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• Programming the isoparametric six-node triangle

  C. Felippa

  Engineering Computations (1990). Vol. 7 (2), pp. 173-177

  
  

  Abstract

  The formulation and programming of the six‐node, curved isoparametric triangle in plane stress is presented. This is intended to fill an apparent vacuum in the open finite element literature

  Abstract
  The formulation and programming of the six‐node, curved isoparametric triangle in plane stress is presented. This is intended to fill an apparent vacuum in the open finite [...]

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• A variational justification of the assumed natural strain formulation of finite elements—II. The C0 four-node plate element

  C. Militello, C. Felippa

  Computers and Structures (1990). Vol. 34 (3), pp. 439-444

  
  

  Abstract

  In Part II the four-node C0 plate bending element is used to explore some of the possibilities opened by the theory presented in Part I [C. Militello and C. A. Felippa, Comput. Struct.34, 431–438 (1990)]. This element is chosen because the version presented by Bathe and Dvorkin [Int. J. Numer. Meth. Engng21, 367–383 (1985)], MITC4, can be considered the simplest assumed natural strain element that allows several possibilities to be studied in a straightforward manner. Attention is focused on the governing functionals R and H presented in Part I, assuming independent strain fields only for the transverse shear strains. Besides MITC4, three formulations (two mixed and one hybrid) are considered that collectively represent a variational justification for the assumed strain technique. In addition, reduced and selective-integration elements are examined to compare their behavior with that of the present assumed strain elements.

  Abstract
  In Part II the four-node C0 plate bending element is used to explore some of the possibilities opened by the theory presented in Part I [C. Militello and C. A. Felippa, Comput. [...]

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• Article Metrics Related Articles Cite Share Request Permissions Explore More Download PDF Detecting and Traversing Bifurcation Points in Nonlinear Structural Analysis

  G. Skeie, C. Felippa

  International Journal of Space Structures (1991). Vol. 6 (2), pp. 77-98

  
  

  Abstract

  We investigate procedures for detecting and traversing bifurcation points that occur in the geometrically nonlinear analysis of elastic structures. In particular, we study a family of test functions for sharp detection and identification of bifurcation points. To accomplish branch switching without recourse to artifical imperfections, the selection of appropriate predictors and correctors which exclude the known branch from the converged solution is considered. These techniques are tried and assesed on several three-dimensional truss structures that exhibit bifurcation behavior

  Abstract
  We investigate procedures for detecting and traversing bifurcation points that occur in the geometrically nonlinear analysis of elastic structures. In particular, we study [...]

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• The Individual Element Test Revisited

  C. Militello, C. Felippa

  (1991). The finite element method in the 1990’s. Springer, Berlin, Heidelberg.

  
  

  Abstract

  The subject of the patch test for finite elements retains several unsettled aspects. In particular, the issue of one-element versus multielement tests needs clarification. Following a brief historical review, we present the individual element test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B, and C of the patch test and to the single element test are clarified.

  Abstract
  The subject of the patch test for finite elements retains several unsettled aspects. In particular, the issue of one-element versus multielement tests needs clarification. [...]

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• Probabilistic FEM for Nonlinear Concrete Structures. II: Applications

  J. Frangopol, S. Sture, C. Felippa

  Journal of Structural Engineering (1991). Vol. 117 (9), pp. 2690-2707

  
  

  Abstract

  This is the second part of an investigation on probabilistic finite element methods for nonlinear concrete structures. The study is concentrated on two reinforced concrete application examples including a simply supported beam and a portal frame. Nonlinearity in material and geometry, and randomness in loading, material, and geometry are considered. Extensive computations using a probabilistic finite element method inbedded in the computer code PFRAME developed at the University of Colorado, Boulder, are carried out to verify analytical results. The effect of Taylor series expansions about different values of various random variables on structural response is demonstrated in both application examples. Furthermore, using the simply supported beam example, it is shown that the probabilistic finite element method proposed is applicable to the assessment of structural safety of material and geometric nonlinear concrete structures. Further investigations are necessary in order to develop this probabilistic finite element approach into a mature structural safety assessment method.

  Abstract
  This is the second part of an investigation on probabilistic finite element methods for nonlinear concrete structures. The study is concentrated on two reinforced concrete [...]

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• Probabilistic FEM for Nonlinear Concrete Structures. I: Theory

  J. Teigen, D. Frangopol, S. Sture, C. Felippa

  Journal of Structural Engineering (1991). Vol. 117 (9), pp. 2674

  
  

  Abstract

  This is the first part of an investigation on probabilistic finite element methods for nonlinear concrete structures under random loads. The formulation of a method that accounts for both randomness and nonlinearity in material and geometryis proposed. The method is an extension of nonlinear finite element techniques, where; (1) The new quantities required at the element level are the derivatives of the external and internal forces with respect to the basic random variables; (2) the loads are applied in increments until collapse; and (3) the equilibrium at each load level is achieved by using a modified Newton iteration scheme. In contrast to currently available methods the proposed formulation allows for Taylor series expansion of the response about arbitrary reference values of the basic random variables. Furthermore, the collapse load of the system associated with a given combination of reference values of the random variables becomes a result of theanalysis. A computer code called PFRAME is developed for the application of the proposed method to concrete frame structures exhibiting geometric and material nonlinear behavior.

  Abstract
  This is the first part of an investigation on probabilistic finite element methods for nonlinear concrete structures under random loads. The formulation of a method that accounts [...]

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• Mixed variational formulation of finite element analysis of acoustoelastic/slosh fluid-structure interaction

  C. Felippa, R. Ohayon

  Journal of Fluids and Structures (1990). Vol. 4 (1), pp. 35-57

  
  

  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. This principle contains a free parameter alpha. Semidiscrete finite-element equations of motion based on this principle are displayed and applied to the transient response and free-vibrations of the coupled fluid-structure problem. It is shown that a particular setting of alpha yields a rich set of formulations that can be customized to fit physical and computational requirements. The variational principle is then extended to handle slosh motions in a uniform gravity field, and used to derive semidiscrete equations of motion that account for such effects.

  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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• A variational justification of the assumed natural strain formulation of finite elements—I. Variational principles

  C. Militello, C. Felippa

  Computers and Structures (1990). Vol. 34 (3), pp. 431-438

  
  

  Abstract

  The assumed natural strain (ANS) formulation of finite elements has undergone rapid development over the past five years. The key formulation step is the replacement, in the potential energy principle, of selected displacement-related strains by independently assumed strain fields in element natural coordinates. These strains are not generally derivable from displacements. This procedure was conceived as one of several competing methods with which to solve the element locking problem. Its most noteworthy feature is that, unlike many forms of reduced integration, it produces no rank deficiency; furthermore, it is easily extendible to geometrically non-linear problems. Many original formulations were not based on a variational principle. The objective of Part I is to study the ANS formulation from a variational standpoint. This study is based on two hybrid extensions of the Reissner-type functional that uses strains and displacements as independent fields. One of the forms is a genuine variational principle that contains an independent boundary traction field, whereas the other one represents a restricted variational principle. Two procedures for element-level elimination of the strain field are discussed, and one of them is shown to be equivalent to the inclusion of incompatible displacement modes. In Part II [C. Militello and C. A. Felippa, Comput. Struct.34, 439–444 (1990)], the four-node C0 plate bending quadrilateral element is used to illustrate applications of this theory.

  Abstract
  The assumed natural strain (ANS) formulation of finite elements has undergone rapid development over the past five years. The key formulation step is the replacement, [...]

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

  J. Schuler, C. Felippa

  Finite Elements in Analysis and Desing (1990). Vol. 6 (4), pp. 321-339

  
  

  Abstract

  We derive electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as primary variable. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are: the number of degrees of freedom per node remains modest as the problem dimensionality increases, jump discontinuities on interfaces are naturally accomodated, and statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady-state forcing conditions. The results are in excellent agreement with analytical solutions.

  Abstract
  We derive electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as primary variable. This choice is used to construct [...]

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• The first ANDES elements: 9-dof plate bending triangles

  C. Militello, C. Felippa

  Computer Methods in Applied Mechanics and Engineering (1991). Vol. 93 (2), pp. 217-246

  
  

  Abstract

  New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element, whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this new formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as ‘gage reading’ points. These samples values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the discrete Kirchhoff triangle (DKT), whereas the third one products two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

  Abstract
  New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) [...]

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