耦合方程的有限元求解及其前后处理

发布时间：2018-01-04 04:08

本文关键词：耦合方程的有限元求解及其前后处理　出处：《上海大学》2015年硕士论文　论文类型：学位论文

【摘要】：碰撞安全问题中粘弹塑性材料的非牛顿边界层现象具有重要的现实意义。本文使用非线性流固耦合偏微分方程组(Cauchy流体方程与P-T/T固体方程)研究接触表面的形变与应力分布变化。宏观上对空间与时间分别使用有限元、有限差分方法离散,最终得到全离散格式。微观上借助高性能计算软件(OASYS与DYNA),通过三维建模再现真实碰撞场景,研究复杂接触表面速度场与应力场变化规律。本文在变分过程中引入三线性泛函。在半离散有限元的基础上(空间上使用Lagrange形状函数,时间上使用Euler向后差分格式),研究耦合方程组的收敛性。并得出结论：在参数固定的情况下,选择合适的步长,耦合方程组可以达到一定的精度。通过数值试验结果也可以看出,步长选择不恰当时,接触表面的网格会产生很大的变形。此外,借助高性能计算平台,对多孔蜂窝材料尤其是边界层处材料的非牛顿力学大变形进行仿真分析。研究蜂窝结构在不同压缩条件下不同的微观变形与应力分布变化。结果显示：蜂窝结构通过接触表面的变形吸收并消耗被传递的能量,材料变形集中在接触边界层区域,远离接触边界层的材料受影响不大。
[Abstract]:Non-Newtonian boundary layer phenomena of viscoelastic-plastic materials in collision safety problems have important practical significance. In this paper, nonlinear fluid-solid coupled partial differential equations are used. Cauchy fluid equation and P-T / T solid equation) are used to study the deformation and stress distribution of contact surface. The finite difference method is used to discretize, and finally the full discrete scheme is obtained. By using the high performance computing software OASYS and dyna, the real collision scene is reproduced by 3D modeling. The variation law of velocity field and stress field of complex contact surface is studied. In this paper, trilinear functional is introduced into the variational process. On the basis of semi-discrete finite element method, Lagrange shape function is used in space. The convergence of the coupled equations is studied by using the Euler backward difference scheme in time, and the conclusion is drawn that the appropriate step size should be chosen when the parameters are fixed. The coupled equations can achieve a certain accuracy. The results of numerical experiments also show that when the step size is not properly selected, the mesh of the contact surface will produce great deformation. In addition, with the help of high performance computing platform. The large deformation of porous honeycomb material, especially at the boundary layer, is simulated and analyzed in non-Newtonian mechanics. The microcosmic deformation and stress distribution of honeycomb structure under different compression conditions are studied. The results show that:. The honeycomb structure absorbs and consumes the transmitted energy through the deformation of the contact surface. The material deformation is concentrated in the contact boundary layer area, and the material far away from the contact boundary layer is not affected.
【学位授予单位】：上海大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.82

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