Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

By Miche Jansen, Geert Lombaert, Mattias Schevenels. 2015

92 citations recorded by the source corpus.

Abstract Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Such imperfections might affect the structural stability and induce large displacement effects in these slender structures. This paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability. Geometric nonlinear effects are incorporated in the optimization by means of a Total Lagrangian finite element formulation in the minimization of end-compliance. Geometric imperfections are modeled as a vector-valued random field in the design domain. The resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem. These stochastic moments are typically estimated by means of sampling methods such as Monte Carlo simulation. However, these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm. An efficient solution algorithm which uses adjoint differentiation in a second-order perturbation method is therefore developed to estimate the stochastic moments during the optimization. Two applications with structures that exhibit different types of structural instabilities are examined. In both cases, it is demonstrated by means of an extensive Monte Carlo simulation that the deterministic design is very sensitive to imperfections, while the design obtained by means of the proposed method is much more robust.

Subfields: Building and Construction, Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f5c6338b959008705046839631c2b1bf349f775c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Building and Construction

In Civil and Structural Engineering

In Computational Theory and Mathematics

Citations in the corpus

Length scale and manufacturability in density-based topology optimization (2016, background): “However, for relatively smooth problems it has been demonstrated in [75] that the perturbation”