Level‐set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

Abstract

SUMMARYLinear buckling constraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient-based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and prohibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level-set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub-problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem.

Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses

“…Therefore, the ratio tEA/tLBA = 0.69 indicates again the efficiency of the multilevel procedure. Comparing to [23], reporting a computational times of about 120s when computing 25 buckling modes for a much smaller 3D problem (≈ 4.6·10 5 DOFs) and using a parallel algorithm, the presented multilevel approach seems to enhance the efficiency considerably. This also considering that no parallelization (which is possible for all the methods presented) was considered for the present examples.…”

“…Other researchers, using alternative parameterizations (e.g. level-set [23]), have experienced similar artifacts; 2. As an intrinsic trend, compliance or mass-optimized designs may show many thin bars, especially for fine discretizations and/or low volume fractions while building up a hierarchical structure with extreme buckling response.…”

“…We now consider the mass minimization problem for the 3D structure sketched in Figure 10, inspired by the example presented in [23] Figure 10: Setting for the 3D cantilever example. The beam is fully clamped at the built in end and a uniform load with total magnitude f = 3.6 · 10 4 acts on the top face.…”

“…The buckling load factor of the fully solid design (f = 1) is λ 1 = 2.393; therefore we are always starting within the feasible set. The fine scale discretization is set to Ω 0 = (134 + 2, 44 + 4, 94 + 2), corresponding to 626,688 design variables and 1,953,483 DOFs, about 4.5 times more than in [23]. The multilevel procedure is built with = 3 and on Ω we just have 34,125 DOFs.…”

Size and Shape Optimization of Space Trusses Considering Geometrical Imperfection-Sensitivity in Buckling Constraints

“…Guo et al [6] applied a new approach for truss topology optimization with stress and local buckling constrains. Many researchers have proposed different methods to handle the truss optimization problems with buckling constrains [7][8][9][10]. New applications of truss elements in robotics to achieve the optimum stiffness-to-weight ratios have brought a new perspective into buckling failure of truss structures.…”