Topology optimization of structures with length-scale effects using elasticity with microstructure theory

• Mindlin’s elasticity with microstructure theory is revisited.
• Eight-node element is used to separately interpolate macro and micro fields.
• Topologies of different designs are presented using SIMP and density filter.
• Microstructure length-scale effects are investigated via parametric studies.
• Results indicate significant influence of microstructure on optimal designs.

This paper presents topology optimization of structures with inclusion of microstructural effects. To this end, Mindlin’s elasticity with microstructure theory is used for investigating the scale effects. For implementation of finite element based topology optimization, a separate interpolation scheme for the displacement and micro-deformation field is adopted based on 8-node quadrilateral element. Numerical results show that although the continuum is associated with material length-scales, the minimal topological length-scale cannot be controlled without using a regularization technique. Results demonstrate that the length-scale of the microstructure may have a significant influence on the optimal topologies.