Rapid solution of 3-D oscillatory elastodynamics using the pFFT accelerated BEM

Boundary element method accelerated by the precorrected-FFT algorithm is developed and implemented for 3-D frequency-domain elastodynamic problems. Some critical implementation issues are described. The accuracy and efficiency of the developed method are validated via the comparison between the simulated results and analytical solutions or FEM results of three examples. Excellent agreements are demonstrated in all three examples.

[1]  Jacob K. White,et al.  Air damping in laterally oscillating microresonators: a numerical and experimental study , 2003 .

[2]  T. A. Cruse,et al.  Numerical solutions in three dimensional elastostatics , 1969 .

[3]  Jacob K. White,et al.  A precorrected-FFT method for electrostatic analysis of complicated 3-D structures , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  L. Gray,et al.  Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids , 2007 .

[5]  O. C. Zienkiewicz,et al.  The Finite Element Method for Solid and Structural Mechanics , 2013 .

[6]  Toru Takahashi,et al.  A fast BIEM for three-dimensional elastodynamics in time domain☆ , 2003 .

[7]  Heow Pueh Lee,et al.  A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles , 2003 .

[8]  Toru Takahashi,et al.  A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model , 2005 .

[9]  Marc Bonnet,et al.  Fast multipole method applied to 3-D frequency domain elastodynamics. , 2008 .

[10]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[11]  Y. Shiah,et al.  Stress Analysis of 3D Generally Anisotropic Elastic Solids Using the Boundary Element Method , 2009 .

[12]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[13]  N. Nishimura,et al.  Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method , 2005 .

[14]  Jiheng Zhang,et al.  Numerical Characterization of Porous Solids and Performance Evaluation of Theoretical Models via the Precorrected-FFT Accelerated BEM , 2010 .

[15]  L. Greengard,et al.  A new version of the Fast Multipole Method for the Laplace equation in three dimensions , 1997, Acta Numerica.

[16]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[17]  Wenjing Ye,et al.  Fast BEM solution for coupled 3D electrostatic and linear elastic problems , 2004 .

[18]  Subrata Mukherjee,et al.  A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity , 1993 .

[19]  Attilio Frangi,et al.  Multipole BEM for the evaluation of damping forces on MEMS , 2005 .

[20]  Wenjing Ye,et al.  A fast integral approach for drag force calculation due to oscillatory slip stokes flows , 2004 .

[21]  Demosthenes Polyzos,et al.  2D and 3D Boundary Element Analysis of Mode-I Cracks in Gradient Elasticity , 2008 .

[22]  S. Lim,et al.  Fast BEM Solvers for 3D Poisson-Type Equations , 2008 .

[23]  P. K. Banerjee The Boundary Element Methods in Engineering , 1994 .

[24]  Stéphanie Chaillat,et al.  A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain , 2008 .

[25]  Zhenhan Yao,et al.  A Rigid-fiber-based Boundary Element Model for Strength Simulation of Carbon Nanotube Reinforced Composites , 2008 .

[26]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[27]  N. Pan,et al.  Predictions of effective physical properties of complex multiphase materials , 2008 .