Back to FAQ
1096x
002339
2017-12-01

Different Quadrature Methods for Elastic and Nonlinear Calculations in Structural Models

Which shape functions are used by RFEM 5 for 1.) solid elements and 2.) shell elements? Are they linear or quadratic shape functions?

Answer:

Generally, identical bilinear approach functions with 2, 3, or 4 boundary nodes are to be used, depending on which element you prefer, but there are differences in the quadrature. The differences in the quadrature are as follows:

Elastic Calculation

  • Truss member: analytically 2 nodes 3 degrees of freedom
  • Beam: analytically 2 nodes 6 degrees of freedom
  • Surface (plate): analytically (LYNN-DHILLON-Element)
  • Surface (wall): Quadrangular Gauss quadrature 2x2, triangular selective quadrature (epsilon_x; epsilon_y; gamma_xy)
  • Solid: Gauss quadrature 2x2

Nonlinear calculation (for example, plasticity, and so on):

  • Beam:
    • 2-point Gauss quadrature in the longitudinal direction of the member
    • across the cross-section Gauss quadrature 2x2
  • Surface (plate):
    • in the element surface: quadrangular Gauss quadrature 2x2 , triangular 3-point Gauss quadrature
    • per thickness 9-point Gauss-Lobatto quadrature
  • Wall: quadrangular Gauss quadrature 2x2 , triangular 3-point Gauss quadrature
  • Solid: 14-point reduced Gauss quadrature (equivalent to the 3x3x3 Gauss quadrature)
FE Elements
FE Elements
;