Topology optimization with structural elements for the design of steel structures

Cuevas Carvajal, Nicolas | 2024

Structural profiles are widely used in structural design, including in aerospace, automotive, and civil engineering structures. Their extensive use owes to the standardization of dimensions and mechanical properties, making them readily available, practical, reliable, and easy to economically assemble. While archetypal frame designs are commonly used and well understood (particularly in civil engineering applications), there are problems for which existing solutions cannot be applied (for instance, when the design region has a non-cuboid shape, as in space frames or vehicle chassis); or where they may work but are suboptimal and therefore undesired (for example, in aircraft structures, where unnecessary weight leads to high fuel costs). In these situations, it is desired to employ efficient computational techniques to design optimal frames. This thesis formulates a topology optimization method based on the geometry projection technique for the design of frames made of structural profiles. Conventional density-based and level-set methods cannot be used for this purpose, as they render organic designs that cannot be easily realized with structural shapes. Geometry projection methods can produce designs exclusively made of primitives like bars; however, they cannot be used to design frames made of structural shapes, because the cross-sections of these shapes have small dimensions that must be captured by the analysis model, which requires a considerable fine mesh and consequently leads to an impractical computational cost. To address these shortcomings, an equivalent-section approach is formulated that represents the cross-section of the structural profiles as a homogeneous rectangular section. The accuracy of this approach is demonstrated by comparison to analyses performed using body-fitted meshes of the original sections for different loads and boundary conditions. A novel geometric representation is also introduced to represent the equivalent section as a cuboid. Like offset solids, this representation is endowed with an explicit expression for the computation of the signed distance to the boundary of the primitive and of its sensitivities, allowing for an efficient implementation. An overlap constraint is imposed via the formulation of auxiliary primitives associated to the structural members, which guarantees the resulting designs do not exhibit impractical intersections of primitives that would preclude their construction. The efficacy and efficiency of the method is demonstrated via 2D and 3D design examples. The examples demonstrate that the proposed method renders optimal designs and exhibits good convergence. They also illustrate the ability to design structures with far lower optimal volume fractions than those typically employed in continuum topology optimization techniques.