Topology Optimisation Including Buckling Analysis

Topology Optimisation Including Buckling Analysis

Van den Boom, S.J.

Langelaar, M. (mentor)
Van Keulen, A. (mentor)

Mechanical, Maritime and Materials Engineering

Precision and Microsystem

Engineering Mechanics

2014-12-19

Buckling is a failure mode of a structure caused by stiffness loss of compressed material. It arises primarily in slender structures, for which the bending stiffness is much lower than the axial stiffness. Slender, buckling sensitive structures occur especially in optimised designs, where an excellent strength-to-weight ratio is required. For this reason, buckling analysis of optimised designs is very important. However, buckling analysis is nowadays only performed in the post-processing phase, after the optimisation is completed. Inclusion of a buckling constraint in topology optimisation should lead to a design where failure by buckling is already excluded. In the following post-processing step, no major changes are needed on account of a buckling requirement, therefore allowing the final design to remain close to the optimal design. Ultimately this should lead to improved results. In literature, linear buckling analysis is included in topology optimisation on a couple of instances, albeit mostly in the role of an objective instead of as a constraint. In this report, an adjoint formulation for the sensitivities of the buckling load is found, resulting in much more efficient computation than other methods, such as finite differences. Furthermore, different practical aspects of inclusion of a buckling constraint are explored, with emphasis on the underlying physical problem. It is found that including a buckling constraint requires careful implementation, tailored to the specific optimisation problem at hand. An educated choice should be made on the admissibility of negative buckling loads. Allowing negative buckling loads leads to a non-convex design space, complicating the search for the globally optimal design. Furthermore, the switching of modes should be considered. While mode switching can introduce a number of issues, preventing this switching limits the design freedom the optimiser has to reach an optimal design. Even more importantly, the point is raised that a linear buckling analysis does not give any information on the post-buckling behaviour of the structure. The stability of the buckling load greatly influences the sensitivity of the structure to imperfections. For practical implementations, an optimal design that is extremely sensitive to imperfections is worthless. Therefore, ideally, an assessment is done on the stability of the structure, during optimisation, in order to enforce stable post buckling behaviour. However, current techniques for post-buckling analysis are elaborate and time-consuming in implementation and use. A method for rapid determination of the stability is required. Such a method for rapid estimation of the buckling load is found in the use of linear buckling analysis for structures that are perturbed with the mode shape of the perfect structure. This method is tested on very simple test structures and is found to be very promising for implementation in topology optimisation, because for a large part it can re-use code that is already available in the original formulation.

topology optimization
buckling

http://resolver.tudelft.nl/uuid:a869dbe4-0280-4443-afb7-a3a386e3824b

Student theses

master thesis

(c) 2014 Van den Boom, S.J.