复杂接触表面问题有限元计算及微观结构分析

The safety test of transportation device, including impact test and elastic-plastic deformation, is now simulated both in laboratory and computer. Contact deformation algorithm is an international standard method to simulate the slip control on complex 3-D surface. In this project, coupled non-Newtonian visco-elastic equations with initial boundary value are used to solve the 3-D layer structure. A finite element method (FEM) based on variational principle is used to solve the perturbation problem. The related data-mining of the uncertainties is processed by high performance software. According to the embedding principle, a stratified element division of the model is processed, and the complex boundary will then be divided into several mutual connected yet not overlapped 3-D hexahedron and 2-D rectangular elements. Micro variables of stochastic contact problem and macro-scale FEM models are established, on which super-convergent calculation and simulation is processed. Varying curves of parameters, including energy and velocity, can then be obtained.. On the other hand, the boundary layer theory of asymptotic perturbation method is also a way to study the discontinuous contact surface. The characteristic function space gained can be used both to optimize the primary function of FEM, and to establish a new asymptotic method to solve the nonlinear eigen-problem. It can be used to estimate the specific parameters of material as well. The characteristic spectrum method of artificial boundary conditions is then used to study the resulting data.

碰撞、弹塑变形问题等交通运输器安全试验目前通常采用实验室实物模型与计.算机模型相结合。对三维复杂区域的接触，滑动控制目前国际标准模拟方法采用接触算法。我们在本课题中采用流固耦合非牛顿流体方程初边值问题求解三维层结构特性。通过基于变分原理的摄动问题有限元方法，在高性能软件的平台上实现不确定数据的挖掘处理。由Sobolev空间嵌入原理将模型按接触区域进行分层单元剖分，将复杂区域剖分为若干相互连接、不重叠的六面体与空间平面四边形单元。同时建立随机接触问题微观变量与宏观有限元计算模型进行超收敛计算与模拟仿真对比，得到模型的能量与速度等一系列参数的变化曲线。.另外，接触表面间断问题又可采用渐近摄动方法的边界层理论进行研究。由此得到的微分方程特征函数既可作为优化有限元基函数的解又可建立一种新型的非线性特征值的渐近方法，这是估计材料特定参数的方法之一。然后使用人工边界条件特征谱处理方法估计间断定解条件。

本课题组从规律原理出发，从数学本质理论结构入手，揭露接触表面复杂边界条件最基本的矛盾.从而更经济有效地解决核心计算问题.三维有限元研究复杂弹塑性应变受多种碰撞初边值条件影响，如碰撞发生的角度、材料性质、碰撞发生的面积等.课题组进一步使用人工边界条件随机处理方法对有限元求解结果的上万组数据进行分析，得到应变的分布函数. 结论是：通过计算建立离散随机系统高精度有效方法可取得极有应用价值的非牛顿力学分析以达到物理实验很难重复的接触表面控制.从而解决接触表面问题中可变形蜂窝材料三维结构的力学性质研究.本课题运用高性能有限元多层网格计算对复杂移动边界层进行非牛顿力学分析并根据正态 “Fisher 法则和中心极限定理”对实际碰撞条件进行仿真与渐近分析。被动安全不确定性问题的研究结果对研究多场耦合模型的多尺度算法具有参考和探索性意义.偶然性存在于客观必然性之中，