A lower-bound formulation for the geometry and topology optimization of truss structures under multiple loading

Authors:
Benoît Descamps;Rajan Filomeno Coelho
Affiliations:
BATir Department, Université libre de Bruxelles, Brussels, Belgium 1050;BATir Department, Université libre de Bruxelles, Brussels, Belgium 1050
Venue:
Structural and Multidisciplinary Optimization
Year:
2013

Citing 4
Cited 0

Approximate solution of the trust region problem by minimization over two-dimensional subspaces

Mathematical Programming: Series A and B
Trust region algorithms for optimization with nonlinear equality and inequality constraints

Trust region algorithms for optimization with nonlinear equality and inequality constraints
Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications

Mathematical Programming: Series A and B
A 99 line code for discretized Michell truss optimization written in Mathematica

Structural and Multidisciplinary Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this contribution, we propose an effective formulation to address the stress-based minimum volume problem of truss structures. Starting from the lower-bound formulation in topology optimization, the problem is further expanded to geometry optimization and multiple loading scenarios, and systematically reformulated to alleviate numerical difficulties related to the melting node effect and stress singularities. The subsequent simultaneous analysis and design (SAND) formulation is well suited for a direct treatment by introducing a barrier function. Using exact second derivatives, this difficult class of problem is solved by sequential quadratic programming with trust regions. These building blocks result into an integrated design process. Two examples---including a large-scale application---illustrate the robustness of the proposed formulation.