This master thesis is devoted to developing methods for decreasing the total solution time
of linear buckling analyses, with a large number of load combinations. Four methods
for decreasing the total solution time is presented, along with performance studies of the
methods, highlighting the methods pros and cons along with limitations.
The thesis starts by giving an introduction to the method that is presently used for performing
linear buckling analyses of structures with a high amount of load combinations.
The introduction includes a flowchart of the solution procedure when calculating the buckling
loads by the finite element method. After the presentation of the solution procedure,
initial studies are conducted to determine the time consumption of some of the steps in
the solution procedure. These studies are conducted in order to determine which steps in
the solution procedure has the best potential for decreasing the solution time.
Based on the initial studies, methods for decreasing the total solution time are proposed.
The possible methods are shortly explained, to give an understanding of the main idea in
each proposed method. Next the methods for further study are selected, based on their
potential to decrease the solution time and if it is possible to implement the method in a
stand alone program, or as add-on to existing commercial software. After the selection of
methods, the geometry, used in the performance studies is presented, and the modeling
of the structure is described.
Theory governing the linear buckling is given. The distinction between bifurcation
buckling and limit point buckling is outlined, and the stability criterion is derived from
the total potential energy of a system. Furthermore, the calculation of buckling loads by
the finite element method is explained. Ending the theory chapter is a presentation of the
limitations concerning the linear buckling analysis.
The solution methods chosen earlier is presented, and explained further. The solution
procedure of each method is explained in a flowchart and the theory governing the features
used in the method is explained. The performance studies is explained and the results
are commented and evaluated. One solution method reduces the total solution time up
to 78%, according to the presently used method. Another solution method reduces the
number of load combinations by 74%.