Mechanics of field-consistency in finite element analysis—a penalty function approach

Although C' continuous beam, plate and shell elements have13; become very popular, a simple understanding of several13; diffcultie such as shear locking, parasitic shear, stress13; oscillations etc. is not yet available in the literature. In displasement type finite element formulations, these difficulties can be easily rationaliscd using 'field-consistency' concepts and of these difficulties can quantitative error estimates also be made using an operational procedure called the 'functional re- constitution' technique. In this paper we demonstrate the mechanics of these concepts using the simplest shear: flexible beam element ( linear Timoshenko beam element) as13; exilayle, and verily its apriori projections through digital computations. The rationale behind the use of optimal stress sampliing at Gaussian points is also derived directly from these argurnents.

[1]  Ray W. Clough,et al.  Improved numerical integration of thick shell finite elements , 1971 .

[2]  Bruce M. Irons,et al.  An 8‐node brick finite element , 1984 .

[3]  Gangan Prathap,et al.  Field-consistent strain interpolations for the quadratic shear flexible beam element , 1986 .

[4]  Gangan Prathap,et al.  A field consistent three‐noded quadratic curved axisymmetric shell element , 1986 .

[5]  Gangan Prathap,et al.  A field-consistent two-noded axisymmetric shell element , 1985 .

[6]  Gangan Prathap,et al.  An additional stiffness parameter measure of error of the second kind in the finite element method , 1985 .

[7]  Gangan Prathap,et al.  The curved beam/deep arch/finite ring element revisited , 1985 .

[8]  Theodore H. H. Pian,et al.  Improvement of Plate and Shell Finite Elements by Mixed Formulations , 1977 .

[9]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[10]  John S. Campbell,et al.  Local and global smoothing of discontinuous finite element functions using a least squares method , 1974 .

[11]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[12]  Accuracy and locking-free property of the beam element approximation for arch problems , 1984 .

[13]  G. A. Mohr.  Application of penalty functions to a curved isoparametric axisymmetric thick shell element , 1982 .

[14]  Gangan Prathap,et al.  The poor bending response of the four‐node plane stress quadrilateral , 1985 .

[15]  Gangan Prathap,et al.  An optimally integrated four‐node quadrilateral plate bending element , 1983 .

[16]  E. Hinton,et al.  A study of quadrilateral plate bending elements with ‘reduced’ integration , 1978 .

[17]  Robert L. Spilker,et al.  The hybrid‐stress model for thin plates , 1980 .

[18]  J. Barlow,et al.  Optimal stress locations in finite element models , 1976 .

[19]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[20]  Ahmed K. Noor,et al.  Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams , 1981 .

[21]  Gangan Prathap,et al.  An isoparametric quadratic thick curved beam element , 1986 .

[22]  Ahmed K. Noor,et al.  Mixed isoparametric finite element models of laminated composite shells , 1977 .

[23]  Gangan Prathap,et al.  Reduced integration and the shear-flexible beam element , 1982 .