Thermomechanical topology optimization of shape‐memory alloy structures using a transient bilevel adjoint method. (26th February 2020)

• Record Type: Journal Article
• Authors: Kang, Ziliang; James, Kai A.
• Is Part Of: International journal for numerical methods in engineering. Volume 121:Number 11(2020)
• Page Start: 2558
• Page End: 2580
• Publication Date: 2020-02-26
• Subjects: computational inelasticity -- pseudoelasticity -- shape‐memory alloys -- topology optimization -- transient adjoint sensitivity analysis -- two‐way shape‐memory effects; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6319
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We present a novel method for computational design of adaptive shape‐memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two‐way shape‐memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient‐based optimization used to perform the optimization search. We derive a transient, bilevel adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two‐dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the TWSME, and design for maximum mechanical advantage while accounting for pseudoelasticity.