Topology optimization for microstructural design under stress constraints

Abstract

This work aims at introducing stress responses within a topology optimization framework applied to the design of periodic microstructures. The emergence of novel additive manufacturing techniques fosters research towards new approaches to tailor materials properties. This paper derives a formulation to prevent the occurrence of high stress concentrations, often present in optimized microstructures. Applying macroscopic test strain fields to the material, microstructural layouts, reducing the stress level while exhibiting the best overall stiffness properties, are sought for. Equivalent stiffness properties of the designed material are predicted by numerical homogenization and considering a metallic base material for the microstructure, it is assumed that the classical Von Mises stress criterion remains valid to predict the material elastic allowable stress at the microscale. Stress constraints with arbitrary bounds are considered, assuming that a sizing optimization step could be applied to match the actual stress limits un

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…Within the aforementioned exciting framework, recently published works include modelling methods for designing hierarchical structures employing non-uniform topologically optimised lattices [504], serving as enhanced energy absorbers in sandwich sheets [505] or facilitating manufacturing [506], even with new methods for mitigating non-smooth surfaces, as the Bézier Skeleton Explicit Density (BSED) Representation Algorithm [507]. The microstructural design for avoiding stress peaks has also been recently addressed [508], as uncertainty-resilient design for inter-diffusion interface issues has been brought forward [509], and advances in buckling of microstructures were published by Bluhm et al [510].…”

A Review of Research on Seismic Metamaterials

“…It was then shown with an original application: tailoring metamaterials for a museum antiseismic stand. [71]…”

“…As can be seen from the existing elastic metamaterials, some of the research is focused on low‐frequency regulation, some is focused on wide‐band range regulation, and some work considers implementing wide low‐frequency bandgaps simultaneously. Since there have been several good review articles on elastic metamaterials, we do not expect comprehensive coverage of elastic metamaterials with wide low‐frequency bandgaps but focus on introducing some novel wide low‐frequency bandgap realization techniques. These techniques have received little attention in SMs and some of them have not even been considered, so it is useful to review them.…”

“…Collet et al introduced stress responses within a topology optimization framework applied to the design of periodic microstructures and validated the developed method with classical academic benchmarks. It was then shown with an original application: tailoring metamaterials for a museum antiseismic stand …”

Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

“…Since the seminal paper by Duysinx and Bendsøe, 7 several works addressing topology optimization with stress constraints have been developed. Among them, there are works that focus on developing more efficient and accurate ways to handle the stress constraints, [8][9][10][11][12][13][14][15][16] and works that focus on novel applications, [17][18][19][20] as the problem of compliant mechanisms with stress constraints. [21][22][23][24][25][26][27] Although not novel, stress-constrained topology optimization has been the subject of intensive research in the literature up to the present day.…”