On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs

DOI10.1007/s11081-007-9005-3zbMath1173.74033OpenAlexW2053345971WikidataQ56050746 ScholiaQ56050746MaRDI QIDQ1026920

Mathias Stolpe

Publication date: 6 July 2009

Published in: Optimization and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11081-007-9005-3

zbMATH Keywords

Stokes flowcomposite materialstruss structuresmaximum stiffness design

Mathematics Subject Classification ID

Convex programming (90C25) Quadratic programming (90C20) Topological methods for optimization problems in solid mechanics (74P15)

Related Items (8)

Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming ⋮ Mixed-integer second-order cone optimization for composite discrete ply-angle and thickness topology optimization problems ⋮ Bridging mixed integer linear programming for truss topology optimization and additive manufacturing ⋮ Global optimization of truss topology with discrete bar areas. II: Implementation and numerical results ⋮ Truss topology optimization with discrete design variables by outer approximation ⋮ Integer linear programming models for topology optimization in sheet metal design ⋮ Towards a lifecycle oriented design of infrastructure by mathematical optimization ⋮ A mixed integer programming approach to designing periodic frame structures with negative Poisson's ratio

Uses Software

• CPLEX

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generating optimal topologies in structural design using a homogenization method
• Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
• An optimal design problem with perimeter penalization
• Local branching
• Multiphase composites with extremal bulk modulus
• A new class of extremal composites
• Design of planar articulated mechanisms using branch and bound
• Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs
• A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations
• Optimal Design of Truss Structures by Logic-Based Branch and Cut
• Simultaneous analysis and design
• The method of moving asymptotes—a new method for structural optimization
• Improved Linear Integer Programming Formulations of Nonlinear Integer Problems
• Modelling topology optimization problems as linear mixed 0-1 programs
• Systematic design of phononic band–gap materials and structures by topology optimization
• Topology optimization of fluids in Stokes flow
• Shape optimization by the homogenization method
• Design of multiphysics actuators using topology optimization. I: One-material structures. II: Two-material structures.

This page was built for publication: On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs