MIXED STRAIN ELEMENTS FOR NON‐LINEAR ANALYSIS

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

[1]  Ted Belytschko,et al.  On flexurally superconvergent four-node quadrilaterals , 1987 .

[2]  T. Pian,et al.  On the suppression of zero energy deformation modes , 1983 .

[3]  Chen Wanji,et al.  Isoparametric hybrid hexahedral elements for three dimensional stress analysis , 1988 .

[4]  T. Pian,et al.  A rational approach for choosing stress terms for hybrid finite element formulations , 1988 .

[5]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .

[6]  Hai-chʿang Hu,et al.  Variational Principles of Theory of Elasticity with Applications , 1984 .

[7]  J. Z. Zhu,et al.  The finite element method , 1977 .

[8]  K. Bathe,et al.  Large displacement analysis of three‐dimensional beam structures , 1979 .

[9]  David R. Owen,et al.  Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells , 1983 .

[10]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .

[11]  Theodore H. H. Pian,et al.  Relations between incompatible displacement model and hybrid stress model , 1986 .

[12]  J. C. Simo,et al.  A return mapping algorithm for plane stress elastoplasticity , 1986 .

[13]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[14]  Y. K. Cheung,et al.  A new approach for the hybrid element method , 1987 .

[15]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

[16]  T. Belytschko,et al.  Efficient implementation of quadrilaterals with high coarse-mesh accuracy , 1986 .

[17]  M. Géradin,et al.  A beam finite element non‐linear theory with finite rotations , 1988 .

[18]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[19]  T. Pian.  Derivation of element stiffness matrices by assumed stress distributions , 1964 .

[20]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[21]  Ted Belytschko,et al.  Nonlinear versions of flexurally superconvergent elements , 1988 .

[22]  T. Pian,et al.  Rational approach for assumed stress finite elements , 1984 .

[23]  K. Sze,et al.  A rational formulation of isoparametric hybrid stress elements for three-dimensional stress analysis , 1990 .

[24]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .