State space solution to 3D multilayered elastic soils based on order reduction method

Zhi-yong AI;Yi-chong CHENG;Peng LIU

doi:10.1007/s10483-012-1629-8

Applied Mathematics and Mechanics >

2012 , Vol. 33 >Issue 11: 1371 - 1380

DOI: https://doi.org/10.1007/s10483-012-1629-8

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State space solution to 3D multilayered elastic soils based on order reduction method

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Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, P. R. China

Received date: 2011-04-27

Revised date: 2012-06-21

Online published: 2012-11-10

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Abstract

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

Key words： state space solution; multilayered elastic soil; double Fourier transform; order reduction method; adaptive structure; active member; state vector approach; frequency; damping ratio

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Zhi-yong AI;Yi-chong CHENG;Peng LIU . State space solution to 3D multilayered elastic soils based on order reduction method[J]. Applied Mathematics and Mechanics, 2012 , 33(11) : 1371 -1380 . DOI: 10.1007/s10483-012-1629-8

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