A two-step, two-field hybrid method for the static and dynamic analysis of substructure problems with conforming and non-conforming interfaces

Abstract The need for assembling independent finite element substructure solutions arises in several engineering and scientific problems including the design and analysis of complex structural systems, component mode synthesis, global/local analysis, adaptive refinement and parallel processing. In this paper, we discuss the solution of such problems by a two-field hybrid method where the substructures are jointed with low-order polynomial or piece-wise polynomial Lagrange multipliers and present a Rayleigh-Ritz based smoothing procedure for improving the accuracy of the computed coupled solution in the presence of various substructure heterogeneities. We consider both conforming and nonconforming substructure meshes, and demonstrate the benefits of the proposed two-step solution method with several examples from structural mechanics.

[1]  C. Farhat,et al.  Partitioned procedures for the transient solution of coupled aroelastic problems Part I: Model problem, theory and two-dimensional application , 1995 .

[2]  Charbel Farhat,et al.  On the spectral stability of time integration algorithms for a class of constrained dynamics problems , 1993 .

[3]  Charbel Farhat,et al.  Matching fluid and structure meshes for aeroelastic computations : a parallel approach , 1995 .

[4]  Charbel Farhat,et al.  A transient FETI methodology for large‐scale parallel implicit computations in structural mechanics , 1994 .

[5]  John D. Whitcomb,et al.  Iterative Global/Local Finite Element Analysis , 1990 .

[6]  Charbel Farhat,et al.  A Lagrange multiplier based divide and conquer finite element algorithm , 1991 .

[7]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[8]  Charbel Farhat,et al.  Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations , 1992 .

[9]  R. Glowinski,et al.  Third International Symposium on Domain Decomposition Methods for Partial Differential Equations , 1990 .

[10]  Garrett Birkhoff,et al.  Elliptic Problem Solvers II , 1984 .

[11]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[12]  Charbel Farhat,et al.  An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems , 1992, SIAM J. Sci. Comput..

[13]  Daniel Rixen,et al.  A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps , 1996 .

[14]  Charbel Farhat,et al.  Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics , 1993 .

[15]  Susan L. Mccleary,et al.  Coupled analysis of independently modeled finite element subdomains , 1992 .

[16]  M. R. Dorr,et al.  A domain decomposition preconditioner with reduced rank interdomain coupling , 1991 .

[17]  J. Z. Zhu,et al.  The finite element method , 1977 .

[18]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[19]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[20]  Charbel Farhat.  Fast structural design and analysis via hybrid domain decomposition on massively parallel processors , 1993 .

[21]  Leonard Meirovitch,et al.  A general substructure synthesis method for the dynamic simulation of complex structures , 1980 .

[22]  C. E. Knight,et al.  The specified boundary stiffness/force SBSF method for finite element subregion analysis , 1988 .

[23]  Charbel Farhat,et al.  A HYBRID FORMULATION OF A COMPONENT MODE SYNTHESIS METHOD , 1992 .

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

[25]  Charbel Farhat,et al.  The Dual Schur Complement Method with Well-Posed Local Neumann Problems: Regularization with a Perturbed Lagrangian Formulation , 1993, SIAM J. Sci. Comput..

[26]  Charbel Farhat,et al.  On a component mode synthesis method and its application to incompatible substructures , 1994 .

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