Shape optimization for large deformations using B-splines.

Abstract

The shape of a Belleville washer ring is optimized with the purpose of tailoring its mechanical response. The optimization is carried out using structural shape optimization with regards to large deformations. In order to accurately model boundaries, B-splines are utilized as they are closely related to the de facto-standard used in most of todays CAD systems. Furthermore, the structural analysis is carried out using the finite element method, which is formulated to include nonlinear elasticity. The washer is optimized to best fit some force-displacement curve under a volume constraint. A formulation for how this optimization can be carried out is derived and then evaluated for some numerical examples. This formulation is shown to produce several examples of designs which are improved with regards to the objective. A method utilizing a manual change in topology is also evaluated, but no optimization with regards to the full topology of the washer ring is performed since topology changes using B-splines proves difficult. Instead a formulation for how a combined shape and full topology optimization could be carried out is presented but not implemented.

Popular Abstract

This thesis has considered the alteration of designs into optimal shape which have desired levels of stiffness at different levels of deflection. This allows the user of this scheme to tailor their designs to carry whatever load their application requires, whilst simultaneously facilitating the possibility of reducing the total amount of material used. To achieve this acombination of mathematical optimization and some classical methods for modelling material mechanics are combined in what is called shape optimization. The field of shape optimization is concerned with finding the best shape a structure can have for various purposes. An example of this could be the problem of finding the lightest possible airplane seat that is able to carry any passenger. With technological demands on products constantly increasing and with today's trends of sustainability shape optimization can help fill a slot by improving the design of products in whatever way is desired. These improvements are even further enabled by the fact that additive manufacturing methods are becoming increasingly sophisticated which enables to manufacturing of designs which are optimal in a mathematical sense, but that might not have been feasible before. In this thesis the optimization of bodies with rotational symmetry such as rings or discs, which are subject to large deformations are considered. The optimization does not handle topological changes such as adding holes as an optimization step, and will require further development if that is to be implemented. Nevertheless, the developed optimization scheme still produces an improved design in several test cases compared to the response of the original designs. The produced work adds to already existing work in the field, which
previously has generally been focused only on optimization for smaller deformations. In the end this is potentially not only valuable from an academic point of view, but the produced results could also have some practical benefits in that it could lead to implementations commercial software and it could help showcase the validity of shape optimization.

• author: Sjövall, Filip
• supervisor: Mathias Wallin
• organization: Department of Construction Sciences; Solid Mechanics
• course: FHLM01 20201
• year: 2020
• type: H3 - Professional qualifications (4 Years - )
• subject: Technology and Engineering
• keywords: Shape Optimization, B-splines, FEM, Nonlinear structures and materials, Axisymmetric elements
• publication/series: ISRN LUTFD2/TFHF-20/5236-SE(1-76)
• report number: TFHF-5236
• language: English
• id: 9023120
• date added to LUP: 2020-07-28 11:12:04
• date last changed: 2020-07-28 11:12:04