ECCOMAS 2024

Multi-Material Topology Optimization of Smart Structures with Embedded Piezoelectric Stack Actuators using Geometry Projection

  • de Almeida, Breno Vincenzo (University of Campinas (UNICAMP))
  • Pavanello, Renato (University of Campinas (UNICAMP))
  • Langelaar, Matthijs (Delft University of Technology (TU Delft))

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Smart structures are composed of multifunctional elements combining sensory, actuator and load-bearing components. Since the interaction between these elements is complex, they are often designed independently, which can lead to suboptimal results when compared to designing the whole system simultaneously. To this end, we propose a numerical framework that yields optimized topologies of conductive load-bearing structures with embedded rectangular piezoelectric stack actuators (PSAs) in a coupled multiphysics setting. In the framework, the size and placement of the PSAs with fixed topologies is calculated with a composite multi--layered geometry projection method. The distribution of the conductive and electric materials of the load--bearing structure is concurrently optimized by applying a multi-material density-based topology optimization method. Since a PSA is composed of multiple layers of thin orthotropic piezoelectric segments, stacked together with alternating polarities, a very fine mesh would be required to properly predict its behaviour. To limit computational expenses, an equivalent piezoelectric material model is proposed to efficiently represent PSAs in a continuum setting. The model includes the size and orientation of the PSA, which can be used as design variables in the geometry projection method. The design optimization problem is solved by maximizing the output displacement of a surface connected to a workpiece represented by a spring, subject to volume and non-overlap constraints. To limit delamination and breakage of the PSAs, a novel polarization constraint is added to inhibit topologies where the PSAs work under tensile stress. The framework will be demonstrated on several 2D problems considering one or two (possibly vanishing) PSAs, with different initial configurations. Results show that the simultaneously optimized design achieves higher performance in comparison to fixed PSA configurations.