The geometric stiffness matrix Kg is added to the system stiffness matrix K, and thus the modified stiffness matrix Kmod is obtained:

To check the influence of the changed material properties on the stiffness matrix, I would like to know how the fields of the stiffness matrix are calculated.

Thereafter, a stiffness matrix for each component of the manipulator can be determined, and a global stiffness matrix for the total manipulator can be determined in order to determine at least one property of the selected axis.

Rigidity index computing means (8) computes the value of the rigidity index U* from the partial rigidity matrix KAC and the displacement value of the basic data.

Here also, the geometric stiffness matrix must be considered.

Compression forces reduce the stiffness and can lead to a singularity in the stiffness matrix.

Bending stiffness can be deducted directly from the stiffness matrix of the surface (see Figure 3).

The geometric stiffness matrix Kg can be derived from the static equilibrium conditions:

Figure 08 - Equivalent loads for Mode Shape 1 (a) without stiffness modifications from DLC1 and (b) with geometric stiffness matrix from DLC2

The spectrum of the stiffness matrix has a great influence on the duration of calculation.

The results with and without the geometric stiffness matrix are displayed in Figure 10.

The stiffness matrix of the orthotropic plate is symmetrical and only applied to the main diagonals.

The consideration of the geometric stiffness matrix leads to larger deformations and internal forces.

The determined equivalent loads, with and without the geometric stiffness matrix, are displayed in Figure 08.

It is also necessary to select an orthotropic material model for the material, otherwise the stiffness material is defined singularly.