GPYS

Purpose

function value, gradient and Hessian of polynomial yield surface

Synopsis

[f,g,h] = GPYS (GPYSC,xyz,ScVec)

Description

GPYS function value, gradient and Hessian of polynomial yield surface    
  [F,G,H] = GPYS (GPYSC,XYZ,SCVEC)
  the function determines the value F(X,Y,Z), the gradient G(X,Y,Z), and
  the Hessian matrix (2nd derivative) H(X,Y,Z) of F at a point XYZ
  for a general polynomial yield surface with coefficients GPYSC
  SCVEC is a scale vector for the variables X, Y, and Z
   G = the gradient (normal)   of the yield surface = [dF/dX; dF/dY; dF/dZ]
   H = the Hessian (2nd deriv) of the yield surface = dG/dXYZ
     = [d2(F)/d(X)^2    d2(F)/d(X)d(Y) d2(F)/d(X)d(Z);
        d2(F)/d(Y)d(X)  d2(F)/d(Y)^2   d2(F)/d(Y)d(Z);
        d2(F)/d(Z)d(X)  d2(F)/d(Z)d(Y) d2(F)/d(Z)^2]

  The coefficients of the polynomial yield surface are specified as follows
  general 3d case
           GPYSC = [d1 a1 b1 c1; d2 a2 b2 c2; d3 a3 b3 c3; ...]
          for  F = Sum_i (di*(X^ai)*(Y^bi)*(Z^ci))
  general 2d case
           GPYSC = [c1 a1 b1; c2 a2 b2; c3 a3 b3; ...]
       for     F = Sum_i (ci*(X^ai)*(Y^bi))

Cross-Reference Information

This function calls:

• BInel2dFrm_wEPLHNMYS 2d elasto-plastic, linear hardening basic frame element