A time domain solution for complex multilayered soil model with circular inhomogeneity by the SBFEM

The scaled boundary finite method (SBFEM) is developed for analyzing wave propagation problem in the two-dimensional unbounded domain with rigid bedrock. It combines the advantages of the finite element method and boundary element boundary method. Moreover, the original scaling center is replaced by a scaling line which is more suitable for analyzing the multilayered soil model. Therefore, the modified SBFEM develops the original SBFEM. A new derivation of the modified SBFEM equation is built in the frame of Hamilton system. A continued fraction solution of the dynamic stiffness of the soil model with bedrock is obtained for the first time. Then, by introducing the continued fraction solution and auxiliary variables, it leads to the model resting on bedrock can be solved in time domain. The global equation of motion is solved by the efficient precise time-integration method. This integral method is firstly employed in the modified SBFEM. The precision of the proposed method can achieve computer precision. Therefore, an extremely efficient and accurate solution of the modified SBFEM in time domain is obtained. The results of the complex soil model with circular inhomogeneity show that the proposed method yields excellent results, and high accuracy is observed.

[1]  W. Zhong,et al.  On precise integration method , 2004 .

[2]  E. Kausel,et al.  Dynamic loads in the interior of a layered stratum: An explicit solution , 1982 .

[3]  Mark Randolph,et al.  Axisymmetric Time‐Domain Transmitting Boundaries , 1994 .

[4]  Marc Bonnet,et al.  An integral formulation for steady-state elastoplastic contact over a coated half-plane , 2002 .

[5]  Somnath Ghosh,et al.  A material based finite element analysis of heterogeneous media involving Dirichlet tessellations , 1993 .

[6]  Enrique S. Quintana-Ortí,et al.  Parallel Computation of 3-D Soil-Structure Interaction in Time Domain with a Coupled FEM/SBFEM Approach , 2012, J. Sci. Comput..

[7]  Carolin Birk,et al.  An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains , 2012 .

[8]  Ajit K. Mal,et al.  Stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique , 2001 .

[9]  Eduardo Kausel,et al.  Point Loads in Cross‐Anisotropic, Layered Halfspaces , 1989 .

[10]  J. Chisholm,et al.  Algorithms for the ?-algebra of electromagnetic form factors1 , 1971 .

[11]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[12]  M. Cemal Genes,et al.  Dynamic analysis of large-scale SSI systems for layered unbounded media via a parallelized coupled finite-element/boundary-element/scaled boundary finite-element model , 2012 .

[13]  Xiuli Du,et al.  3D viscous-spring artificial boundary in time domain , 2006 .

[14]  S. C. Fan,et al.  Dynamic Fluid-Structure Interaction Analysis Using Boundary Finite Element Method–Finite Element Method , 2005 .

[15]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[16]  R. J. Astley,et al.  The performance of spheroidal infinite elements , 2001 .

[17]  J. Wolf,et al.  The scaled boundary finite-element method – a primer: derivations , 2000 .

[18]  Chuhan Zhang,et al.  A coupling procedure of FE and SBFE for soil–structure interaction in the time domain , 2004 .

[19]  M. Dokainish,et al.  A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods , 1989 .

[20]  Chen Deng-hon,et al.  A high-order time-domain model of dam-foundation dynamic interaction , 2014 .

[21]  J. Zhang,et al.  A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions , 1995 .

[22]  D. Givoli.  Non-reflecting boundary conditions , 1991 .

[23]  Chongmin Song,et al.  The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics , 1997 .

[24]  Chongmin Song,et al.  The scaled boundary finite element method in structural dynamics , 2009 .

[25]  Eduardo Kausel,et al.  Wave propagation in anisotropic layered media , 1986 .

[26]  W. S. Hall,et al.  Boundary element methods for soil-structure interaction , 2004 .

[27]  John P. Wolf,et al.  The scaled boundary finite-element method – a primer: solution procedures , 2000 .

[28]  Carolin Birk,et al.  A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method , 2014 .

[29]  Eduardo Kausel,et al.  Dynamic Stiffness of Circular Foundations , 1975 .

[30]  W. Zhong.  Duality system in applied mechanics and optimal control , 2004 .

[31]  Bin Teng,et al.  A modified scaled boundary finite-element method for problems with parallel side-faces. Part I. Theoretical developments , 2005 .

[32]  Subra Suresh,et al.  Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites , 1993 .

[33]  E. Kausel.  Thin‐layer method: Formulation in the time domain , 1994 .

[34]  Chongmin Song.  A matrix function solution for the scaled boundary finite-element equation in statics , 2004 .

[35]  Xiaojun Chen,et al.  Transient analysis of wave propagation in layered soil by using the scaled boundary finite element method , 2015 .

[36]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis , 1987 .

[37]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[38]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[39]  F. Afagh,et al.  Anisotropic stress analysis of inclusion problems using the boundary integral equation method , 1992 .

[40]  Carolin Birk,et al.  A modified scaled boundary finite element method for three‐dimensional dynamic soil‐structure interaction in layered soil , 2012 .

[41]  Ch. Song,et al.  A local high-order doubly asymptotic open boundary for diffusion in a semi-infinite layer , 2010, J. Comput. Phys..

[42]  V. Buryachenko,et al.  A series solution of the volume integral equation for multiple-inclusion interaction problems , 2000 .

[43]  Wang Biao,et al.  Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material , 1992 .

[44]  C. Katz,et al.  A high performance scaled boundary finite element method , 2010 .

[45]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis: Part II (1986-1996) , 1997 .

[46]  Xiong Zhang,et al.  Three-dimensional dynamic soil-structure interaction analysis in the time domain , 1999 .

[47]  J. Wolf,et al.  The scaled boundary finite element method , 2004 .

[48]  W. Zhong,et al.  A Precise Time Step Integration Method , 1994 .

[49]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[50]  Chongmin Song,et al.  A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry , 2008, International Journal for Numerical Methods in Engineering.