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• An algebraically partitioned FETI method for parallel structural analysis: algorithm description

  K. Park, M. Justino, C. Felippa

  International Journal for Numerical Methods in Engineering (1997). Vol. 40 (15), pp. 2717-2737

  
  

  Abstract

  An algebraically partitioned FETI method for the solution of structural engineering problems on parallel computers is presented. The present algorithm consists of three attributes: an explicit generation of the orthogonal null‐space matrix associated with the interface nodal forces, the floating subdomain rigid‐body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized. Comparisons of the present method with the previously developed differentially partitioned FETI method are offered in terms of the saddle‐point formulations at the end of the paper. A companion paper reports implementation details and numerical performance of the proposed algorithm.

  Abstract
  An algebraically partitioned FETI method for the solution of structural engineering problems on parallel computers is presented. The present algorithm consists of three [...]

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• A direct flexibility method

  C. Felippa, K. Park

  Computer Methods in Applied Mechanics and Engineering (1997). Vol. 149 (1-4), pp. 319-337

  
  

  Abstract

  We present a Direct Flexibility Method (DFM) for the solution of finite element equations. This method is based on a decomposition of the finite element model into substructures, which may reduce to individual elements. Substructures are preprocessed by the Direct Stiffness Method (DSM) to generate free-free flexibility matrices for floating substructures. The interface problem is solved for the interface forces and the solution recovered over substructure interiors. The DFM shares with the DSM the advantages of being automatic, maintaining locality and sparseness, efficiently handling continuum elements, and requiring only the availability of element stiffness libraries. The new method appears to be advantageous for specific applications. These include: massively parallel processing, inverse problems, treatment of rigid members and inclusions, and use of under-integrated elements without spurious-mode stabilization.

  Abstract
  We present a Direct Flexibility Method (DFM) for the solution of finite element equations. This method is based on a decomposition of the finite element model into substructures, [...]

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• A Variational Framework for Solution Method Developments in Structural Mechanics

  K. Park, C. Felippa

  Journal of Applied Mechanics (1998). Vol. 65 (1), pp. 242-249

  
  

  Abstract

  We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variationally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.

  Abstract
  We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual [...]

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• ETA Expressions for the High Frequency Impedance of a Uniformly Pulsating Submerged Torus

  C. Felippa

  (1998). IUTAM Symposium on Computational Methods for Unbounded Domains. Fluid Mechanics and Its Applications, vol 49. Springer, Dordrecht.

  
  

  Abstract

  The present abstract was motivated by the search for clean yet nontrivial benchmark problems for wave propagation and scattering in an infinite acoustic medium. The submerged sphere, cylinder and disk illustrate important aspects of scattering and radiation while admitting complete analytical solutions. These three classical configurations are thus indispensable part of any set of benchmark problems.

  Abstract
  The present abstract was motivated by the search for clean yet nontrivial benchmark problems for wave propagation and scattering in an infinite acoustic medium. The submerged [...]

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• The construction of free–free flexibility matrices as generalized stiffness inverses

  C. Felippa, K. Park, M. Justino

  Computers and Structures (1998). Vol. 68 (4), pp. 411-418

  
  

  Abstract

  We present generalizations of the classical structural flexibility matrix. Direct or indirect computation of flexibilities as ‘influence coefficients’ has traditionally required pre-removal of rigid body modes by imposing appropriate support conditions. Here the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free–free stiffness matrix. This entity is called a free–free flexibility matrix. It preserves exactly the rigid body modes. The definition is element independent. It only involves access to the stiffness generated by a standard finite element program as well as a separate geometric construction of the rigid body modes. With this information, the computation of the free–free flexibility can be done by solving linear equations and does not require the solution of an eigenvalue problem or performing a singular value decomposition. Flexibility expressions for symmetric and unsymmetric free–free stiffnesses are studied. For the unsymmetric case two flexibilities, one preserving the Penrose conditions and the other the spectral properties, are examined. The two versions coalesce for symmetric matrices

  Abstract
  We present generalizations of the classical structural flexibility matrix. Direct or indirect computation of flexibilities as ‘influence coefficients’ has [...]

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• Construction of optimal 3-node plate bending triangles by templates

  C. Felippa, C. Militello

  Computational Mechanics (1999). Vol. 24 (1), pp. 1-13

  
  

  Abstract

  A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. The present study concerns Kirchhoff Plate-Bending Triangles (KPT) with 3 nodes and 9 degrees of freedom. A 37-parameter template is constructed using the Assumed Natural Deviatoric Strain (ANDES). Specialization of this template includes well known elements such as DKT and HCT. The question addressed here is: can these parameters be selected to produce high performance elements? The study is carried out by staged application of constraints on the free parameters. The first stage produces element families satisfying invariance and aspect ratio insensitivity conditions. Application of energy balance constraints produces specific elements. The performance of such elements in benchmark tests is presently under study.

  Abstract
  A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. The present study [...]

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• Recent Developments In Basic Finite Element Technologies

  C. Felippa

  (1999). Computational Mechanics in Structural Engineering, pp. 141-155

  
  

  Abstract

  High performance (HP) elements are simple finite elements constructed to deliver engineering accuracy with arbitrary coarse meshes. This chapter reviews original developments based on parametrized variational principles, which provide a common foundation for various approaches to HP element construction. Templates are parametrized algebraic forms of finite element stiffness equations, which hold future promise in the unification of finite element methods and connection to arbitrary grid finite differences. Essential to this unification work is the availability of powerful computer algebra systems. The application of templates to the construction of an optimal 3-node plate bending element is outlined in the chapter.

  Abstract
  High performance (HP) elements are simple finite elements constructed to deliver engineering accuracy with arbitrary coarse meshes. This chapter reviews original developments [...]

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• A localized version of the method of Lagrange multipliers and its applications

  K. Park, C. Felippa, U. Gumaste

  Computational Mechanics (2000). Vol. 24 (6), pp. 476-490

  
  

  Abstract

  This paper describes a novel version of the method of Lagrange multipliers for an improved modeling of multi-point constraints that emanate from contact-impact problems, partitioned structural analysis using parallel computers, and structural inverse problems. It is shown that the classical method of Lagrange multipliers can lead to a non-unique set of constraint conditions for the modeling of interfaces involving more than two or multi-point substructural interface nodes. The proposed version of the method of Lagrange multipliers leads not only to unique construction of constraints but also encounters no singularity in modeling an arbitrary number of multi-point constraints. An important utilization of the present method is in the regularized modeling of interfaces whose rigidities are radically different from one to another. The present approach is demonstrated via several examples for its simplicity in modeling constraints, ease of implementation and computational advantages

  Abstract
  This paper describes a novel version of the method of Lagrange multipliers for an improved modeling of multi-point constraints that emanate from contact-impact problems, partitioned [...]

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• A variational principle for the formulation of partitioned structural systems

  K. Park, C. Felippa

  International Journal for Numerical Methods in Engineering (2000). Vol. 47 (1-3), pp. 395-418

  
  

  Abstract

  A continuum‐based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems. This application includes coupled substructures as well as subdomains obtained by mesh decomposition. The present variational principle is derived by a series of modifications of a hybrid functional originally proposed by Atluri for finite element development. The interface is treated by a displacement frame and a localized version of the method of Lagrange multipliers. Interior displacements are decomposed into rigid‐body and deformational components to handle floating subdomains. Both static and dynamic versions are considered. An important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures, independent mesh refinement, and global–local analysis. The present principle is compared with that of a globalized version of the multiplier method. 

  Abstract
  A continuum‐based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems. This application includes [...]

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• On the Original Publication of the General Canonical Functional of Linear Elasticity

  C. Felippa

  Journal of Applied Mechanics. (2000). Vol. 67 (1), pp. 217-219

  
  

  Abstract

  The general canonical functional of linear elastostatics is associated with the names of Hu and Washizu, who published it independently in 1955. This note discusses how that functional, in a generalized four-field form, had been derived by B. M. Fraeijs de Veubeke in a 1951 technical report. This report presents five of the seven canonical functionals of elasticity. In addition to the general functional, it exhibits what is likely the first derivation of the strain-displacement dual of the Hellinger-Reissner functional. The tour of five variational principles takes only a relatively small portion of the report: 8 pages out of 56. The bulk is devoted to the use of energy methods for analysis of wing structures. The title, technology focus, and limited dissemination may account for the subsequent neglect of this original contribution to variational mechanics.

  Abstract
  The general canonical functional of linear elastostatics is associated with the names of Hu and Washizu, who published it independently in 1955. This note discusses how that [...]

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