# Fail-Safe Topology Optimization Using Damage Scenario Filtering
## 1 Introduction  
Topology optimization (TO) has the capacity to generate innovative designs without assuming any structural connectivity, making it a powerful and beneficial driver to reduce the structural weight while meeting specific performance requirements. TO optimizes objective functions by distributing materials within the design domain, resulting in greater economic efficiency and attracting increased attention from engineering designers. Various topology optimization methods have been proposed since the pioneering work of [PERSON] and [PERSON] [1], including the Solid Isotropic Material with Penalization (SIMP) approach for solid isotropic materials [2; 3], the Evolutionary Structural Optimization (ESO) and Bi-directional Evolutionary Structural Optimization (BESO) methods [4; 5], the Level Set Method (LSM) [6; 7; 8], and feature-driven methods such as the Moving Morphable Components (MMCs) method [9; 10] and Moving Morphable Voids (MMVs) method [11]. On the other hand, topology optimization focused on lattice structures has also garnered increasing scientific interest [12; 13; 14; 15]. In general, topology optimization methods emphasize altering the macro-scale structure's configuration to enhance its robustness. Another powerful way to achieve this goal is by enhancing the material's strength. However, overall, optimized designs obtained through topology optimization often resemble statically structured designs. For these structures, material utilization reaches its limits, and a lack of redundancy makes them susceptible to stiffness loss due to material damage. Especially when facing structural stiffness loss caused by material defects, vibrational impacts, and various environmental factors, their elasticity becomes severely limited [16; 17; 18]. Even minor stiffness failures in structures can lead to a sharp decline in the overall structural performance. In the field of engineering, the demand for safety often far exceeds the need to reduce costs. Therefore, there is a growing focus on research aimed at mitigating the sharp decline in structural performance caused by local damage in engineering structures. Building upon the traditional topology optimization design, the fail-safe optimization approach enhances a structure's ability to withstand localized damage scenarios [19; 20; 21; 22; 23]. Considering the inherent fail-safe requirements, a simplified local damage model is introduced into the topological optimization process for fail-safe design, simulating the intricate phenomena of localized damage in a structure. Throughout the structural optimization process, all potential impacts of local damage on a structure are taken into account. By mitigating the effects of localized damage on a structure, a robust and highly redundant optimized design is achieved. In comparison to conventional topology designs [24; 25; 26], a fail-safe optimization design demonstrates strong resilience against risks, allowing for continued operation until the position of local damage is rectified or components are repositioned. However, in the process of fail-safe optimization, numerous scenarios of local damage must be considered. Given that each local damage scenario necessitates an individual finite element analysis and sensitivity calculations, the computational workload is significantly immense compared to that of traditional structural topology optimization algorithms. For a given optimization model, the computational complexity of fail-safe optimization algorithms is often many times that of traditional topology optimization algorithms. To alleviate the computational demands associated with fail-safe optimization design, it becomes imperative to filter out redundant local failure scenarios while traversing through them. This strategy aims to enhance the efficiency of fail-safe structural optimization by reducing the computational load imposed by an excessive number of local damage scenarios.