解析层元法求解层状横观各向同性地基轴对称问题

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摘要提出了一个求解横观各向同性层状地基轴对称问题的解析层元方法。从弹性力学基本方程出发并利用 Hankel 变换，得到横观各向同性单层地基的传递矩阵解，进而推导出单层地基的解析层元刚度矩阵。利用有限元方法组装总体刚度矩阵，通过求解总体刚度矩阵，并采用 Hankel 逆变换的数值积分方法，可求出层状横观各向同性弹性体轴对称问题在物理域内的精确解。刚度矩阵元素中不存在正指数并具有对称的特点，不仅使计算过程简化，还提高了计算精度。最后文中给出了算例来证明推导结果的准确性。

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	艾智勇
	仓乃瑞
	成怡冲

关键词 ：横观各向同性, 轴对称问题, 解析层元, 成层土体

Abstract：An analytical layer-element method is proposed to solve the axisymmetric problem of transversely isotropic multi-layered soils. From the basic equations of elasticity and by using the Hankel transform, the transfer matrix of a single soil layer is obtained. Based on the transfer matrix, a precise stiffness matrix of a single soil layer is deduced. By employing the finite element method, we can further get the total stiffness matrix of multi-layered soils. A numerical inversion technique of the Hankel transform is adopted to obtain the exact solutions of axisymmetric problems of transversely isotropic multi-layered soils in the physical domain. Because of no existence of positive functions and the symmetry of the matrix, we can not only simplify the calculation but also improve its accuracy. Finally, a numerical example is given to prove the accuracy of the present results.

Key words： transverse isotropy axisymmetric problem analytical layer-element multi-layered soil

收稿日期: 2012-06-25

TU443

基金资助:国家自然科学基金项目(50578121)

作者简介: 艾智勇 (1966 – ),男，江西余江人，博士，教授，主要从事岩土及地下工程方面的教学和研究工作。

引用本文:

艾智勇, 仓乃瑞, 成怡冲. 解析层元法求解层状横观各向同性地基轴对称问题[J]. 岩土工程学报, 2012, 34(5): 863-867. AI Zhi-yong, CANG Nai-rui, CHENG Yi-chong. A nalytical layer-element method for axisymmetric problem of transversely isotropic multi-layered soils. Chinese J. Geot. Eng., 2012, 34(5): 863-867.

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http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/ 或 http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/Y2012/V34/I5/863

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