Density-based shape optimization for fail-safe design

Abstract

This paper presents a two-stage procedure for density-based optimization towards a fail-safe design. Existing approaches either are computationally extremely expensive or do not explicitly consider fail-safe requirements in the optimization. The current approach trades off both aspects by employing two sequential optimizations to deliver redundant designs that offer robustness to partial failure. In the first stage, a common topology optimization or a topology optimization with local volume constraints is performed. The second stage is referred to as “density-based shape optimization” since it only alters the outline of the structure while still acting on a fixed voxel-type finite element mesh with pseudo-densities assigned to each element. The performance gain and computational efficiency of the current approach are demonstrated by application to various 2D and 3D examples. The results show that, in contrast to explicitly enforcing fail-safety in topology optimization, the current approach can be carried out with reasonable computational cost. Compared to the local volume constraint approach, the suggested procedure further increases the fail-safe performance by 47% for the example considered.

Simultaneous topology and fastener layout optimization of assemblies considering joint failure

“…Since in practice the number of joints is relatively small, also the computational effort of considering failure of joints is small, compared to optimizations considering failure of the continuum structure. 15,17 The examples shown in Section 7 have a maximum number of n j = 4 joints, which leads to n d = 4 failure cases for failure mode m = 1 and n d = 6 failure cases for failure mode m = 2.…”

“…The NDS are defined by parametric shapes that are mapped to a general mask vector 15 . The masks can either be used to remove material (denoted by ), add material (denoted by ), or do both by subsequent application.…”

“…The joint's mask will define a circular shape (or cylindrical shape in 3D) around the joint's reference point in the x ‐ y ‐plane, which is considered as the contact plane here. The entries of have values between 0 and 1 and are calculated for every element j : 15 …”

“…In practical applications, holes have to be present to mount fasteners like bolts or rivets. Following the method of the authors, 15 a multiplicative mask is used to model the holes in the structure. The holes move according to the reference points and always enforce that the affected regions are kept free of solid material.…”

“…Therefore, only the failure scenarios from the highest studied failure mode need to be evaluated, when optimizing for the worst case. Since in practice the number of joints is relatively small, also the computational effort of considering failure of joints is small, compared to optimizations considering failure of the continuum structure 15,17 …”