Fail-safe topology optimization

Abstract

Fail-safe robustness of critical load carrying structures is an important design philosophy for aerospace industry. The basic idea is that a structure should be designed to survive normal loading conditions when partial damage occurred. Such damage is quantified as complete failure of a structural member, or a partial damage of a larger structural part. In the context of topology optimization fail-safe consideration was first proposed by Jansen et al. Struct Multidiscip Optim 49(4):657-666, (2014). While their approach captures the essence of fail-safe requirement, it has two major shortcomings: (1) it involves analysis of a very large number of FEA models at the scale equal to the number of elements; (2) failure was introduced in generic terms and therefore the fundamental aspects of failure test of discrete members was not discussed. This paper aims at establishing a rigorous framework for failsafe topology optimization of general 3D structures, with the goal to develop a computationally viable solution for industrial applications. We demonstrate the effectiveness of the proposed approach on several examples including a 3D example with over three hundred thousand elements.

Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures

“…Note that the bar forces appearing in (6) are not part of the semidefinite model, so we need to introduce them into (4). As long as the geometry matrix B is invertible, this can be done by adding variables q s ∈ R m and the equilibrium constraint Bq s = f s for each force scenario f s ∈ S.…”

“…While robust optimization based approaches to truss topology design have been heavily pursued over the last decades, complete bar failures have only been investigated very recently, apart from some early work of Sun et al [4], which only considers a small, predetermined set of failure scenarios. Jansen et al [5] and Zhou and Fleury [6] work on continuous topology optimization problems, distributing material among a space of "pixels" under the constraint that even after erasing all material within a ball or cube of given size, the structure should still be able to sustain its load. Mohr et al [7] consider a ground structure approach, but in their model not only single bars can fail, but instead n complete trusses have to be built from a given ground structure such that either a single one of them or each set of n − 1 trusses together can withstand the given load after complete failure of all the remaining trusses.…”

Optimization Simulation of the Light Aircraft’s Cockpit Made of Carbon Fiber Reinforced Composites

“…However, if the weight factor is considered, the composites still have better specific energy absorption (SEA) as compared to metals [15]. Zhou et al [16] pointed out that the steps of topology optimization for composite structure are different from those for metal structure; the optimization of metal structure in the first stage is the general design concept and the second stage is sizing and shape optimization. Their paper considers that the first stage of composite structure optimization is to use the Free-Size optimization to generate the initial layout of composite stacking laminates, the second stage is to give appropriate parameters to modify the stacking design, and the final stage is to optimize stacking arrangement to meet all the constraints.…”

Game formulations for structural optimization under uncertainty

“…In these cases, the Stackelberg games reduce to min‐max optimization problems, in which one tries to minimize the worst response. Examples include minimizing the maximum compliance obtained when varying the load or the design . Existence of Stackelberg equilibria is guaranteed under weak conditions (eg, compactness of the feasible sets), which can, in practice, always be satisfied.…”

“…Examples include minimizing the maximum compliance obtained when varying the load 2,4,[8][9][10] or the design. [11][12][13][14] Existence of Stackelberg equilibria is guaranteed under weak conditions (eg, compactness of the feasible sets), which can, in practice, always be satisfied. Therefore, the main issue is to find numerically efficient formulations.…”