时间极短,衰减段持续时间较长且主要由填塞情况控制;考虑岩体破坏分区的爆炸荷载历程理论计算结果与实测炮孔爆炸压力曲线的变化趋势一致,验证了考虑岩体破坏分区的岩石爆破爆炸荷载理论公式的可靠性;考虑岩体破坏分区的爆炸荷载工况下,单孔爆破振动波形的数值模拟结果与现场实测结果的主要特征一致,该荷载工况下质点峰值振速计算结果与现场实测值偏差率最小,绝大部分在7%以内,表明了其应用于数值模拟的优越性;考虑岩体破坏分区的爆炸荷载可随岩石爆破系统条件的变化而动态调整,其可靠性好、适应性强、应用效果佳。     

可压流几何分区计算

综合讨论计算流体力学可压流几何分区计算,以期对分区算法的选择与正确使用提供一些指导,所涉及的重要问题有,分区网格的构造、耦合条件的建立、各种理论问题（守恒性,稳定性,收敛性,解的唯一性等）的分析、综合讨论等．      

基于自动网格法测量橡胶平面拉伸试验位移场的分区拟合方法

本文提出一种新的分区拟合方法用于拟合橡胶材料非均匀平面拉伸变形的位移场。该方法根据橡胶材料平面拉伸位移场的特点,将其分为均匀区和非均匀区(用分区系数来表征),且分别用不同的多项式来拟合,同时计及区域间位移及其一阶导数的连续条件。与试验结果的对比证实了对于橡胶的平面拉伸试验,采用分区系数f∈[0.2,0.4]、利用不完整二次多项式拟合均匀区和完整四次多项式拟合非均匀区的方案是最佳的。分区拟合方法还可推广至其它非均匀位移场的试验数据后处理中。     

三维Euler方程的分区和并行计算

三维全机绕流区域分解成多块子区域,多块区域之间采用迎风型通量守恒内边界耦合条件,分区计算总体区域,形成总体耦合流场的分区数值解。利用PVM并行环境,采用纯结点并行计算编程方式和“先进先出”的同步控制等待机制,对三维复杂流动跨音速流场相应分区实现了多区域并行计算。分析了影响并行效率的主要因素,将并行计算结果与串行计算结果和实验结果作了比较,讨论了多种区域分解数目的并行计算效率。在负载平衡程度较好时,可得到较高的并行效率。     

基于动态分区概念的高超声速燃烧大涡模拟

本文基于动态分区概念开展了亿级网格的高马赫数全尺寸超燃冲压发动机内外流耦合一体化改进延迟分离涡(IDDES)模拟研究. 研究建立了包括动态分区火焰面湍流燃烧模型(DZFM)、分区自适应化学(Z-DAC)和分区并行自适应建表(Z-ISAT)的完整动态分区燃烧模拟框架, 并通过1.15亿网格的马赫数12 REST标准高超声速燃烧室模型初步验证了分区模拟框架的保真性. DZFM通过分区解耦的思想既准确表征了当地湍流化学交互作用关系, 又有效提升了整场湍流燃烧的计算效率. Z-DAC和Z-ISAT通过在分区框架内对化学反应机理进行动态实时简化和建表查询, 可进一步提升当前分区内化学反应的求解效率. 基于1.25和1.4亿网格动态分区框架对比分析了马赫数10条件下中心支板(strut)和壁面撑挡型(pylon)两类构型氢气高超声速燃烧室特性. 支板或撑挡结构均诱发了明显的边界层分离和头部回流区, 由此两种燃烧室均出现了较长区域的喷注点前部燃烧现象. 基于Borghi图的数值分析表明当前氢气高超声速燃烧室中广泛存在扩散控制为主的火焰面模式, 效率提升的瓶颈在于高效增混. 壁面撑挡燃烧室具有较高的穿透深度和近场混合效率, 因而燃烧效率高于净推力准则80%, 相应的比冲1234 s也远高于中心支板燃烧室的437 s. 分区自适应化学方法在将近一半的计算域上降低了反应求解计算代价, 特别是在无燃料区反应机理的简化幅度更加明显. 相比与传统的有限速率PaSR模型, DZFM模型实现了高达11倍的加速比.      

开挖卸荷条件下深部圆形洞室各向同性围岩分区破裂化机理

论文提出了一种静水压力条件下动态开挖卸荷对深埋圆形洞室各向同性围岩分区破裂化影响的力学模型,获得了动态开挖卸荷条件下深埋圆形洞室围岩的弹性应力场,确定了卸荷速率和岩体动态力学参数对深埋洞室各向同性围岩分区破裂化现象的影响.利用动态Hoek-Brown准则,获得了围岩破裂区和非破裂区的数量和宽度.数值计算结果表明卸荷速率和岩体动态力学参数对破裂区与非破裂区的数量和宽度有较大影响.     

含层间长裂纹的对称正交层合板的解析－分区广义变分解法

本文首先将层板横截面分为含裂尖区、韧带区以及裂纹区等三个区域，用复变函数理论与特征函数展开法，得到了各区内满足所有基本方程、裂纹表面边界条件与层间连续条件的位移与应力的特征展开式。然后利用分区广义变分原理满足裂纹表面边界以外的边界条件以及各区之间的交界条件，并由此求得奇异场控制量（广义应力强度因子）。     

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法,本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法,基于有限体积方法和迎风型矢通量分裂方法,建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件,区域内部采用隐式格式和局部时间步长等,以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较,二者基本吻合。计算结果表明采用分析“V”型多重网格方法,能提高计算效率,加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。     

高原多年冻土地区遥感图像工程地质分区的探讨

简要叙述了利用遥感图像进行高原多年冻土工程地质分区的优越性,将高原多年冻土工程地质分区分为 3个大区和 10个亚区,着重叙述高原多年冻土工程地质分区判释特征,对判释特征进行了较系统的归纳,并以实例说明遥感工程地质分区判释在青藏铁路线方案比选中的作用。     

含层间长裂纹的对称正交层合板的角析—分区广义变分解法

本文首先将层板横截面分为含裂尖区、韧带区以及裂纹区等三个区域，用复变函数理论与特征函数层开法，得到了各区内满足所有基本方程、裂纹表面边界条件与层间连续条件的位移与应力的特征展开式，然后利用分区广义变分原理满足裂纹表面边界以外的边界条件以及各区之间的交界条件，并由此求得奇异场控制量。     

Energy functional derivative with respect to the length of a curvilinear oblique cut in the equilibrium problem for a Timoshenko plate

This paper describes the dependence of the solution of the equilibrium problem for a Timoshenko plate and the total energy functional of the plate on the perturbation of an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which describe mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.     

Differentiation of energy functionals in the problem of a curvilinear crack in a plate with a possible contact of the crack faces

A problem of equilibrium of a cracked plate is considered within the framework of the Kirchhoff-Love model. Non-penetration conditions in the form of inequalities (Signorini-type conditions) are set on the crack faces. The behavior of the energy functional is studied for the case of a rather smooth perturbation of the domain of the general form. Sufficient conditions for the existence of the energy functional derivative with respect to the parameter of domain perturbation are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 153–168, September–October, 2008.     

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.     

A Simple Energetic Explanation of the Polygon-Circle Paradox for Classical (Kirchhoff) Plate Theory

The divergence part of the energy functional for an elastically isotropic plate is replaced by a boundary integral, thus showing that the energy functional of a simply-supported Kirchhoff plate under a surface load approaches that of a circular plate with clamped boundary conditions. This conclusion does not depend on series solutions, singularity analysis, or elaborate, three-dimensional functional analysis.     

Further study of the equivalent theorem of Hellinger-Reissner and Hu-Washizu variational principles

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Removing of vortices in incompressible flows by distributed controls

We consider an optimal control problem of fluids flow. The fluid motion is governed by the incompressible time-dependent Navier-Stokes equations. A new optimal control formulation for the reduction and possibly extinction of vortices is proposed. A cost functional based on a local dynamical systems characterization of vortices is investigated. The resulting functional is a non-convex function of the velocity gradient tensor. The optimality system describing first order necessary optimality conditions is derived. The gradient and the second derivative of the cost functional with respect to the distributed control are established.     

Higher-order continua derived from discrete media: continualisation aspects and boundary conditions

In this paper, the derivation of higher-order continuum models from a discrete medium is addressed, with the following aims: (i) for a given discrete model and a given coupling of discrete and continuum degrees of freedom, the continuum should be defined uniquely, (ii) the continuum is isotropic, and (iii) boundary conditions are derived consistently with the energy functional and the equations of motion of the continuum. Firstly, a comparison is made between two continualisation methods, namely based on the equations of motion and on the energy functional. They are shown to give identical results. Secondly, the issue of isotropy is addressed. A new approach is developed in which two, rather than one, layers of neighbouring particles are considered. Finally, the formulation and interpretation of boundary conditions is treated. By means of the Hamilton–Ostrogradsky principle, boundary conditions are derived that are consistent with the energy functional and the equations of motion. A relation between standard stresses and higher-order stresses is derived and used to make an interpretation of the higher-order stresses. An additional result of this study is the non-uniqueness of the higher-order contributions to the energy.     

Dynamical systems‐based optimal control of incompressible fluids

For optimal control problems related to fluid flow the choice of an adequate cost functional for suppression of vortices is of significant importance. In this research we propose a cost functional based on a local dynamical systems characterization of vortices. The resulting functional is a non‐convex function of the velocity gradient tensor. The resulting optimality system describing first order necessary optimality conditions is derived, a possible strategy for numerical realization of the optimal control problem is provided and a numerical feasibility study is conducted. Copyright © 2004 John Wiley & Sons, Ltd.     

A variational principle for the laplace's operator with application in the torsion of composite rods

The Ritz method with relaxed coordinate functions is used here to establish a minimizing sequence for an extended functional. The integrand of the functional involves discontinuous functions, which implies that the gradient of the related extremal curve or surface also admits discontinuities. It is discussed a systematic way to form an extended functional allowing the minimizing sequence to approach the exact solution displaying the discontinuities in the gradient of the extremal surface. The extra terms added to the classical functional are shown to be related to the Erdman-Weierstrass corner conditions. Finally the method is applied to the torsion of a composite rod, and the results compared with a solution obtained through the finite elements method.     

The conditions of minimum potential energy and Castigliano's functional in a non-linear media

The behaviour of many polymeric materials under an external load may be described by a general form of non-linear relationship between stress and strain. In order to investigate such models, for example by a finite element method, it is necessary to construct the functional of energy (Castigliano or Lagrange's functional) and to find the extremum of the functional. Therefore, it is important to find the conditions under which functionals have a minimum. In this paper, the conditions when the functionals have a minimum for general stress-strain relations were investigated and an iterative method for the solution of the non-linear problems was proposed. The numerical results of the convergence speed of various iterative methods were discussed. This work is the continuation of the research presented in the literature by Oshhkunov and Ozden (The general stress and strain relationship in non-linear materials, Int. J. Non-Linear Mech. 35 (2000) 763-767.)