Full Article - Open Access.

Idioma principal


Gallegos, S.; Lecona, S.;

Full Article:

Beam elements are some of the most used finite elements in structural analysis. Formulations for these types of elements date from the first years of finite element applications; however, there are still some interesting details to be found in their formulations. In our search for accuracy and computational efficiency, different approaches have been taken to formulate them. Cubic Hermite polynomials were used with potential energy to produce the first beam elements, however, it was difficult to formulate plate and shell elements compatible with them. Compatible two noded elements with linear interpolations were devised but they tend to lock in shear forcing us to under integrate the shear stiffness, and still they were not as accurate. In our quest for accuracy other types of variational principles have been used, mainly the Hellinger-Reissner and the Hu-Washizu principles. Hellinger-Reissner beam elements are accurate and efficient but have difficulties when non linear strain driven constitutive relationships are needed to model the material behavior. Hu-Washizu type elements, on the other hand, have no such problem and are therefore excellent candidates for these formulations, but it is difficult to devise adequate stress, strain and displacement interpolations that offer the same accuracy and efficiency. Different alternatives are used to improve the response of the base linear element; two of them are linked interpolations and bubble functions. In this work it is shown how linked interpolations can be used to avoid the shear locking problem, and bubble functions can be used to generate equivalent strain interpolations that improve the accuracy by using a Hu-Washizu type formulation. The resulting element is as efficient and accurate as a Hellinger-Reissner one but has no problem handling strain driven constitutive relationships for the material.

Full Article:

Palavras-chave: Hu-Washizu Principle, linked interpolations, bubble functions, beam elements,


DOI: 10.5151/meceng-wccm2012-19749

Referências bibliográficas
  • [1] K.D. Hjelmstad and E. Taciroglu , “Mixed methods and flexibility approaches for nonlinear frame analysis”, Journal of structural steel research 58, 967-993, 2002.
  • [2] Ciampi V. and Carlesimo L., “A nonlinear beam element for seismic analysis of structures”, Proc. European Conference on Earthquake Engineering, Lisbon, Portugal, 73-80, 1986.
  • [3] Spacone E., Ciampi V. and Fillipou F.C., “Mixed formulation of nonlinear beam finite element”, Computers Andamp; Structures, 1, 71-83, 1996.
  • [4] Ayoub A.S. and Fillipou F.C., “Mixed formulation of nonlinear steel-concrete composite beam element”, J. of Structural Engineering, 126(3), 371-381, 2000.
  • [5] Taylor R.L., Fillipou F.C. Saritas A. and Auricchio F., “A mixed finite element method for beam and frame problems”, Computational Mechanics, 31, 192-203, 2003.
  • [6] Kasper E.P. and Taylor R.L., “A mixed enhanced strain method, Part I: Geometrically linear problems”, Computers Andamp; Structures, 75, 237-250, 2000.
  • [7] Zienkiewicz O.C., Xu, Zeng, Samuelsson, Wiberg., “Linked Interpolation for Reissner-Mindlin plate elements: Part I- A simple quadrilateral”, International Journal For Numerical Methods In Engineering, 36, 3043-3056, 1993.
  • [8] Gallegos S., “Análisis de sólidos y estructural mediante el método de elementos finitos”, Limusa, México, 200
Como citar:

Gallegos, S.; Lecona, S.; "A MIXED BEAM ELEMENT COMBINING LINKED AND BUBBLE INTERPOLATIONS", p. 4147-4162 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19749

últimos 30 dias | último ano | desde a publicação