非均质材料零件几何和材料的并行设计研究

为了解决非均质材料零件设计中几何特征和材料特征的耦合问题,提出了一种基于可行方向法和遗传算法的几何和材料的并行设计方法。通过设定关键点来表示不断变化的零件几何特征,引入虚拟节点以描述其材料特征,构建非均质材料零件几何和材料并行设计的优化模型。在优化设计过程中,关键点的坐标增量采用可行方向法求解,虚拟节点的材料体积分数增量通过遗传算法获得,两种优化算法交替迭代,便得到了零件几何形状和材料分布的组合最优解。采用该方法设计了一个非均质材料的等温器具,通过有限元技术对其温度场和应力场进行模拟和分析,并利用ANSYS软件对设计结果进行验证,从而说明了该方法的有效性和实用性。     

基于无网格Galerkin法的灵敏度分析与形状优化

结构形状优化已经在工程应用中得到重视,将无网格法与形状优化相结合能够从根本上解决优化过程中出现的有限单元扭曲或畸变问题。为此在无网格Galerkin法的基础上,利用离散导数法,提出一种基于离散型的节点位移灵敏度分析方法,其中采用了拉格朗日乘子法来施加本质边界条件。该方法的最大优势是求解过程与无网格Galerkin法的求解过程相似,容易实现。另外对形状优化的数学模型和节点位移的设计速度域进行了讨论。采用具有解析解的实例,对所提出的灵敏度分析方法进行了验证,所得结果显示两者非常吻合。利用上述所建立的形状优化算法,完成了两个工程实例的形状优化设计。     

无网格伽辽金方法在线弹性断裂力学中的应用研究

通过对移动最小二乘形函数进行局部修正,将混合变换法应用于无网格伽辽金方法,给出分析线弹性断裂力学问题的有效的无网格伽辽金方法。这一方法克服了无网格伽辽金方法中常用的拉格朗日乘子法和罚函数法的缺点,实现了本质边界条件在节点处的精确施加。运用线弹性断裂力学理论,采用基于t-分布的新型权函数和部分扩展基函数,对有限板单边裂纹的应力强度因子和拉剪复合型裂纹的扩展进行分析。由于该方法仅需节点信息,而不需要节点的连接信息,从而避免了有限元方法中的网格重构,大大简化了裂纹扩展的分析过程。数值计算结果表明了方法的有效性。     

面向数控加工的三角网格法矢量及曲率估算

在面向三角网格曲面的数控加工中,网格曲面的曲率估算精度对数控加工刀具路径设计和加工质量具有重要的影响。针对数控加工需求,提出了一种三角网格曲面中网格节点曲率的精确估算方法。该方法引入网格形状因子,综合考虑三角形的形状和面积两个因素对网格节点法矢量的影响,得到了更为精确的法矢量,从而获得网格节点处更为精确的曲率估算值。此方法能够有效提高三角网格节点曲率估算的精确度,提高了三角网格曲面刀具路径设计中的刀位点计算精度和数控加工精度。     

承受轴压的X管节点极限荷载有限元分析

采用有限元法分析轴力作用下X管节点所能承受的极限荷载。在对X管节点进行数值模拟的时候,考虑焊缝对其强度的影响。在有限元分析中,采用分区网格产生法形成X管节点的有限元网格,即把整个X管节点根据计算精度的需要划分成几个不同的子区域,每个子区域的网格单独产生,整个管节点的有限元网格通过合并各个子区域的网格而形成。这种分区网格产生法可以针对不同应力梯度的区域形成不同质量和精度的网格,从而可以保证有限元结果的准确性并节省存储空间和计算时间。在分区网格法的基础上,用ABAQUS(2000)通用软件分析X管节点在承受压力作用时的荷载和位移之间的关系,并得到X管节点所能承受的极限荷载大小。此外,通过对50个X管节点模型进行分析,研究几何参数以及材料参数对X管节点极限荷载的影响。     

基于多点约束法的人字齿轮精确有限元建模方法

应力位置处足够细化的网格是齿轮有限元分析得到精确齿面接触应力和齿根弯曲应力的基础。在保证有限元分析结果精度的情况下,降低求解时间和对计算机性能的要求是研究的热点问题之一。基于Ansys软件网格划分方法对齿面和齿根网格细化,采用多点约束法(Multipoint constraint,MPC)耦合大小不一致网格节点的自由度,进行了有限元建模和仿真分析计算。结果表明,该方法较普通方法能够大幅减少网格和节点数量,缩短计算时间,且能够保证人字齿轮齿根弯曲应力和齿面接触应力的求解精度。另外,采用ISO标准计算人字齿轮的齿根弯曲应力和齿面接触应力得到的结果均大于有限元分析的结果,对人字齿轮的工程实际应用提供了重要参照。     

Neumann展开Monte Carlo随机无网格点插值法

用Neumann展开Monte Carlo随机无网格点插值法(NMC-SMPIM)进行随机结构分析。在随机无网格点插值法(stochastic meshless point interpolation method,SMPIM)中,所求解问题的域由分布的节点表示;并且利用具有Delta函数性质的多项式进行节点插值,为此,很容易类似有限元法一样处理本质边界条件。同时利用Neumann展开法,建立随机结构分析的Neumann展开Monte Carlo随机无网格点插值法。数值实例表明,Neumann展开Monte Carlo随机无网格点插值法适用于材料变异系数大和要求精度高的随机结构分析。     

弧齿锥齿轮齿面坐标法测量的研究

介绍了使用坐标法测量弧齿锥齿轮,并进行数据处理,以便对齿轮的加工参数进行修正的思路和方法。它重在建立齿面的理论数学模型,在其轴截面的旋转投影面上进行网格节点的规划,得到网格节点的三坐标值和该节点的法向矢量,根据理论的齿面坐标值控制三坐标测量机进行测量,从而得到齿面的误差。     

用随机无网格点插值法分析齿轮弯曲疲劳强度的可靠性

用摄动随机无网格点插值法（PSMPIM）分析了齿轮弯曲疲劳强度的可靠性。在无网格点插值法中，所求解问题的域由分布的节点表示；并且利用具有Delta函数性质的多项式进行节点插值，为此，很容易类似有限元法一样处理本质边界条件。同时利用摄动技术，建立了随机结构分析的摄动随机无网格点插值法。并应用随机无网格点插值法分析了齿轮弯曲疲劳强度的可靠性。数值实例表明在随机结构分析与可靠性计算方面随机无网格法具有明显的优势。     

用无网格法进行大变形柔性机构拓扑优化设

基于连续体结构的拓扑优化理论,将无网格伽辽金数值方法引入分布式大变形柔性机构拓扑优化设计,并解决了优化中的几何非线性问题。在优化问题中,基于各向同性固体材料惩罚模型（solidisotropic material with penalization,SIMP)和折衷规划法,同时考虑结构的柔性和刚度要求,建立了柔性机构拓扑优化的多准则优化模型,并利用优化准则法求解。采用无网格伽辽金法将求解域离散成节点,避免了有限元方法在处理大变形问题时由于使用网格而产生网格畸变等问题。求解经典算例,与基于线性理论的优化结果相比较分析,说明了该方法的正确性和有效性。     

基于积分弱形式的无网格-有限元法耦合方法研究

无网格伽辽金法是基于移动最小二乘法的一种求解偏微分方程非常有效的方法,但是对于一些规模较大的问题,其计算费用较高,将无网格法与有限元耦合可以极大提高求解效率.文中根据D. Hegen提出的基于积分弱形式耦合方法,进一步明确处理耦合区域部分的数学、物理意义, 有效地引入一个综合控制因子反映权函数的紧支性, 并经算例验证方法的正确性及控制因子的有效性.     

面向对象的无网格伽辽金法

采用Schmidt法对无网格伽辽金法(EFGM)形函数的基函数进行正交化,避免了形函数中的矩阵求逆运算,同时也减少了运算量并提高计算精度。对EFGM中的权函数、节点影响半径等关键问题进行了改进,并利用对象设计思想将无网格伽辽金法的对象抽象为独立的数据类,研究了无网格伽辽金法数据类的设计方法和组织方式并编制了相应的计算程序。数值算例结果表明,理论正确、方法有效。     

An element-free Galerkin forward solver for the complete-electrode model in electrical impedance tomography

An element-free Galerkin method (EFGM) is used for solving forward problem based on the complete electrode model (CEM) in electrical impedance tomography (EIT). The EFGM requires only nodal data and has the ability of providing mesh-independent solutions because no element connectivity is needed to be used in this method. However, direct imposition of Dirichlet boundary conditions for the EFGM is difficult because the shape functions employed in this method do not have the property of Dirac delta function. Solving the EIT forward problem based on the CEM by the EFGM, the effects of electrodes and contact impedances are taken into account and the complete solution of equations is provided without imposing Dirichlet boundary conditions. The numerical results are validated with experimental results obtained from a 2D circular homogeneous phantom, and the performance of the EFGM compared with the finite element method is also illustrated. Moreover, results obtained from the EFGM are presented for an inhomogeneous numerical phantom.     

Numerical simulation of three-dimensional bulk forming processes by the element-free Galerkin method

A new approach for simulating three-dimensional (3D) bulk metal forming processes is proposed by combining element-free Galerkin method (EFGM) with the flow theory of 3D rigid-plastic/viscoplastic mechanics. Different from the conventional rigid-plastic FEM, the velocity field is constructed by the moving least-squares (MLS) approximation. Special emphasis is placed on the treatments of essential boundary conditions, incompressibility constraint and friction boundaries. The stiffness equation for the analysis of 3D bulk metal forming using EFGM is derived and its key algorithms are given. To test the validity of the proposed meshless approach, a typical 3D upsetting forming process is analyzed and the numerical results are compared with those obtained by commercialized rigid-plastic FEM software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures unavoidable in conventional FEM, and still provides results that are in good agreement with finite element predictions.     

Elastic analysis of exponentially graded piezoelectric cylindrical structures as sensors and actuators

An analytical solution is obtained for functionally graded piezoelectric cylindrical structures, and the electroelastic behavior is investigated. The material properties are assumed to vary as an exponential function along the radial direction of the cylinder. The cylindrical structure acts as sensor or actuator and is subjected to mechanical and electrical loads at its inner and outer cylindrical surfaces. Based on the linear piezoelectricity theory, the governing equation in terms of the radial displacement is obtained as a second-order nonhomogeneous ordinary differential equation with variable coefficients, and its solution is obtained by the Frobenius series method. The illustrative examples show that the material nonhomogeneity has significant effect on the electroelastic fields of functionally graded piezoelectric cylindrical sensors and actuators.     

Dual reciprocity boundary element analysis for the laminar forced heat convection problem in concentric annulus

This paper presents a study of the dual reciprocity boundary element method (DRBEM) for the laminar heat convection problem in a concentric annulus with constant heat flux boundary condition. DRBEM is one of the most successful technique used to transform the domain integrals arising from the nonhomogeneous term of the Poisson equation into equivalent boundary only integrals. This recently developed and highly efficient numerical method is tested for the solution accuracy of the fluid flow and heat transfer study in a concentric annulus. Since their exact solutions are available, DRBEM solutions are verified with different number of boundary element discretizations and internal points. The results obtained in this study are discussed with the relative error percentage of velocity and temperature solutions, and potential applicability of the method for the more complicated heat convection problems with arbitrary duct geometries.     

Finite Element Method on Shape Memory Alloy Structure and Its Applications

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software.This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation.Two scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA structure.An incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of SMA.The incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure.Two SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element method.Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.     

Numerical simulation of thermo-elastic fracture problems using element free Galerkin method

In the present work, element free Galerkin method (EFGM) has been extended to solve thermo-elastic fracture problems in homogeneous and inhomogeneous materials (bi-materials). A thermo-elastic fracture problem is decoupled into two separate problems. At first, the temperature distribution is obtained by solving the heat transfer problem. The temperature field is then employed as input for the mechanical problem to determine the displacement and stress fields. The disturbances due to the presence of crack results in a non-smooth temperature distribution, and induces a singularity in the heat flux at the crack tip. Thermal as well as mechanical problems are enriched intrinsically in order to represent the discontinuous temperature, heat flux, displacement and traction across the crack surfaces. Both isothermal and adiabatic conditions are considered at the crack surfaces. Jump function technique has been employed to model a bi-material interface, and intrinsic enrichment has been used to model a crack at the bi-material interface. The conservative M-integral technique has been modified in order to extract the mixed mode stress intensity factor for thermo-elastic fracture problems. The present analysis shows that the results obtained by EFGM are in good agreement with those available in the literature.     

基于弹塑性解析方程的薄片试样低周疲劳试验方法

针对薄片漏斗试样,基于能量密度等效和量纲分析,提出了移幅-载荷幅关系(Relation between displacement-amplitude and load-amplitude, RDL)半解析方程;能量密度等效代表性体积单元(Representative volume element, RVE)的循环等效应力幅、等效应变幅(Cyclic equivalent stress-amplitude and strain-amplitude, CESS)解析方程;漏斗根部材料RVE单轴应变幅(Uniaxial strain-amplitude of material RVE at funnel root, US-R)半解析方程;材料与几何普适的薄片试样低周疲劳试验新方法。针对5种几何尺寸和13种预设材料组合的18种试样工况进行有限元分析,及对G115和16Mn进行薄片试样低周疲劳试验,结果表明,CESS解析方程预测的薄片漏斗试样等效应力幅-应变幅曲线与有限元预设曲线密切吻合,且新试验方法得到的G115和16Mn循环等效应力幅-应变幅关系和Manson-Coffin律与标准圆棒试样低周疲劳试验结果密切吻合。     

基于无单元伽辽金法和Matlab遗传算法工具箱的结构形状优化研究

将无网格Galerkin法(element-free Galerkin method,EFGM)和改进的Matlab遗传算法工具箱(matlab genetic toolbox,MGT)相结合,提出了一种新的连续体结构形状优化设计方法。针对形状优化设计的特点,建立了一种规则网格与有限元网格混合的EFG积分背景网格法。详细介绍了M函数文件的修改方法,解决了现有Matlab遗传算法工具箱不能直接施加的非线性与隐性约束条件的难题。最后,完成了一个工程实例的结构形状优化,优化结果表明该方法是有效可行的。