Topology optimization of planar shape memory alloy thermal actuators using element connectivity parameterization

This paper presents the direct application of topology optimization to the design of shape memory alloy (SMA) thermal actuators. Because SMAs exhibit strongly nonlinear, temperature-dependent material behavior, designing effective multidimensional SMA actuator structures is a challenging task. We pursue the use of topology optimization to address this problem. Conventional material scaling topology optimization approaches are hampered by the complexity of the SMA constitutive behavior combined with large actuator deflections. Therefore, for topology optimization we employ the element connectivity parameterization approach, which offers improved analysis convergence and robustness, as well as an unambiguous treatment of nonlinear materials. A path-independent SMA constitutive model, aimed particularly at the NiTiR-phase transformation, is employed, allowing efficient adjoint sensitivity analysis. The effectiveness of the proposed SMA topology optimization is demonstrated by numerical examples of constrained and unconstrained formulations of actuator stroke maximization, which provide insight into the characteristics of optimal SMA actuators. Key words: shape memory alloys; NiTi; topology optimization; element connectivity parameterization; geometric nonlinearity; material nonlinearity