各向异性轴对称问题的弹性动力学解

呈现一种简便的解析方法，求解了各向异性轴对称有界结构的弹性动力学问题在实例中，计算了各向异性带孔圆板的动应力响应历程和分布规律     

各向异性弹性体中矩形孔边缘应力分布

推导了各向异性平面弹性体中矩形孔洞边缘的应力分布公式并给出了数值计算结果。工程中会遇到矩形孔洞的问题，而矩形孔导致的应力集中增加了工程问题的复杂性。目前尚没有简单实用的公式计算矩形孔在各向异性体中应力的分布。本文采用复变函数保角变换的方法推导了矩形孔边缘的应力公式。在利用本文给出的方法，可以计算矩形孔在不同性质的各向异性材料中，承受任意的双轴荷载下孔边缘的应力分布情况。     

各向异性层状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质位移位，应力传播矩阵，给出了直角坐标系各向异性层状介质中弹性波的传播矩阵解法，该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题，数值结果表明，计算效率，准确性及稳定性均较好。     

各向异性展状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质内位移、应力传递矩阵，给出了直角坐标系下各向异性层状介质中弹性波的传播矩阵解法．该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题．数值结果表明，计算效率、准确性及稳定性均较好．     

正交各向异性平面热弹性问题的边界元分析

给出了正交各向异性平面热弹性问题的边界积分方程、内点应力公式和常单元离散化时计算奇异积分的解析式，计算了正交各向异性板的热应力强度因子，结果表明了文中所导公式的正确性     

正交各向异性薄板的弹塑性屈曲分析

本文应用混合硬化正交各向异性塑性理论和屈曲的能量法则，推导了正交各向异性薄板在面内压缩情况下的弹塑性稳定方程，计算了相应的临界荷载，并讨论几何形状、边界条件及诱导荷载比等对临界应力的影响。分析表明材料的各向异性性质对弹塑性临界应力的有较大的影响。     

新型各向异性核工业石墨断裂力学行为的实验研究和数值分析

本文分别采用激光和白光DSCM(数字散斑相关测量)方法对一种新型各向异性核工业石墨的裂纹尖端位移、应变场进行了实验研究，两种方法都取得了较好的结果。考虑核工业石墨制备过程形成的各向异性特点，本文构建了三维各向异性有限元模型，采用奇异单元，计算模拟石墨裂纹尖端的变形和应力场，通过对实验结果和有限元计算结果的比较可以发现两者具有相近的趋势。     

各向异性弹塑性中厚度板壳的有限元分析

本文在文献［２，３］的基础上，提出了一个解各向异性弹塑性中厚度板壳问题的有限元方法。考虑材料各向异性的特点，采用了Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应；为了避免“自锁”现象，文中采用了９节点的Ｈｅｔｅｒｏｓｉｓ二次壳单元；特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了确定变形路径的计算效率。几个数值算例表明本文给出的有限元方法对于各向异性中厚度板壳的弹塑性分析有较好的精度，尤其是对具有复杂变形路径的结构计算，收敛速度提高更快。     

锅炉炉墙板梁结构随机响应的边界元方法

锅炉炉墙可简化成板，梁的组合结构，在燃烧脉动的激励下会形成随机性的振动。本文提出了一种借助于边界元方法进行随机激励作用下正交各向异性板，梁组合结构动力响应计算的一般方法。文中首先导出各向异性板，梁结构动力问题的边界积分方程，进而得到用于随机响应计算的板，梁结构的频率响应函数矩阵。在此基础上可以求出板，梁结构上任意点响应的均方值。这一方法的有效性在文中电站锅炉实际算例中得到了验证。     

脆性材料动态破坏过程的数值模拟

根据连续介质力学基本原理和离散元法基本思想，针对脆性材料动态破坏过程问题，推导出基于圆盘单元的正交各向异性离散元二维计算模型，并利用此模型计算了各向异性薄板在冲击载荷下的应力波传播问题。通过将计算结果与LS－DYNA程序相比较，表明了本文提出的离散元模型的精确性。另外，对钢弹侵彻下滑凝土圆板破坏过程这个典型的发生连续介质向非连续介质转化的动力学问题进行了数值模拟和动画显示，并同侵彻实验中出现的几种破坏形式进行了分析和对比，从而证明了本计算方法是计算和模拟脆性材料出现从连续介质向非连续介质转变的动态破坏问题的有力工具。     

A NUMERICAL METHOD OF MODELING ELASTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA

The velocity-stress finite-difference method is adopted to simulate the elastic wave propa-gation in azimuthal anisotropic media.The difference grids are completely staggered in the numerical im-plementation.To reduce the computational work,the absorbin8 boundary conditions for anisotropic mediaare introduced first and the corner points are specially treated.Examples show that more accurate resultscan be obtained from the modeling algorithm,which cost much less computational time than the conven-tional methods.Therefore,the algorithm has broad application prospects in engineering.     

蠕变－弹塑性－损伤耦合响应的有限元分析

本文处理各向异性非线性材料的蠕变。弹塑性－损伤耦合响应的数值计算。建议了一个计算应力的三级向后欧拉积分算法。导出了一个利用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ迭代的一般的直接应力返回映射算法。同时求解应力向量和蠕变、塑性、损伤的内状态变量。也导出了用于全局Ｎｅｗｔｏｎ－Ｒａｐｈ－ｓｏｎ迭代过程的一致性切线矩阵公式。给出的数值例题结果表明所提出的算法和公式在模拟耦合本构行为上的能力和可靠性。     

NUMERICAL SIMULATION OF ELASTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA

A new numerical simulation algorithm is presented for the elastic wave propagation in heterogeneous anisotropic media. We make discretization of the computational domain by using triangular and quadrangular grids. The scheme is based on integral equilibrium at each node to simulate the elastic wave propagation in heterogeneous anisotropic media. The scheme is very flexible in dealing with arbitrary surface topography, inner openings, liquid-solid boundaries and irregular interfaces. Moreover, the free-surface condition of complex geometrical boundaries can be satisfied naturally. This work is an extension of the grid method for the elastic wave propagation in heterogeneous isotropic media, and a quadrangular grid with low computational cost is also introduced. Project supported by the National Natural Science Foundation of China(19672016).     

Anisotropic density growth of bone—A computational micro-sphere approach

Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties.The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots.     

各向异性介质中弹性波的数值模拟

提出了一种非均匀各向异性介质中弹性波传播的数值模拟算法。该方法可以灵活地运用于具有任意地表形状、内部孔洞、固液边界和不规则内部交界面的介质情况,另外,该方法自然满足复杂几何边界的自由表面条件。这种基于三角形和四边形离散网格的算法使用的是围绕每个节点的积分平衡方程,而不是其它有限差分法中使用的各个节点满足的弹性动力学的微分方程。该文工作是非均匀各向同性介质中弹性波传播格子法研究的继续。除了研究各向异性介质中波的传播以外,还给出了一种能够省时的四边形网格的格子法。     

适应复杂外形的三维粘性混合网格生成算法

提出一类适应复杂外形的粘性混合网格生成算法。表面网格由前沿推进三角形曲面网格程序获得,边界层布置各向异性的三棱柱体网格,远物面区域采用Delaunay方法生成四面体网格。针对模型的复杂几何特征,综合采用了各种网格处理技术,以保证边界层网格的质量,并避免算法失效问题。网格实例及计算结果表明了本文算法的实用性及和效性。     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

Toward an accurate numerical simulation of radiation hydrodynamics in laser ablation plasmas

A radiation hydrodynamics code has been developed for more accurate prediction of laser-produced low-density ablation plasmas with appropriately describing anisotropic radiation field by using Monte-Carlo technique for variable Eddington tensor with reasonable computational loads. The Eddington tensor estimated by thousand of sample particles per single fluid step can reproduce the anisotropic radiation field in the low-density region and will not result in large computational consumption. Prediction of the emitted light from ablation plasma can be corrected by the proposed method. Ablation structure sustained by a compact radiation source, which is sometimes found in experiments of collisionless shock relevant to laboratory astrophysics, may also be changed by anisotropic transfer computation in optically thin region.     

Bi-directional fluid–structure interaction for large deformation of layered composite propeller blades

Bi-directional fluid–structure interaction becomes important when viscous flow changes the geometry of the domain significantly because of the pressure load. Large deformation in domain causes numerical convergence problems, which are solved by mesh smoothing, re-meshing and a time discrete iterative solver algorithm using industrial computational fluid dynamics and finite element analysis code. In this paper, this approach is used for laminated composite propellers considered as mixers. It experiences heavy thrust, which causes large deformations. Each layer of laminate is modeled as a solid element with anisotropic material data. Comparative study is presented between uni-directional and bi-directional fluid–structure interaction for mixer blades. Change in pressure distribution, stress distribution, thrust, torque and pitch angle of the blade are presented in later parts of the paper.