A family of implicit partitioned time integration algorithms for parallel analysis of heterogeneous structural systems

Abstract An implicit time integration algorithm is presented for the solution of linear structural dynamics problems on parallel computers. The present algorithm is derived from the partitioned equations of motion for a structure which consist of the equilibrium equations of each substructure due to its deformation energy, the self-equilibrium condition for each substructure under rigid-body motions, the partition boundary displacement compatibility condition and Newton's 3rd law along the partition boundary forces. A novel feature of the present algorithm is a flexibility normalization along the partitioned boundary nodes by using a localized version of the method of Lagrange multipliers, thus making the algorithm insensitive to both material and kinematic heterogeneities among the partitioned substructures. Numerical performance of the present algorithm demonstrates both its simplicity and efficiency. Hence, we recommend it for production analysis of heterogeneous structures modeled.

[1]  C. Farhat,et al.  A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems , 1995 .

[2]  G. TEMPLE,et al.  Relaxation Methods in Engineering Science , 1942, Nature.

[3]  C. Farhat,et al.  The two-level FETI method for static and dynamic plate problems Part I: An optimal iterative solver for biharmonic systems , 1998 .

[4]  S. R. Searle,et al.  On Deriving the Inverse of a Sum of Matrices , 1981 .

[5]  P. Tallec.  Domain decomposition methods in computational mechanics , 1994 .

[6]  R. P. Fedorenko.  A relaxation method for solving elliptic difference equations , 1962 .

[7]  Carlos A. Felippa,et al.  Staggered transient analysis procedures for coupled mechanical systems: Formulation , 1980 .

[8]  J. Mandel.  Balancing domain decomposition , 1993 .

[9]  C. Felippa,et al.  A Variational Framework for Solution Method Developments in Structural Mechanics , 1998 .

[10]  Carlos A. Felippa,et al.  A direct flexibility method , 1997 .

[11]  Thomas J. R. Hughes,et al.  IMPLICIT-EXPLICIT FINITE ELEMENTS IN TRANSIENT ANALYSIS , 1978 .

[12]  C. Farhat,et al.  The two-level FETI method. Part II: Extension to shell problems, parallel implementation and performance results , 1998 .

[13]  K. C. Park,et al.  Partitioned Transient Analysis Procedures for Coupled-Field Problems. , 1979 .

[14]  Charbel Farhat,et al.  Implicit parallel processing in structural mechanics , 1994 .

[15]  T. Belytschko,et al.  Stability of explicit‐implicit mesh partitions in time integration , 1978 .

[16]  Carlos A. Felippa,et al.  An algebraically partitioned FETI method for parallel structural analysis: algorithm description , 1997 .

[17]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[18]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .