层状和非均质地基附加弹性场的计算方法  

COMPUTATIONAL METHOD FOR ADDITIONAL ELASTIC FIELDS IN LAYERED AND NON-HOMOGENEOUS FOUNDATIONS

作　　者：肖莎 岳中琦[2] XIAO Sha;YUE Zhongqi(Key Laboratory of Urban Security and Disaster Engineering of China Ministry of Education,Beijing University of Technology,Beijing 100124,China;Department of Civil Engineering,The University of Hong Kong,Hong Kong,China)

机构地区：[1]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124 [2]香港大学土木工程系,中国香港

出　　处：《力学与实践》2024年第5期1051-1058,共8页Mechanics in Engineering

基　　金：国家自然科学基金项目(42207182),北京市博士后经费(2023-zz-138);北京市朝阳区博士后经费(2022-zz-22)资助。

摘　　要：地基中附加应力的计算是土力学教学的重要内容。本文发展了层状和非均质地基中附加弹性场的计算方法。该方法采用点集中载荷作用下横观各向同性层状半无限空间基本解,并对加载域进行二维积分。采用加载域离散的方式考虑任意形状加载域上非均匀载荷的影响,精确计算了地基弹性场表达式中的非奇异和奇异积分。数值验证表明,本文方法具有很高的计算精度,可分析沿深度方向弹性参数任意变化的地基。计算公式表达清晰简洁,便于讲授和学习。Computational methods for additional stresses in foundations are an important topic in soil mechanics.This paper develops a new numerical method for additional elastic fields in layered and non-homogeneous foundations.The techniques adopted primarily involve the use of a two-dimensional integration to integrate the fundamental solutions of a transversely isotropic and layered halfspace under point loads over the distributed pressure.To analyze non-uniform loads over an arbitrary area,the loading area needs to be discretized into a finite number of quadrilateral elements.The regular and singular integrals in the expressions of elastic fields in foundations are accurately calculated.Numerical examples show that the proposed method can provide highly accurate results and can be used to analyze the foundations with the elastic parameters arbitrarily varying with depth.The proposed method is explicitly and concisely expressed for effective teaching and learning.

关 键 词：层状和非均质地基 横观各向同性 附加弹性场 计算方法 

分 类 号：O343.7[理学—固体力学]