Response of multilayered transversely isotropic medium due to axisymmetric loads

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 40; no. 6; pp. 827 - 864
• Main Authors: Zhang, Pengchong, Lin, Gao, Liu, Jun, Wang, Wenyuan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 25.04.2016; Wiley Subscription Services, Inc
• Subjects: Accuracy; Axisymmetric; axisymmetric loads; Differential equations; dual vector; Isotropy; Mathematical analysis; Mathematical models; multilayered media; Powder injection molding; precise integration method; Soil (material); Soil surfaces; transverse isotropy; Vectors (mathematics)
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2429

Summary A novel procedure associated with the precise integration method (PIM) and the technique of dual vector is proposed to effectively calculate the magnitude and distribution of deformations in a homogeneous multilayered transversely isotropic medium. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the soil system. The linearly elastic medium is subjected to four types of vertically acting axisymmetric loads prescribed either at the external surface or in the interior of the soil medium. There are no limits for the thicknesses and number of soil layers to be considered. By virtue of the governing equations of motion and the constitutive equations of the transversely isotropic elastic body, and based on the Hankel integral transform and a dual vector formulation in a cylindrical coordinate system, the partial differential motion equations can be converted into first‐order ordinary differential matrix equations. Applying the approach of PIM, it is convenient to obtain the solutions of ordinary differential matrix equations for the continuously homogeneous multilayered transversely isotropic elastic soil in the transformed domain. The PIM is a highly accurate algorithm to solve the sets of first‐order ordinary differential equations, which can ensure to achieve any desired accuracy of the solutions. What is more, all calculations are based on the standard method with the corresponding algebraic operations. Computational efforts can be reduced to a great extent. Finally, numerical examples are provided to illustrate the accuracy and effectiveness of the proposed approach. Some more cases are analyzed to evaluate the influences of the elastic parameters of the transversely isotropic media on the load‐displacement responses. Copyright © 2015 John Wiley & Sons, Ltd.