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• Penalty Spring Stabilization of Singular Jacobians

  C. Felippa

  Journal of Applied Mechanics (1987). Vol. 54 (3), pp. 728-729

  
  

  Abstract

  A limit-point treatment is presented which is a synthesis of two earlier techniques. To traverse limit points, Sharifi and Popov (1970) introduced fictitious stiffnesses in the form of rank-one updates but did not use auxiliary systems. Rheinboldt (1981) discussed the use of auxiliary systems in conjunction with the partition of the Jacobian matrix. The procedure presented in this paper avoids the need for partitioning and consequent special treatment of the elements in the ith row and column of K; only the diagonal entry is changed. It enjoys the added advantage that none of the auxiliary system right-hand sides requires access to elements of the K matrix.

  Abstract
  A limit-point treatment is presented which is a synthesis of two earlier techniques. To traverse limit points, Sharifi and Popov (1970) introduced fictitious stiffnesses in [...]

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• Symmetrization of coupled eigenproblems by eigenvector augmentation

  C. Felippa

  Communications in Applied Numerical Methods (1988). Vol. 4 (4), pp. 561-563

  
  

  Abstract

  The problem of elastoacoustic vibrations of a fluid enclosed in a flexible container leads to a generalized unsymmetric eigensystem of special form. This system can be symmetrized in eight different ways by eigenvector augmentation followed by static condensation.

  Abstract
  The problem of elastoacoustic vibrations of a fluid enclosed in a flexible container leads to a generalized unsymmetric eigensystem of special form. This system can be symmetrized [...]

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• Partitioned analysis of coupled mechanical systems

  C. Felippa, T. Geers

  Engineering Computations (1988). Vol. 5 (2), pp. 123-133

  
  

  Abstract

  Partitioned analysis is a method by which sets of time-dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby avoiding brute-force simultaneous solution. The coupled systems addressed pertain to fluid—structure, fluid—soil, soil—structure, or even structure—structure interaction. The paper describes the partitioning process for certain discrete-element equations of motion, as well as the associated computer implementation. It then delineates the procedure for designing a partitioned analysis method in a given application. Finally, examples are presented to illustrate the concepts. It is seen that a key element in the implementation of partitioned analysis is the use of integrated, as opposed to monolithic software.

  Abstract
  Partitioned analysis is a method by which sets of time-dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby avoiding [...]

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• Treatment of coupled fluid-structure interaction problems by a mixed variational principle

  C. Felippa, R. Ohayon

  (1989). Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems

  
  

  Abstract

  A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. Semidiscrete finite-element equations of motion based on this principle are displayed.

  Abstract
  A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition [...]

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• Parametrized multifield variational principle in elasticity. I: Mixed functionals

  C. Felippa

  Communications in Applied Numerical Methods (1989). Vol. 5 (2), pp. 79-88

  
  

  Abstract

  A one-parameter family of mixed variational principles for linear elasticity is constructed. This family includes the generalized Hellinger-Reissner and total potential energy principles as special cases. The presence of the free parameter offers an opportunity for the systematic derivation of energy-balanced finite elements that combine displacement and stress assumptions. It is shown that Fraeijs de Veubeke's stress-assumption limitation principle takes a particulary elegant expression in terms of the parametrized discrete form. Other possible parametrizations are briefly discussed.

  Abstract
  A one-parameter family of mixed variational principles for linear elasticity is constructed. This family includes the generalized Hellinger-Reissner and total potential energy [...]

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• Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the Free Formulation

  C. Felippa

  Communications in numerical methods in engineering (1989). Vol. 5 (2), pp. 89-98

  
  

  Abstract

  A one-parameter family of d-generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision. The family includes the d-generalized Hellinger-Reissner and potential energy principles as special cases. The parametrized principle is discretized by independently varied internal displacements, stresses and boundary displacements. The resulting finite element equations are studied following a physically motivated decomposition of the stress and internal displacement fields. The free formulation of Bergan and Nygård is shown to be a special case of this element type, and is obtained by assuming a constant internal stress field. The parameter appears as a scale factor of the higher-order stiffness.

  Abstract
  A one-parameter family of d-generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision. The family includes the d-generalized [...]

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• The Extended Free Formulation of Finite Elements in Linear Elasticity

  C. Felippa

  Journal of Applied Mechanics (1989). Vol. 56 (3), pp. 609-616

  
  

  Abstract

  The free formulation of Bergan and Nyga˚rd (1984) has been successfully used in the construction of high-performance finite elements for linear and nonlinear structural analysis. In its original form the formulation combines nonconforming internal displacement assumptions with a specialized version of the patch test. The original formulation is limited, however, by strict invertibility conditions linking the assumed displacement field to the nodal displacements. The present paper lifts those restrictions by recasting the free formulation within the framework of a mixed-hybrid functional that allows internal stresses, internal displacements, and boundary displacements to vary independently. This functional contains a free parameter and includes the potential energy and the Hellinger-Reissner principles as special cases. The parameter appears in the higher-order stiffness of the element equations

  Abstract
  The free formulation of Bergan and Nyga˚rd (1984) has been successfully used in the construction of high-performance finite elements for linear and nonlinear structural analysis. [...]

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• Towards parallel I/O in finite element simulations

  C. Farhat, E. Pramono, C. Felippa

  International Journal for Numerical Methods in Engineering (1989). Vol. 28 (11)

  
  

  Abstract

  I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.

  Abstract
  I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is [...]

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• Electromagnetic axisymmetric finite elements based on a gauged four-potential variational principle

  J. Schuler, C. Felippa

  Computing Systems in Engineering (1990). Vol. 1 (2-4), pp. 273-284

  
  

  Abstract

  Electromagnetic finite elements are derived based on a variational principle that uses the electromagnetic four-potential as a primary variable. The Lorentz gage normalization is incorporated as a constraint condition through a Lagrange multiplier field to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of high-temperature superconductor devices with aerospace applications. The main advantages are: jump discontinuities on interfaces are naturally handled; no a priori approximations are invoked; and the number of degrees of freedom per node remains modest as the problem dimensionality increases. The new elements are tested on two magnetostatic axisymmetric problems. The results are in excellent agreement with analytical solutions and previous solutions for the 1D problem of a conducting infinite wire, in which case the multiplier field has no effect. For materials of widely different permeability, jump conditions are naturally accommodated by the present formulation.

  Abstract
  Electromagnetic finite elements are derived based on a variational principle that uses the electromagnetic four-potential as a primary variable. The Lorentz gage normalization [...]

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• The Effect of Wall Motions on the Governing Equations of Contained Fluids

  R. Ohayon, C. Felippa

  Journal of Applied Mechanics (1990). Vol. 57 (3), pp. 783-785

  
  

  Abstract

  The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.

  Abstract
  The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account [...]

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