Designing modular 3D printed reinforcement of wound composite hollow beams with semidefinite programming

Abstract

Fueled by their excellent stiffness-to-weight ratio and the availability of mature manufacturing technologies, filament wound carbon fiber reinforced polymers represent ideal materials for thin-walled laminate structures. However, their strong anisotropy reduces structural resistance to wall instabilities under shear and buckling. Increasing laminate thickness degrades weight and structural efficiencies and the application of a dense internal core is often uneconomical and labor-intensive. In this contribution, we introduce a convex linear semidefinite programming formulation for truss topology optimization to design an efficient non-uniform lattice-like internal structure. The internal structure not only reduces the effect of wall instabilities, mirrored in the increase of the fundamental free-vibration eigenfrequency, but also keeps weight low, secures manufacturability using conventional three-dimensional printers, and withstands the loads induced during the production process. We showcase a fully-automatic procedure in detail for the design, prototype manufacturing, and verification of a simply-supported composite machine tool component, including validation with roving hammer tests. The results confirm that the 3D-printed optimized internal structure almost doubles the fundamental free-vibration eigenfrequency, allowing to increase working frequency of the machine tool, even though the ratio between elastic properties of the carbon composite and the ABS polymer used for 3D printing exceeds two orders of magnitude.

Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy

“…Second, the computational demands could be decreased by exploiting the structural sparsity via clique-based chordal decomposition in the spirit of (Kim et al, 2010;Kočvara, 2020). Another research directions may explore eigenvalue constraints and optimization (Achtziger and Kočvara, 2008;Tyburec et al, 2019), the minimum-weight setting, or, eventually, investigate performance of the hierarchy for different topology optimization formulations.…”

“…This latter formulation handles multiple load cases with stress constraints efficiently (Tyburec et al, forthcoming). Convexity prevails even for fundamental free-vibration constraints, in which case semidefinite programming can be used (Achtziger and Kočvara, 2008;Tyburec et al, 2019).…”

Mechanical Vibration Damping and Compression Properties of a Lattice Structure

“…In this study, the frequency response predictions of a finite element-based model of the gyroid sandwich structure were first validated in terms of its natural frequencies and mode shapes, while the effects of plate and gyroid wall thickness on dynamic properties were investigated. Tyburec [ 21 ] examined a convex linear semidefinite programming formulation for truss topology optimization to design an efficient non-uniform lattice as an internal structure. The internal structure not only reduces the effect of wall instabilities, reflected in the increase of fundamental natural frequency of free-vibration, but also keeps the weight low, ensures the manufacturability with conventional three-dimensional printers, and withstands the stresses during the production process.…”

Research of the Problem of Loss of Stability of Cylindrical Thinwalled Structures Under Intense Local Temperature Exposure

“…Presently, three-dimensional printing technology is developing rapidly (You et al, 2017;Jacobs and Lin, 2017;Park et al, 2017;Smith et al, 2018;Tyburec et al, 2019). This happens due to the need to create products of complex shape, the production of which by existing standard methods is very laborious and disadvantageous, and sometimes technically impossible (Kinash et al, 2017;Boitsov et al, 2018;Du et al, 2018).…”