结构可靠度响应面法的混沌动力学分析及其改进方法研究

引入混沌动力学理论讨论了结构可靠度响应面法收敛失败的非线性动力学根源.给出了几个典型非线性极限状态函数在参数区间上的可靠指标分岔图,展示了极限状态函数经过响应面法迭代成为非线性映射后计算结果的周期振荡、分岔和混沌等复杂动力学现象,说明了响应面法的收敛行为取决于极限状态函数的动力学性质和响应面法的迭代步长.在此基础上提出了改进响应面法用以改善经典响应面法收敛失败和计算误差大的缺点,算例结果证实了所提方法的可行性与精度.     

一种求算结构可靠度指标的新方法

为解决结构功能函数在结构设计点附近非线性程度较高时,一次可靠度计算方法(如JC法)不收敛的问题,提出一种新的可靠度计算方法.该算法根据结构可靠指标的几何意义,先将迭代点靠近极限状态面,再通过在极限状态面上搜索下一迭代点,逐渐减小极限状态面上的点到标准正态空间中坐标原点的距离,从而达到收敛的目的.与其他方法相比,该方法不用选取算法参数,在计算效率和鲁棒性方面都有较好的优势,尤其在极限状态函数非线性强的情况下优势更为明显.     

基于Armijo准则的自适应稳定转换法

结构可靠度分析是结构不确定性设计的关键环节,计算效率和鲁棒性是评估可靠度分析算法性能的两个重要指标。首先针对两个已有的一次二阶矩算法（iHL-RF算法和方向性稳定转化法）进行分析,发现iHL-RF算法根据Armijo准则可以自适应调整迭代步长,但计算效率低;方向性稳定转化法根据振荡的方向性可以提高计算效率,但自适应性差。结合两种算法的优点,将Armijo准则用于自适应调整方向性稳定转化法的混沌控制因子,提出了基于Armijo准则的自适应稳定转换法。通过四个非线性算例将本文提出的算法与HL-RF、iHL-RF、混沌控制法以及方向性稳定转换法等四种算法的收敛性和计算效率进行比较。结果表明,相比其他四种可靠度分析算法,本文算法在求解二维和多维非线性极限状态函数时均具有更好的收敛性和更高的计算效率。     

基于Armijo准则的自适应稳定转换法

结构可靠度分析是结构不确定性设计的关键环节,计算效率和鲁棒性是评估可靠度分析算法性能的两个重要指标。首先针对两个已有的一次二阶矩算法(iHL-RF算法和方向性稳定转化法)进行分析,发现iHL-RF算法根据Armijo准则可以自适应调整迭代步长,但计算效率低;方向性稳定转化法根据振荡的方向性可以提高计算效率,但自适应性差。结合两种算法的优点,将Armijo准则用于自适应调整方向性稳定转化法的混沌控制因子,提出了基于Armijo准则的自适应稳定转换法。通过四个非线性算例将本文提出的算法与HL-RF、iHL-RF、混沌控制法以及方向性稳定转换法等四种算法的收敛性和计算效率进行比较。结果表明,相比其他四种可靠度分析算法,本文算法在求解二维和多维非线性极限状态函数时均具有更好的收敛性和更高的计算效率。     

求解非线性反问题的大范围收敛梯度正则化算法

基于同伦映射的思想,改进了求解非线性反问题的梯度正则化算法。通过路径跟踪有效地拓宽了梯度正则化算法求解的收敛范围。对于正则化参数的修正,通过引入拟Sigmoid函数,提出了一种下降速率可调的连续化参数修正方法,在保证迭代稳定的条件下,得到较好的计算效率,同时保证该算法具有很好的抵抗观测噪声能力。实际算例表明,该方法收敛范围宽,计算效率高,在存在较强观测噪声的条件下也能得到很好的反演结果。     

基于单纯形寻优的响应面可靠性分析方法

结构可靠度计算常采用经典的响应面法拟合隐式功能函数或高维功能函数,而对于强非线性功能函数的实际工程问题,尽管其能够计算出结构可靠度的结果,但此时多项式响应面的拟合精度不够,很容易造成不收敛的现象。为了解决上述问题,将响应面法与单纯形寻优的思路进行结合来探求一种有效的计算方法。本文利用单纯形算法对每次迭代的验算点进行优化;再以优化后的设计验算点为中心进行取样,利用响应面法循环迭代计算;最后,沿着真实响应面逐渐逼近最终的验算点。该方法能够解决高维非线性的隐式极限状态方程可靠度计算收敛性的问题,可以提高计算精度和计算效率,具有一定的工程适用性。     

基于单纯形寻优的响应面可靠性分析方法

结构可靠度计算常采用经典的响应面法拟合隐式功能函数或高维功能函数，而对于强非线性功能函数的实际工程问题，尽管其能够计算出结构可靠度的结果，但此时多项式响应面的拟合精度不够，很容易造成不收敛的现象。为了解决上述问题，将响应面法与单纯形寻优的思路进行结合来探求一种有效的计算方法。本文利用单纯形算法对每次迭代的验算点进行优化；再以优化后的设计验算点为中心进行取样，利用响应面法循环迭代计算；最后，沿着真实响应面逐渐逼近最终的验算点。该方法能够解决高维非线性的隐式极限状态方程可靠度计算收敛性的问题，可以提高计算精度和计算效率，具有一定的工程适用性。     

节点梯度光滑有限元配点法

配点法构造简单、计算高效, 但需要用到数值离散形函数的高阶梯度,而传统有限元形函数的梯度在单元边界处通常仅具有C$^{0}$连续性,因此无法直接用于配点法分析. 本文通过引入有限元形函数的光滑梯度,提出了节点梯度光滑有限元配点法. 首先基于广义梯度光滑方法,定义了有限元形函数在节点处的一阶光滑梯度值,然后以有限元形函数为核函数构造了有限元形函数的一阶光滑梯度,进而对一阶光滑梯度直接求导并用一阶光滑梯度替换有限元形函数的标准梯度,即完成了有限元形函数二阶光滑梯度的构造.文中以线性有限元形函数为基础的理论分析表明,其光滑梯度不仅满足传统线性有限元形函数梯度对应的一阶一致性条件,而且在均布网格假定下满足更高一阶的二阶一致性条件.因此与传统线性有限元法相比,基于线性形函数的节点梯度光滑有限元法的$L_{2}$和$H_{1}$误差均具有二次精度,即其$H_{1}$误差收敛阶次比传统有限元法高一阶, 呈现超收敛特性.文中通过典型算例验证了节点梯度光滑有限元配点法的精度和收敛性,特别是其$H_{1}$或能量误差的精度和收敛率都明显高于传统有限元法.      

基于缩减样本窗口的响应面重构方法

具有隐式功能函数的复杂结构可靠度分析常采用响应面方法。对于功能函数非线性程度较高的结构可靠度分析的响应面迭代重构问题,由于一般响应面方法样本窗口过大,导致迭代分析精度难以提高。本文提出了响应面重构中样本窗口的确定原则,并建立了结构可靠度分析的缩减窗口序列响应面重构方法。多个数值试验表明：该方法迭代收敛迅速,计算精度较高...     

结构可靠度FORM方法的混沌动力学分析

引入混沌动力学理论讨论了FORM收敛失败的非线性动力学根源. 给出了几个典 型函数在参数区间上的可靠指标分岔图，展示了极限状态函数经过FORM迭代成为 非线性映射后计算结果的周期振荡、分岔和混沌等复杂动力学现象，计算了非线性映射的 Lyapunov指数. 结果表明，极限状态函数设计点的曲率大小与FORM的收敛性没有简单的联 系，判别FORM迭代计算收敛性的指标是非线性映射的Lyapunov指数.     

并行冲击/侵彻有限元数值模拟技术

探讨了冲击/侵彻问题涉及到的非线性材料模型、接触搜索算法、接触力计算公式、破坏模式等理论和算法,介绍了基于集群并行计算机的有限元法并行化基本思路和方法。应用实例表明本文中提出的有限元计算格式和并行化方法能够有效求解冲击/侵彻问题。     

A structured tri-tree search method for generation of optimal unstructured finite element grids in two and three dimensions

A new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea-Skagerrak area.     

Parameter determination and response analysis of viscoelastic material

The parameter determination of viscoelastic material is a multi-variable, multi-aim nonlinear optimization problem, which made the optimization process very complicated. In this paper a hybrid optimal algorithm was proposed to determine the viscoelastic parameters in the constitutive relation according to the experimentally obtained mechanical properties. This algorithm merges the Broydon–Fletcher–Goldfarb–Shanno search into a genetic algorithm framework as a basic operator in order to enhance the local search capability. The proposed hybrid algorithm not only can reduce the iterative times greatly but can abolish the limitation of initial parameter values. Nonlinear material characteristic curve-fitting was carried out using the proposed algorithm and other existing approaches. And the comparison results show this algorithm is accurate and effective. The numerical simulation and experimental study of viscoelastic cantilever beam also indicates that the finite element formulation and the calculative viscoelastic model parameters are reliable. The proposed optimization method can be extended to further complex parameter estimation researches.     

金属互连焊球的电迁移试验设计研究与灵敏度分析

综合考虑多种电迁移驱动机制, 基于ANSYS软件和FORTRAN程序提出电迁移失效算法, 导出了电迁移灵敏度分析方程, 并建立相应的数值算法. 在此基础上考虑设计变量为激活能、初始自扩散系数和材料力学性能参数等对金属互连焊球进行电迁移灵敏度分析, 同时基于三维有限元分析的全因子试验设计法对CSP封装结构的电迁移寿命进行仿真预测.     

Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulations

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.     

A Eulerian approach to the finite element modelling of neo-Hookean rubber material

A Eulerian approach is applied to the finite element modelling of neo-Hookean rubber material. Two major problems are encountered. The first problem is the construction of an algorithm to calculate stresses in the rubber material from velocities instead of displacements. This problem is solved with an algorithm based on the definition of the velocity gradient. The second problem is the convection of stresses through the finite element mesh. This problem is solved by adapting the so-called Taylor-Galerkin technique. Solutions for both problems are implemented in a finite element program and their validity is shown by test problems. Results of these implementations are compared with results obtained by a standard Lagrangian approach finite element package and good agreement has been found.     

岩质圆形隧洞围岩应力场弹塑性新解

针对动态接触问题的有限元并行计算，提出了一种新的接触算法. 新算法引入局部拉氏 乘子技术来计算接触力. 由于同时考虑了无穿透的接触约束条件和相邻接触对的相互影响， 较之广泛使用的罚参数法，新算法使接触约束条件和系统平衡方程得到更充分的满足. 虽然 为提高接触计算精度而在局部采用了迭代技术，但算法仍然具有较高的效率，且与显式时间 积分方案完全相容. 此外，通过构造专门的区域分解方案，实现了将现有为串行程序开发的 搜索算法平滑移植到并行环境的目标. 数值算例表明，所提出的接触算法具有很好的并行性， 在保证了接触问题并行计算精度的同时，取得了满意的并行效率.     

A local search algorithm for natural neighbours in the natural element method

A local basis algorithm for searching natural neighbours in Natural Element Method (NEM) is presented for solving the elasticity problems in this paper. Comparison with the global sweep algorithm used in natural element method or Natural Neighbour Method (NNM) for searching natural neighbours, the proposed algorithm is more expedient and convenient in the constructions and computation of natural neighbour interpolations. In the proposed NEM based on local search, the Laplace (non-sibson) interpolations are constructed with respect to the natural neighbour nodes of the given point which have been locally defined. The shape functions from the Laplace approximations have the delta function property and the Laplace interpolants are strictly linear between adjacent nodes, which facilitate imposition of essential boundary conditions and treatment of material discontinuity with ease as it is in the conventional finite element method. The Laplace interpolants derived from the local algorithm and the global algorithm in NEM are identical because of the uniqueness of the Voronoi diagram. Numerical results and convergence studies also show that the present NEM based on local search algorithm possesses the same accuracy and rate of convergence as they are in previous NEM.     

Simulation of fabric drape using a thin plate element with finite rotation

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated.     

一类基于点-面模式的低阶单元接触搜索方法

本文基于三个接触搜索准则提出接触预搜索概念。在接触预搜索阶段通过分级筛选方法逐步缩上可能接触点副的单元集;然后,给出动态有限元分析中适用分析中适用于大骨移的低阶单元接触点副的自动搜索算法。针对非线性动态接触问题有限元分析中常用低阶单元和点－面模式的搜索方式的情况,本文应用最近点投影搜索算法提出似以等参坐标为参数的另一种接触搜索算法。该搜索算法不须预先指定可能接触范围,从而极大地降低了数据的准备工作