Topological Optimization of Beam Cross Section by Employing Extrusion Constraint

Abstract

Optimal cross‐section design of beams plays a characteristic role which signifies the rigidity of the member in bending, shear and torsion load conditions. Practically modern overhead crane girders, railway bridge girders or rail tracks etc. require constant cross‐section along the axial direction. Conventional topological optimization modeling procedures in such cases prove inadequate for the reason that these procedures generate non‐uniform topologies along the axis of the bending member. To examine optimal topology of those structural bending members which commonly possess constant cross‐section along the axis the topology optimization with extrusion constraint is more appropriate. The extrusion constraint method suggests a fresh approach to investigate optimal topologies of beam cross‐section under the influence of realistic loading condition across the section at the beginning of design cycle. Presented study is focused upon the influence of various configuration and location of the load and boundary conditions on the topology of the of the beam cross‐section which was not possible prior to the materialization of the extrusion or stamping constraint method. Several realistic loads and boundary conditions have been applied on the 3D beam model and optimal cross‐section topologies obtained have uniform compliance history and convergent solutions. The lowest compliance criteria have been suggested to choose topologies as furthers shape and size optimization candidates during beam design process.