By Bastian Kuhn, Dlubal Engineering Software

With the add-on modules RF-STABILITY and RF-IMP you can evaluate the overall stability of a structural system. The evaluation is based on a determination of critical load factors and stability modes. To receive sufficiently accurate results, it is necessary for members to relate the division to the FE mesh length. This division is describing the points where the critical axial force will be calculated.

RF-STABILITY always calculates the critical load factor as unknown value:

([K] + lambda Krit x [KG]) x {U} = 0 -> lambda Krit

– K = stiffness matrix

– lambda Krit = eigenvalue (critical load factor)

– [KG] = geometric stiffness matrix

– {U} = eigenmode (as vector)

With the option “Non Linear Analysis” in RF-STABILITY the geometric stiffness matrix KG in the equation above is calculated due to III. Order Theorie. The term KG is replaced in this case.

Summary:

– In the non linear calculation in contrast to the linear calculation of the own value the load is increased step by step.

– On a certain load the system gets instable. In this case the buckling load factor is found.

– In order to define the own value it is done a linear own value analysis with the static system that was given in the time of the instability.

– Advantage: All non linear elements oft he structure are regarded in the calculation of the own value.

– Disadvantage: With this method only the lowest own value can be calculated precisely.

Work Flow RF-STABILITY -> RF-IMP:

– Define a load case.

– Find the correct failure form in RF-STABILITY and set it.

– Define the buckling form in RF-IMP and get the pre-deformed structure from this form.

– Calaculate the ordinate of the pre-deformation due to the norm.

– Define a new LG and overtake the imperfect structure from RF-IMP here.

– Receive bending moments also in a linear calculation due to I. Order Theorie.

– Design of stability in another RF-STABILITY case.