摘要
从横观各向同性平面应变弹性体的基本控制方程出发,通过Fourier积分变换和Cayley-Hamilton定理推导出单层横观各向同性地基的传递矩阵,然后再通过矩阵变换求得单层地基的精确刚度矩阵,即解析层元解;根据有限层法原理组合得到总刚度矩阵,通过求解总刚度矩阵得到横观各向同性层状地基平面应变问题在积分变换域内的解答,应用Fourier逆变换得到物理域内的精确解。编制相应的计算程序,计算结果与有限元软件模拟结果吻合。算例分析表明土的分层特性和横观各向同性性质对土体变形有明显影响。
Based on the governing equations of plane strain problem, the transfer matrix of a single soil layer of transversely isotropic multilayered soils is obtained by using the Fourier transform and Cayley-Hamilton theorem. Then its exact stiffness matrix is deduced by means of the matrix transformation, which is called analytical layer element. The total stiffness matrix is established on the basis of the principle of finite layer method, and the solutions to the plane strain problem of transversely isotropic multilayered soils in the integral transform domain are obtained by solving it. The actual solutions in the physical domain are acquired by inverting the Fourier transform. The calculated results acquired by corresponding computer program agree fairly well with those by finite element analysis software. Numerical analysis shows that the influence of the stratification and transverse isotropy on the deformation of soils is significant.
出处
《岩土工程学报》
EI
CAS
CSCD
北大核心
2012年第10期1787-1791,共5页
Chinese Journal of Geotechnical Engineering
基金
国家自然科学基金项目(50578121)
