Structural shape optimisation is a field that has been studied since early on in the development of finite element methods. The sub-fields of shape and topology optimisation are continuously growing in industry and aim to leverage the benefits of technologies such as 3D printing and additive manufacturing. These fields are also being used to optimise designs to improve quality and reduce cost. Gradient-based optimisation is well understood as an efficient method of obtaining solutions. In order to implement gradient-based optimisation methods in the context of structural shape optimisation, sensitivities describing the change of the domain stiffness are required. To obtain the stiffness sensitivities, mesh deformation sensitivities are required. In this study, a mesh generating method is developed that provides mesh deformation sensitivities. For shape optimisation it is advantageous to employ an optimisation algorithm that allows for the manipulation of CAD geometry. This means that the CAD geometry is finalised upon completion of the optimisation process. This, however, necessitates the calculation of accurate sensitivities associated with non-linear geometries, such as NURBS (those present in CAD), by the mesher. The meshing method developed in this study is analogous to a linear truss system. The system is solved for static equilibrium through a geometrically non-linear finite element analysis using Newton’s method. Sensitivities are made available by Newton’s method for use in generating mesh sensitivities for the system. It is important for the mesher to be able to accurately describe the geometrical domain which approximates the geometry being modelled. To do so, nodes on the boundary may not depart from the boundary. Instead of prescribing all boundary nodes, this mesher frees the boundary nodes to move University of Pretoria ii Department of Mechanical and Aeronautical Engineering along, but not away from the boundary. This is achieved using multipoint constraints since they allow for an analytical relationship between boundary node movement and the boundary. Two multipoint constraint (MPC) methods are investigated for boundary discretisation, namely, the Lagrangian and master-slave elimination methods (MSEM). The MSEM presents several difficulties in obtaining convergence on non-linear boundaries in general when compared to the Lagrangian method. The MSEM has reduced computational requirements for a single Newton step, especially when direct solvers are used. However, when indirect solvers are implemented the time difference between the two MPC methods reduces significantly. For a “medium” curvature geometry the Lagrangian implementation has only a 6% time penalty. The Lagrangian method is selected as the preferred MPC method for implementation in the mesher to avoid the convergence problems associated with the MSEM. This is justified on the basis of reliability outweighing the 6% time penalty for what is intended to be a tool in the shape optimisation process. Analytical sensitivities are obtained for the truss system in order to account for the MPC boundaries. The analytical mesh sensitivities are proven to be accurate through comparison with numerical sensitivities. The method is demonstrated to be able to accurately described the mesh deformation throughout the domain for both uniform and non-uniform meshes in the presence of non-linear boundaries. / Dissertation (MEng)--University of Pretoria, 2020. / Mechanical and Aeronautical Engineering / MEng (Mech) / Unrestricted

This study proposes novel optimization methodologies for the optimization of problems that reveal non-physical step discontinuities. More specifically, it is proposed to use gradient-only techniques that do not use any zeroth order information at all for step discontinuous problems. A step discontinuous problem of note is the shape optimization problem in the presence of remeshing strategies, since changes in mesh topologies may - and normally do - introduce non-physical step discontinuities. These discontinuities may in turn manifest themselves as non-physical local minima in which optimization algorithms may become trapped. Conventional optimization approaches for step discontinuous problems include evolutionary strategies, and design of experiment (DoE) techniques. These conventional approaches typically rely on the exclusive use of zeroth order information to overcome the discontinuities, but are characterized by two important shortcomings: Firstly, the computational demands of zero order methods may be very high, since many function values are in general required. Secondly, the use of zero order information only does not necessarily guarantee that the algorithms will not terminate in highly unfit local minima. In contrast, the methodologies proposed herein use only first order information, rather than only zeroth order information. The motivation for this approach is that associated gradient information in the presence of remeshing remains accurately and uniquely computable, notwithstanding the presence of discontinuities. From a computational effort point of view, a gradient-only approach is of course comparable to conventional gradient based techniques. In addition, the step discontinuities do not manifest themselves as local minima. / Thesis (PhD)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

This Master's thesis deals with the detailed design of the supporting structure of the bridge with two sections, with the rise in the direction of the intermediate support, and cross-cut single-beam construction. The supporting structure is designed from the prestressed concrete, prestressing losses are accurately quantified. It also deals with the assessment of pillar base threshold and pilot groups. The assessment was carried out according to the limit states.