Methods for Decreasing the Total Solution Time of Linear Buckling Finite Element Analyses

Larsen, Kasper Skindhøj ; Frank, Allan Leth

4. term

Design of Mechanical Systems, Master

2012

2012-06-01

75 pages

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%.

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