基于半解析有限元的沥青路面结构分析方法

论文总字数：28653字

摘 要

由于沥青路面结构在我国道路工程中的广泛的应用范围与广阔的发展前景，对其受力响应进行快速精准的仿真模拟是十分必要的，在路面结构设计等领域存在着对专用快速有限元分析工具的需求。本文以半解析有限元法为理论依据，编制了相关的算法，开发了一种简易高效的沥青路面结构力学响应分析软件，以MATLAB^®为平台编写，可在个人电脑上独立安装运行。该软件能够通过简便的操作步骤实现建模、构网、计算、展示等有限元分析的基本功能。

建模时生成长方体形状的块体结构模型，按不同材料分层，模型范围包含荷载在路面结构上的影响范围。在结构模型的长度方向端面上施加道路长度方向位移约束和竖直方向位移约束，道路宽度方向不提供支承力；在土基底部限制三维方向的所有位移。在路表施加车轮荷载，与构网方式相适应，将荷载等效为均布矩形荷载。

构网由于半解析有限元法的简化，仅在长度和高度两个方向上离散，将长方形投影平面分割成矩形网格，控制构网有自动构网算法和手动输入网格尺寸两种方式，辅以结构三维图形用于检查。采用Serendipity八结点单元，对离散误差进行的理论分析证实了其较高的精度。

由于理论、编程等方面的优化，软件对计算机硬件要求低、运行速度快。为了控制半解析有限元法的解析误差，研究了解析函数——傅里叶级数的项数取值对计算精度的影响规律，并提出了一种较保守的傅里叶级数项数取值方法。

在后处理阶段，可展示任意垂直于坐标轴的截面的位移、应力、应变云图和变形图，在图像中观察现象和提取数据。

在实际运行测试中，本软件与ANSYS^®在相同工况下的计算结果相当一致，且本软件一般情况下所需的建模、计算时间更短，验证了工具的准确性与高效性。

关键词：半解析有限元法，沥青路面，力学响应，快速分析工具

Abstract

Because of the wide application range and broad development prospect of asphalt pavement structure in China, it is necessary to carry out rapid and accurate simulation of its mechanical response. There is a demand for special rapid finite element analysis tools in the field of pavement structure design. In this paper, based on the semi-analytical finite element method, the relevant algorithms are compiled, and a simple and efficient software for analyzing the mechanical response of asphalt pavement structure is developed, which is written on the platform of MATLAB, and can be installed and run on a personal computer independently. The software has basic finite element analysis functions of modeling, netting, computation and demonstration through simple operation steps.

In the modeling process, a cuboid shape block structure model is generated, which is layered according to different materials. The scope of the model includes the influence scope of the load on the pavement structure. The length direction constraint and vertical displacement constraint are applied to the length direction end of the structural model, and the direction of the road does not provide the supporting force; all the displacement of the three-dimensional direction is restricted at the base of the soil base. The wheel load is applied to the road surface, and the load is equivalent to the uniform rectangular load.

As a result of the simplification of semi-analytical finite element method, the network is discrete only in two directions of length and height, and the rectangular plane is divided into rectangular grids. The two ways of controlling network are automatic mesh construction and manual mesh size input. Using Serendipity eight-node element, the theoretical analysis of discrete error confirms its high accuracy.

Due to the optimization of theory and programming, this software has low requirement for computer hardware and fast running speed. In order to control the analytical error of the semi-analytical finite element method, the influence of the number of Fourier series (the analytical function) on the calculation precision is studied, and a more conservative method of the value of the number of Fourier series is proposed.

In the post processing stage, the displacement, stress, strain diagram of the cross section which are perpendicular to the axis can be displayed, and the phenomena and the data can be extracted in the image.

In the actual running test, the calculation results of this software and ANSYS's are quite consistent in the same working condition, and the modeling and calculation time required of the software are shorter under the general condition, which verifies the accuracy and efficiency of the tool.

KEY WORDS: semi-analytical finite element method, asphalt pavement structure, mechanical response, rapid analysis tool

目录

摘要 I

Abstract II

第一章 绪论 1

1.1选题背景及意义 1

1.2国内外现状 1

1.2.1沥青路面分析软件现状 1

1.2.2半解析有限元理论现状 1

第二章 理论方法论证 4

2.1通用有限元方法 4

2.1.1基本理论 4

2.1.2网格与单元形式 5

2.1.3离散误差 6

2.2沥青路面结构求解模式 8

2.2.1结构模型形状与坐标系类型 9

2.2.2坐标方向与约束条件 10

2.3半解析有限元法 10

2.3.1基本理论 10

2.3.2简支单元推论 12

第三章 软件工具开发 13

3.1软件架构 13

3.2软件功能 14

3.2.1结构区 14

3.2.2网格区 15

3.2.3荷载区 17

3.2.4图形框 17

3.2.5后处理区 18

3.2.6控制按钮 18

3.2.7图形窗口 19

3.3细部计算简化 19

3.3.1等效结点荷载 20

3.3.2计算刚度矩阵 20

第四章 计算结果检验 22

4.1 解析误差 22

4.2 算例 23

4.2.1 模型选取 23

4.2.2 计算处理 24

4.2.3 荷载影响的扩散 25

4.2.4 与ANSYS对比 27

第五章 结论 29

致谢 30

参考文献 31

第一章 绪论

1.1选题背景及意义

沥青路面在道路工程中应用广泛，路面结构设计过程中必须进行路面结构验算，需要使用计算机模拟路面结构的受力响应。目前很多沥青路面的分析软件仍基于弹性层状体系理论。在弹性层状体系理论对于路面的几项层状体系假设^[1]中，只能求解在半无限空间路面施加均布单圆荷载这一轴对称情况，或者将两个均布圆形荷载的解叠加作为双圆荷载的解，这与路面结构的实际形状及荷载的实际分布有很大差距；还假设层间接触仅有竖向应力而无摩阻力，而实际上层间存在水平约束力，这同样会造成理论与实际之间产生较大差异。与之相比，有限元方法能够灵活地建立各种形状的路面结构模型，施加任意荷载，在层间传递各个方向的力，使数值仿真模拟在约束条件上接近实际情况成为可能。

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