3D应力场的可视化技术研究.doc

河北大学2010届本科生毕业论文（设计） PAGE  3D应力场的可视化技术研究 摘　　要 装 订 线 众所周知，场是现实世界中的物理量与空间或时间关系的一种表现形式，它是物质存在的一种形态。物理量在空间区域内的分布可表示为空间位置的函数，这样的函数称为场。在空间区域内，如果某物理量为标量函数，那么这个物理量就称为数量场或标量场；如果为向量函数，那么这个物理量称为向量场或矢量场；如果为张量函数，那么这个物理量就称之为张量场。张量场广泛地存在于自然界中，其信息量丰富，数据量庞大，难于表达。力学工程计算中有很多问题是张量场问题，比如布西内斯克问题中的应力场就是典型的张量场，这对于进一步的理解场中各物理量之间的关系和规律带来了很大的困难。张量场可视化旨在能够直观的表现场中应力的分布情况，进而揭示场中各物理???之间的关系和规律，具有重要的现实意义和工程价值。 本文以弹性理论为基础，导出应力张量可视化模型。并用矢量点图标和标量点图标来表达一点的应力状态。关于应力张量场的可视化，本文介绍了应力张量场的可视化的步骤，并以弹性理论中的布西内斯克等问题为例，说明了应力张量场的可视化的基本步骤，给出了可视化结果。 关键词：应力状态 点图标 张量场 可视化 Research for Visual Technique of 3D Stress Field ABSTRACT As we know, a field in the natural world is a representation form of physical quantity with respect to space or time; it is a state of material existence. A physical quantity can be expressed with a function defined in a three dimensional domain, called a field. If the physical quantity is a scalar function, it called a scalar field; if the physical quantity is a vector function, it called a vector field; if the physical quantity is a tensor function, it called a tensor field. The tensor fields have common existence in the natural world, which contain a lot of data sets and a large of information, hard to represent. In mechanics and engineering computing, many problems refer to the tensor field, for example, the stress field of Boussinesq problem is a tensor field. This has led to great difficulties for us to understand the law of physical relationship. Visualization of tensor field aims to indicate the physical law, which has great theory and engineering significance. Based on elastic theory, this paper gets the stress tensor visualization models; gains the scalar icon and vector icon representation to describe a point of stress station; gives the visualization of the tensor field taking two typical examples. 装 订 线 Key words：Stress state Icon Tensor field Visualization 目　　录 　　一　引言………………………………………………………………01 　　二　应力张量的可视化模型…………………………………………02 　　 装 订 线 2.1　应力张量的矢量点图表达……………………… ………………0