shape2d

Purpose

shape functions for 4-9 node quadrilateral element

Synopsis

[N,dNdx,J] = shape2d (nat,xyz,nodix)

Description

SHAPE2D shape functions for 4-9 node quadrilateral element
  [N,dNdx,J] = SHAPE2D (NAT,XYZ,NODIX) shape functions for 4-9 node quadrilateral element

  Input Parameters
  ----------------
  nat   = [ xi eta ] natural coordinates of point of interest
  xyz   = nodal coordinates for element (row i for node i)
  nodix = node index, e.g. [1:4 7 8] if nodes 1 through 4 (always), 7 and 8 are present 
  ----------------
  Return Variables
  ----------------
  N     = shape function values for point of interest
  dNdx  = dNdx(i,j) = derivative of shape function j with respect to geometric coordinate x_i
  J     = Jacobian of transformation from geometric to natural coordinates

  Reference: T.J.R. Hughes, The Finite Element Method, pp. 135

Cross-Reference Information

This function calls:

• Inel4nodeMindlinReShellwITC isoparametric inelastic 4 node quad Mindlin RC layer shell element with ITC
• Inel4nodeMindlinShellwITC isoparametric inelastic 4 node quad Mindlin layer shell element with ITC
• Inel4to9nodeMindlinReShell inelastic isoparametric 4-9 node quad Mindlin element with reinforcing layers
• Inel4to9nodeMindlinShell isoparametric 4-9 node quad layer shell element with inelastic material
• Inel4to9nodeQuad isoparametric 4-9 node quadrilateral element with inelastic material
• Inel4to9nodeReQuad isoparametric 4-9 node quad element with inelastic material and reinforcing layers
• LE4nodeMindlinPlate linear elastic isoparametric 4-node quadrilateral Mindlin plate element
• LE4nodeMindlinPlatewITC linear elastic isoparametric 4-node quadrilateral Mindlin plate element with ITC
• LE4nodeMindlinShellwITC linear elastic isoparametric 4-node quadrilateral Mindlin shell element with ITC
• LE4nodeQuad isoparametric 4-node quadrilateral element with linear elastic material
• LE4nodeQuadwIM isoparametric 4-node quad element with linear elastic material and incompatible bending modes
• LE4to9nodeMindlinPlate linear elastic isoparametric 4-9 node quadrilateral Mindlin plate element
• LE4to9nodeMindlinShell linear elastic isoparametric 4-9 node quadrilateral Mindlin shell element
• LE4to9nodeQuad isoparametric 4-9 node quadrilateral element with linear elastic material
• LE9nodeQuad isoparametric 9 node quadrilateral element with linear elastic material
• shapeBhat shape function Bhat