An economical assumed stress brick element and its implementation

In this paper, a highly economical 8-node brick element consolidated from the previous work on admissible matrix formulation and selective scaling is discussed. The element is modified from the Pian-Tong element in a way that the latter's good bending response, applicability in nearly incompressible materials and insusceptibility to mesh distortion are retained. Moreover, the selective scaling technique is incorporated such that the element can also be used thin plate/shell analysis. Focus is on systematic and economical construction of the element stiffness matrix. Using the present implementation which employs numerical integration, it is found that the element is less costly than the 8-node displacement element. CPU time comparisons, benchmark problems and FORTRAN-subroutines are presented.

[1]  K. Y. Sze,et al.  An explicit hybrid-stabilized 9-node Lagrangian shell element , 1994 .

[2]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[3]  Robert L. Taylor,et al.  Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems☆ , 1993 .

[4]  E. Hinton,et al.  A new nine node degenerated shell element with enhanced membrane and shear interpolation , 1986 .

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

[6]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[7]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[8]  Ekkehard Ramm,et al.  On alternative hybrid stress 2d and 3d elements , 1994 .

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

[10]  Amin Ghali,et al.  Hybrid hexahedral element for solids, plates, shells and beams by selective scaling , 1993 .

[11]  Eduardo N. Dvorkin,et al.  A 3D element for non-linear analysis of solids , 1994 .

[12]  Amin Ghali,et al.  A TWO‐FIELD SOLID ELEMENT SUITING THIN‐MESH ANALYSIS BY ADMISSIBLE MATRIX FORMULATION , 1992 .

[13]  Theodore H. H. Pian,et al.  Finite elements based on consistently assumed stresses and displacements , 1985 .

[14]  K. Y. Sze,et al.  Finite element formulation by parametrized hybrid variational principles: Variable stiffness and removal of locking , 1994 .

[15]  William E. Bachrach,et al.  An efficient formulation of hexahedral elements with high accuracy for bending and incompressibility , 1987 .

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

[17]  L. Morley.  Skew plates and structures , 1963 .

[18]  K. Y. Sze,et al.  Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolants and admissible matrix formulation , 1992 .