采用刚度矩阵法的弹性层状体系数值解法

阳恩慧; 艾长发; 邱延峻

采用刚度矩阵法的弹性层状体系数值解法

阳恩慧^{1, 2,},
艾长发^{1, 2},
邱延峻^{1, 2}

1.
西南交通大学土木工程学院, 四川成都 610031
2.
西南交通大学道路工程四川省重点实验室, 四川成都 610031

基金项目:

国家自然科学基金项目 51308477

中央高校基本科研业务费专项资金项目 2682013BR030

详细信息

作者简介:
阳恩慧(1982-), 男, 湖南洞口人, 西南交通大学讲师, 工学博士, 从事道路工程计算力学及新材料研究

中图分类号: U213.1
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出版历程
- 收稿日期: 2014-03-16
- 刊出日期: 2014-08-25

Numerical method of multi-layer elastic system by using stiffness matrix method

YANG En-hui^{1, 2
,},
AI Zhang-fa^{1, 2},
QIU Yan-jun^{1, 2}

1.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China
2.
Highway Engineering Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

More Information

Author Bio:
YANG En-hui(1982-), male, lecturer, PhD, +86-28-87634347, yeh1982@163.com

Article Text (Baidu Translation)

摘要

摘要: 从弹性力学基础理论出发, 采用刚度矩阵法, 推导了应用于直角坐标系下的三维多层弹性层状体系静力学数值解法。引入二维傅里叶变换及高斯积分求解法, 基于MATLAB数学软件平台编制计算程序, 实现三维多层弹性层状体系理论计算方法的数值求解。针对典型有砟轨道轨下基础结构, 采用提出的计算方法和编制的相应计算程序对其进行静力学分析, 并将所获得的计算结果与采用通用有限元程序ABAQUS的计算结果进行对比。分析结果表明: 采用提出的计算方法和通用有限元计算方法获得有砟轨道轨下基础最大竖向位移分别为1.50、1.95 mm, 最大竖向应力分别为0.34、0.21 MPa, 计算结果较为接近, 计算反映出来的各状态分量变换规律基本一致, 提出的计算方法及其相应计算程序可应用于多层弹性层状体系的静力学计算。
- 路基工程 /
- 弹性层状体系 /
- 刚度矩阵法 /
- 数值解法
Abstract: By using the theory of elastic mechanics and stiffness matrix method, a numerical method of static mechanics for calculating 3D multi-layer elastic system under rectangular coordinate system was developed.2D Fourier transform and Gauss integral method were used, a calculation program was given based on MATLAB mathematical software platform, and the numerical solution of 3D multi-layer elastic system was got.The static mechanics analysis of ballast track foundation structure was carried out by using the numerical method and program, and the calculation results were compared with the results obtained by using general finite element program ABAQUS.Analysis result shows that the maximum vertical displacements of ballast track foundation are 1.50, 1.95 mm respectively by using the numerical method and general finite element calculation method, and the maximum vertical stresses of the foundation are 0.34, 0.21 MPa respectively by using the two methods.The calculation results are close to each other, and the conversion rules of state components are basically the same according to the calculation, so the proposed numerical method and program can be applied to the static mechanics calculation of multi-layer elastic system.
- subgrade engineering /
- multi-layer elastic system /
- stiffness matrix method /
- numerical method

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图 1 三维多层弹性层状体系理论计算

Figure 1. Theoretical calculation of 3D multi-layer elastic system

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图 2 单一层应力及位移

Figure 2. Stress and displacement of each layer

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图 3 有砟轨道系统整体结构计算模型

Figure 3. Calculation model of ballast track system overall structure

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图 4 轨枕节点力链杆等效转换

Figure 4. Equivalent conversion of sleeper nodal force

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图 5 有砟轨道结构单元划分及节点编号

Figure 5. Structure units and node numbers of ballast track

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图 6 有砟轨道轨下基础顶面竖向位移

Figure 6. Vertical displacement above ballast track foundation

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图 7 有限元计算模型

Figure 7. Finite element calculating model

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图 8 竖向位移计算结果对比

Figure 8. Comparison of vertical displacement calculating results

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图 9 竖向应力计算结果对比

Figure 9. Comparison of vertical stress calculating results

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表 1 有砟轨道计算参数

Table 1. Calculating parameters of ballast track

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表 2 最大竖向位移对比

Table 2. Comparison of maximum vertical displacements

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