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

• Published in: Computational mechanics 2000-01, Vol.24 (6), p.463-475
• Main Authors: GUMASTE, U. A, PARK, K. C, ALVIN, K. F
• Format: Article
• Language: English
• Subjects: Algorithms; Chemical partition; Computer simulation; Deformation; Equations of motion; Equilibrium equations; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Lagrange multiplier; Mathematical methods in physics; Numerical approximation and analysis; Numerical differentiation and integration; Parallel computers; Partitions; Physics; Rigid-body dynamics; Solid mechanics; Structural and continuum mechanics; Substructures; Time integration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s004660050006

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.