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• Doubly asymptotic approximations for vibration analysis of submerged structures

  T. Geers, C. Felippa

  Journal of the Acoustical Society of America (1983). Vol. 73 (4), pp. 1152-1159

  
  

  Abstract

  Doubly Asymptotic Approximations (DAAs) are differential equations for boundary-element analysis of the interaction between a complex structure and a surrounding infinite medium. In this paper, the use of first- and second-order DAAs for steady-state vibration analysis of submerged structures is examined. First, the governing discrete-element equations for the general problem are set down and discussed. Then the accuracy of three DAA forms is studied through the generation of numerical results for a submerged spherical shell. Although the first-order DAA is found to be inadequate, the two second-order forms show considerable promise.

  Abstract
  Doubly Asymptotic Approximations (DAAs) are differential equations for boundary-element analysis of the interaction between a complex structure and a surrounding infinite [...]

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• Professional workstations

  C. Felippa

  Engineering Computations (1984). Vol. 1 (2), pp. 183-188

  
  

  Abstract

  Professional workstations are dedicated computers that possess sufficient hardware power and software capabilities to allow the routine performance of job-related activities by professional users. The advent of these computers reflects current trends in decentralization and specialization of computer equipment. The paper presents an informal review of classes of workstations of potential interest to engineers and scientists. The review was motivated by projected computing needs in a software- intensive research-and-development industrial laboratory.

  Abstract
  Professional workstations are dedicated computers that possess sufficient hardware power and software capabilities to allow the routine performance of job-related activities [...]

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• A triangular element with rotational degrees of freedom

  P. Bergan, C. Felippa

  Computer Methods in Applied Mechanics and Engineering (1985). Vol. 50 (1), pp. 25-69

  
  

  Abstract

  A new plane-stress triangular element is derived using the free formulation of Bergan and Nygård. The triangle possesses nine degrees of freedom: six corner translations and three corner normal rotations. The element is coordinate-invariant and passes the patch test for any geometry. Two free parameters in the formulation may be adjusted to optimize the behavior for in-plane bending patterns. With the recommended parameter choices the element performance is significantly better than that of the constant-strain triangle. Because of the presence of the rotational freedoms, this new element appears especially suitable as membrane component of a flat triangular element for modelling general shell structures.

  Abstract
  A new plane-stress triangular element is derived using the free formulation of Bergan and Nygård. The triangle possesses nine degrees of freedom: six corner translations [...]

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• Finite element analysis of shock-induced hull cavitation

  C. Felippa, J. DeRuntz

  Computer Methods in Applied Mechanics and Engineering (1985). Vol. 44 (3), pp. 297-337

  
  

  Abstract

  This paper describes the theoretical formulation and computational implementation of a method for treating hull cavitation in underwater‐shock problems. In addition, the method can be applied to the analysis of submerged structures that contain internal fluid volumes. In the present implementation, the doubly asymptotic approximation (DAA) serves to simulate a radiation boundary that is located away from the fluid‐structure surface at a distance sufficient to contain any cavitating region. The enclosed fluid is discretized with volume finite elements that are based upon a displacement‐potential formulation. An explicit time‐integration algorithm is used to advance the solution in the fluid‐volume region, implicit algorithms are used for the structure and DAA boundary, and a staggered solution procedure has been developed to treat the interface condition. Results for two example problems obtained with the present implementation show close agreement with those obtained by other methods.

  Abstract
  This paper describes the theoretical formulation and computational implementation of a method for treating hull cavitation in underwater‐shock problems. In addition, the [...]

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• A command reader for interactive programming

  C. Felippa

  Engineering Computations (1985). Vol. 2 (3), pp. 203-237

  
  

  Abstract

  A simplified command line reader suitable for building interactive programs based on Fortran 77 is presented. The reader is a 20:1 condensation of the comprehensive command language interpreter CLIP that supports the NICE integrated software system. The present reader, called TinyCLIP. has been prepared to illustrate basic elements of command-driven programming for beginners interested in writing Fortran-based interactive applications software. The reader is table driven. Data lines given to the reader are parsed into items which are stored in a table. The table can be subsequently accessed by the program that processes the commands. Tools for extending the basic language are briefly discussed and specific extensions suggested.

  Abstract
  A simplified command line reader suitable for building interactive programs based on Fortran 77 is presented. The reader is a 20:1 condensation of the comprehensive command [...]

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• Penalty‐function iterative procedures for mixed finite element formulations

  C. Felippa

  International Journal for Numerical Methods in Engineering (1986). Vol. 22 (1), pp. 267-279

  
  

  Abstract

  Iterative methods for solving mixed finite element equations that correct displacement and stress unknowns in ‘staggered’ fashion are attracting increased attention. This paper looks at the problem from the standpoint of allowing fairly arbitrary approximations to be made on both the stiffness and compliance matrices used in solving for the corrections. The resulting iterative processes usually diverge unless stabilized with Courant penalty terms. An iterative procedure previously constructed for equality-constrained displacement models is recast to fit the mixed finite element formulation in which displacements play the role of Lagrange multipliers. The penalty function iteration is shown to reduce to an ordinary staggered stress-displacement iteration if the weight is set to zero. Convergence conditions for these procedures are stated and the potentially troublesome effect of prestress modes noted.

  Abstract
  Iterative methods for solving mixed finite element equations that correct displacement and stress unknowns in ‘staggered’ fashion are attracting increased attention. [...]

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• Symmetrization of the contained compressible‐fluid vibration eigenproblem

  C. Felippa

  Communications in Applied Numerical Methods (1985). Vol. 1 (5), pp. 726-734

  
  

  Abstract

  This paper studies the symmetrization of the problem of coupled vibrations of an acoustic fluid enclosed in an elastic container. The container structure is discretized by a displacement finite element formulation and the acoustic fluid by a displacement‐potential formulation. The vibrations of this physically conservative coupled system are governed by an unsymmetric algebraic eigenvalue problem. Eight equivalent symmetric forms of this problem are exhibited. The fluid‐pressure formulation leads to a similar unsymmetric eigenproblem, which in turn can be converted to another eight equivalent symmetric forms.

  Abstract
  This paper studies the symmetrization of the problem of coupled vibrations of an acoustic fluid enclosed in an elastic container. The container structure is discretized by [...]

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• Traversing Critical Points with Penalty Springs

  C. Felippa

  (1987). Transient/Dynamic Analysis and Constitutive Laws for Engineering Materials

  
  

  Abstract

  We present aspects of computer implementation of finite element structural analysis capabilities into a series of concurrent machines. We approach the implementation issues from the viewpoint that the design of data structures for finite element computations will play a crucial role in the constructs of computational modules, data transfer mechanisms among processes, and, consequently, desirable non-numerical and numerical algorithms. We account for the essential architectural features of local memory machines, shared memory machines and connection machines that are pertinent to finite element computations. We outline a concurrent FEM system that we advocate, and report our activities on system design and algorithm development. We report also on our 'hands-on' experience in concurrent finite element computations using some of the existing multiprocessors such as Intel's hypercube iPSC, Encore's Multimax, Alliant/FX8, and the CRAY as a benchmark case.

  Abstract
  We present aspects of computer implementation of finite element structural analysis capabilities into a series of concurrent machines. We approach the implementation issues [...]

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• A triangular element based on an energy-orthogonal free formulation

  C. Felippa, P. Bergan

  Computer Methods in Applied Mechanics and Engineering (1987). Vol. 61 (2), pp. 129-160

  
  

  Abstract

  A new Kirchhoff triangular plate-bending element with nine degrees of freedom is derived. The assumed shape functions are nonconforming and consist of a complete quadratic expansion complemented by three cubic modes that are energy-orthogonal to the quadratic expansion. The derivation is based on the free formulation of Bergan and Nygård, which satisfies the conditions of invariance and the patch test. An explicit expression is obtained for the inverse transformation matrix required in this formulation, which makes the stiffness computations extremely efficient. The aspect ratio sensitivity of the element under cylindrical bending modes can be lessened by scaling the higher-order stiffness through coefficients determined by a superlinear patch test technique. Numerical experiments indicate that the new element outperforms previously derived 9-dof triangular elements based on displacement modes.

  Abstract
  A new Kirchhoff triangular plate-bending element with nine degrees of freedom is derived. The assumed shape functions are nonconforming and consist of a complete quadratic [...]

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• Will the Force Method Come Back?

  C. Felippa

  Journal of Applied Mechanics (1987). Vol. 53 (3), pp. 726-728

  
  

  Abstract

  The force method of structural analysis was overtaken by the displacement method in the mid Sixties, and has disappeared from the scene for few specialized applications. Virtually all existing general-purpose finite element programs are based on the direct stifness method (DSM) introduced three decades ago by Turner et al. (1956) and Turner (1959). The DSM combines the displacement method of solution with the direct, element-by-element assembly of the stifness equations. The simplicity and efficiency of the DSM for general applications have not been matched to date; it has the polished "black box" feeling of Lagrange's analytical mechanics. 

  Abstract
  The force method of structural analysis was overtaken by the displacement method in the mid Sixties, and has disappeared from the scene for few specialized applications. Virtually [...]

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