自适应无网格方法在弹塑性接触中的应用

应用h型自适应无网格方法对二维弹塑性接触问题进行研究.无网格方法结点排布灵活 ,计算中可根据需要增减结点,便于自适应分析,通过对弹塑性本构关系和弹塑性接触问题的 阐述,给出了自适应无网格方法求解弹塑性接触问题的计算模型和程序流程.采用自适应方 法分别对圆柱体弹塑性接触和粗糙表面弹塑性接触算例进行求解,并分别与其均匀密化解进 行比较.结果表明,在同等条件下采用自适应无网格方法对弹性-理想塑性和弹塑性接触问题进行计算能在较小的计算耗费下取得较好的计算结果.     

无网格伽辽金-有限元耦合方法在温度场中的应用

为了充分利用无网格法和有限元法的优点,将无网格伽辽金-有限元耦合方法用于分析温度场问题。根据无网格伽辽金-有限元耦合计算原理得出了耦合区域的形函数,从能量泛函弱变分形式中得到控制方程,从而求出数值解。EFGM-FE耦合法克服了单纯使用无网格法带来的边界条件难处理及计算效率较低的缺点。数值算例表明了这种方法是可行的,有效的。     

基于无单元伽辽金法的混凝土通水温度计算

利用无单元伽辽金法的高精度优势,探讨研究其在大体积混凝土智能通水及精准温控中的应用.首先将大体积混凝土通水冷却问题近似为轴对称热传导问题,使用二维背景网格来离散对称截面,提出了基于无单元伽辽金法的基本理论及数值计算过程;当不考虑沿程水温变化时,问题进一步简化为轴对称平面问题,并给出了相应的计算公式;对于典型二期通水冷却问题,建立了不同密度的背景网格模型并进行了计算分析,结果显示无单元伽辽金法在求解这种问题时具有良好收敛性,且采用相同节点时计算精度明显高于有限元法.进一步的工程应用则还需开展三维问题沿程水温模拟及无单元伽辽金法与有限元法的耦合等研究.     

圆柱壳在静水压力作用下的弹塑性稳定

本文推导出大挠度圆柱壳在静水压力作用下弹塑性稳定问题增量形式的基本方程,并采用伽辽金配点法分析了两端简支圆柱壳的算例,所得计算结果与已有文献和实验结果基本一致。     

二维接触问题的无网格伽辽金-有限元耦合方法

研究了二维接触问题的无网格伽辽金-有限元耦合方法。给出了接触问题的数学模型，对其中的线性规划法进行深入分析，并将它与无网格伽辽金-有限元耦合方法结合求解接触问题。通过编程对光滑表面圆柱体与刚性平面的弹性接触问题以及粗糙表面与刚性平面的弹性-理想塑性接触进行求解，在对无网格区域相关参数研究的基础上，指出了用无网格伽辽金-有限元方法求解接触问题时的合理参数范围。     

两相多孔介质弹塑性动力反应计算分析的显式有限元方法

应用连续介质力学的基本原理,针对流体饱和两相多孔介质的特点,建立起增量形式的两相多孔介质弹塑性波动方程组,以实现对两相多孔介质弹塑性动力反应的描述．运用伽辽金方法对该波动方程组进行空间离散,得到两相多孔介质弹塑性波动方程组的伽辽金弱式,并应用中心差分法与Newmark常平均加速度法相结合的时域积分方法,对上述波动方程组进行时间离散,构造求解两相多孔介质弹塑性波动方程组的显式时间积分列式,从而形成流体饱和两相多孔介质弹塑性动力反应计算分析的时域显式有限元方法．该方法采用了解耦技术,不需要求解联立方程组,具有节省计算机内存空间和能够提高计算速度等优点．     

多材料开口薄板弯曲问题无网格分析

无网格方法计算含裂纹多材料薄板弯曲小变形问题具有节点自由度少,计算模型容易建立的优点.针对含有长直裂纹、材料界面开裂的双材料方形薄板问题,利用无网格伽辽金(EFG)方法进行计算分析,结果表明,无网格EFG方法使用更少的节点能够达到与有限元方法相近的计算精度.     

关于无网格法的几点研究

无网格伽辽金法（EFGM）是近几年发展起来的与有限元相似的一种数值算法，它采用移动的最小二乘法构造形函数，从能量泛函的弱变分形式中得到控制方程．本文讨论了无网格的两种处理本征边界条件的方法：拉格朗日乘子法和引入罚参数的方法．讨论了用不同的基函数对插值函数及对无单元法的计算精度的影响，并用算例说明了处理本征边界条件和基函数不同时的影响．     

三维无网格法与有限元法工程应用对比分析探讨

无网格伽辽金法基于移动最小二乘法的基础上,建立全计算域的高阶连续可导的插值函数,并只利用节点信息来建立离散模型的平衡方程。非线性有限单元法是在离散单元的基础上,构造连续可导的插值函数,进而建立平衡方程。本文应用无网格伽辽金法和非线性有限单元法及其相关理论编制三维计算程序,通过对工程算例的分析表明:无网格伽辽金法的计算精度高于有限单元法,应用于工程实例分析是有效可行的,已经成为有限单元法的有力补充。     

薄壁钢管杆件结构几何和材料非线性性能研究

本文根据Von Misses屈服准则及Prandtl-Reuss增量关系推导出了理想弹塑性材料、薄壁钢管杆件单元的弹性及弹塑性增量本构关系。采用根据上述本构关系和有限分割有限元法编制的程序,本文首先对国外近来发表的一些实验结果及理论计算结果进行了分析比较,其次对一个具有42个杆件的穹顶网壳进行了非线性全过程分析。     

Mean-field homogenization of elasto-viscoplastic composites based on a new mapping-tangent linearization approach

In this work, a new homogenization method of elasto-viscoplastic composites is developed. Using the fully implicit backward Euler's integration algorithm, the nonlinear ordinary differential equations in the constitutive laws of the matrix and inclusion phases are discretized. Three classical incremental linearization approaches, i.e., direct, secant and tangent ones are adopted and an affine relationship between the stress and strain increments is deduced. In order to reduce the interaction between the inclusion and matrix phases, a second-ordered mapping tensor is introduced and a new mapping-tangent linearization approach is proposed. Different linearization approaches are implemented by the incremental self-consistent scheme to predict the overall stress-strain response of particle-reinforced composites. It is shown that the predicted stress-strain curves given by the proposed mapping-tangent linearization approach are softer than that by other three classical ones, and are much closer to that from a fullfield finite element simulation. Moreover, the linearized elasto-viscoplastic constitutive equation based on the proposed mapping-tangent approach has the same mathematical structure as the rate-independent elasto-plastic constitutive law. In this sense,the homogenization problems faced in the elasto-plastic and elasto-viscoplastic heterogeneous materials can be unified.     

An element-free Galerkin method for ground penetrating radar numerical simulation

An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.     

Buckling analysis of super-long rock-socketed filling piles in soft soil area by element free Galerkin method

In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditional first type, and a newly invented numerical analysis method, i.e. the element-free Galerkin method (EFGM), was introduced to consider the non-concordant deformation and nonlinearity of the pile-soil interface. Then, based on the nonlinear elastic-ideal plastic pile-soil interface model, a nonlinear iterative algorithm was given to analyze the pile-soil interaction, and a program for buckling analysis of piles by the EFGM (PBAP-EFGM) and arc length method was worked out as well. The application results in an engineering example show that, the shape of pile top load-settlement curve obtained by the program agrees well with the measured one, of which the difference may be caused mainly by those uncertain factors such as possible initial defects of pile shaft and the eccentric loading during the test process. However, the calculated critical load is very close with the measured ultimate load of the test pile, and the corresponding relative error is only 5.6%, far better than the calculated values by linear and nonlinear incremental buckling analysis (with a greater relative error of 37.0% and 15.4% respectively), which also verifies the rationality and feasibility of the present method.     

含两个圆形孔洞岩盐路基稳定性的数值分析

用无网格伽辽金法（EFGM）按平面应变问题对含两个圆形孔洞的岩盐路基进行稳定性分析,给出了针对不同孔洞埋深的临界载荷.数值结果表明,EFGM对于解决含两个孔洞的应力集中问题是有效且灵活的.     

FRP增强砖砌体墙在平面内荷载作用下有限元模型

为研究承受平面内荷载的FRP增强砖砌体墙片的力学行为,建立了分离式平面有限元模型,分别用四节点平面单元,联结单元和膜单元模拟块体,砂浆和FRP.块体材料采用增量弹塑性本构模型以及Mises屈服准则结合最大拉应力准则,砂浆材料采用弹性本构模型以及Mohr-Coulomb屈服准则,FRP采用一维线弹性本构模型,有限元模型的求解采用增量初应力法.最后,利用两个算例对模型进行了验证,计算结果与试验结果的对比表明二者符合程度较好,说明模型是有效的.     

Application in metal rheological forming of element-free Galerkin method

The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.     

The interpolating element-free Galerkin method for elastic large deformation problems

This paper presents an interpolating element-free Galerkin(IEFG) method for solving the two-dimensional(2D) elastic large deformation problems. By using the improved interpolating moving least-squares method to form shape function, and using the Galerkin weak form of 2D elastic large deformation problems to obtain the discrete equations, we obtain the formulae of the IEFG method for 2D elastic large deformation problems. As the displacement boundary conditions can be applied directly, the IEFG method can acquire higher computational efficiency and accuracy than the traditional element-free Galerkin(EFG)method, which is based on the moving least-squares approximation and can not apply the displacement boundary conditions directly. To analyze the influences of node distribution, scale parameter of influence domain and the loading step on the numerical solutions of the IEFG method, three numerical examples are proposed. The IEFG method has almost the same high accuracy as the EFG method, and for some 2D elastic large deformation problems the IEFG method even has higher computational accuracy.     

改进型无网格Galerkin法与有限元法的耦合及其应用研究

采用改进型无网格Galerkin法与有限元(IEFG-FE)耦合的方法来计算裂纹问题。改进型无网格伽辽金法是基于一种改进的移动最小二乘(ani mproved moving least-squares,I MLS)近似。I MLS近似比现有的MLS近似有更高的计算效率和精度,且不会导致系统方程产生病态。这种耦合的方法不仅解决了无网格Galerkin法力学边界条件施加的难点,避免系统方程产生病态,而且还克服了无网格Galerkin法耗时较多的缺点。本文运用线弹性断裂力学理论,采用加权正交基函数对有限板单边裂纹的应力强度因子和受拉单边斜裂纹矩形板进行了分析。数值计算结果表明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。