Geometric stiffness matrix for a beam element
Geometric stiffness matrix for a beam element
(OP)
Hello all!
Can anyone tell me where I can find the geometric stiffness matrix for a 12-dof beam element.
ps. I allready posted this question last week, but it somehow disappeared ....
Can anyone tell me where I can find the geometric stiffness matrix for a 12-dof beam element.
ps. I allready posted this question last week, but it somehow disappeared ....





RE: Geometric stiffness matrix for a beam element
I believe that the matrix is also laid out in the COSMIC NASTRAN Theoretical Manual, although I don't have my copy at hand.
If you still need more info, let me know.
Bob
RE: Geometric stiffness matrix for a beam element
I'll try to derive it. If I think of it quickly, I would just place the same terms (as in the 4 dof element) for the rest of the four dofs. This would give me the needed 8 dofs. The rest of the dofs would be zero (axial and the torsion terms). I hope this isn't a problem in the buckling analysis, where it needs to be positive definite. I guess the standard stiffness matrix have to be suppressed before the buckling analysis.
Regards
Kim
RE: Geometric stiffness matrix for a beam element
framel3d - Compute three-dimensional, frame-element, local stiffness matrix as defined in V. James Meyers, Matrix Analysis of Structures, 1983, p. 409.
double E,area,Iy,Iz,J,G,k[12][12];
int i,j;
/* Compute member local stiffness matrix. (Meyers, p. 409, Eq. 8.18.) */
k[ 1][ 1] = E*area/L;
k[ 1][ 7] = -k[1][1];
k[ 2][ 2] = 12.0*E*Iz/(L*L*L);
k[ 2][ 6] = 6.0*E*Iz/(L*L);
k[ 2][ 8] = -k[2][2];
k[ 2][12] = k[2][6];
k[ 3][ 3] = 12.0*E*Iy/(L*L*L);
k[ 3][ 5] = -6.0*E*Iy/(L*L);
k[ 3][ 9] = -k[3][3];
k[ 3][11] = k[3][5];
k[ 4][ 4] = G*J/L;
k[ 4][10] = -k[4][4];
k[ 5][ 5] = 4.0*E*Iy/L;
k[ 5][ 9] = 6.0*E*Iy/(L*L);
k[ 5][11] = 2.0*E*Iy/L;
k[ 6][ 6] = 4.0*E*Iz/L;
k[ 6][ 8] = -6.0*E*Iz/(L*L);
k[ 6][12] = 2.0*E*Iz/L;
k[ 7][ 7] = k[1][1];
k[ 8][ 8] = k[2][2];
k[ 8][12] = -k[2][6];
k[ 9][ 9] = k[3][3];
k[ 9][11] = k[5][9];
k[10][10] = k[4][4];
k[11][11] = k[5][5];
k[12][12] = k[6][6];
/* Fill in lower part of symmetric member local stiffness matrix. */
for(i=2;i<=12;i++)
for(j=1;j<ii;j++)
k[i][j] = k[j][i];
Good luck.
RE: Geometric stiffness matrix for a beam element
RE: Geometric stiffness matrix for a beam element
Matrix Structural Analysis By William Weaver and James Gere
Second Edition page 182