Optimal design of responsive structures

With recent advances in both responsive materials and fabrication techniques it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such structures through topology optimization. By applying a typical interpolation scheme and filtering technique, we prove existence of an optimal design to a class of objective functions which depend on the compliances of the stimulated and unstimulated states. In particular, we consider the actuation work and the blocking load as objectives, both of which may be written in terms of compliances. We study numerical results for the design of a 2D rectangular lifting actuator for both of these objectives, and discuss some intuition behind the features of the converged designs. We formulate the optimal design of these integrated responsive structures with the introduction of voids or holes in the domain, and show that our existence result holds in this setting. We again consider the design of the 2D lifting actuator now with voids. Finally, we investigate the optimal design of an integrated 3D torsional actuator for maximum blocking torque.

[1]  G. Allaire,et al.  Shape optimization of a layer by layer mechanical constraint for additive manufacturing , 2017 .

[2]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[3]  Ole Sigmund,et al.  Optimal design of robust piezoelectric microgrippers undergoing large displacements , 2017 .

[4]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[5]  J. Lewis,et al.  3D Printing of Liquid Crystal Elastomeric Actuators with Spatially Programed Nematic Order , 2018, Advanced materials.

[6]  Xiaoping Qian,et al.  Undercut and overhang angle control in topology optimization: A density gradient based integral approach , 2017 .

[7]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[8]  Gilles A. Francfort,et al.  Homogenization and optimal bounds in linear elasticity , 1986 .

[9]  Grégoire Allaire,et al.  Optimizing supports for additive manufacturing , 2018, Structural and Multidisciplinary Optimization.

[10]  G. Buttazzo,et al.  An optimal design problem with perimeter penalization , 1993 .

[11]  B. Bourdin.  Filters in topology optimization , 2001 .

[12]  Gil Ho Yoon,et al.  Topological layout design of electro-fluid-thermal-compliant actuator , 2012 .

[13]  Jeonghoon Yoo,et al.  Structural Optimization of a Multi-Physics Problem Considering Thermal and Magnetic Effects , 2012, IEEE Transactions on Magnetics.

[14]  Grégoire Allaire,et al.  On optimal microstructures for a plane shape optimization problem , 1999 .

[15]  Kevin C. Galloway,et al.  A Dexterous, Glove-Based Teleoperable Low-Power Soft Robotic Arm for Delicate Deep-Sea Biological Exploration , 2018, Scientific Reports.

[16]  Paolo Cignoni,et al.  Elastic textures for additive fabrication , 2015, ACM Trans. Graph..

[17]  Robert J. Wood,et al.  Nitinol living hinges for millimeter-sized robots and medical devices , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[18]  Robert V. Kohn,et al.  Optimization of Structural Topology in the High-Porosity Regime , 2008 .

[19]  S. Magdassi,et al.  A New Approach to 3D Printing Dense Ceramics by Ceramic Precursor Binders , 2019, Advanced Engineering Materials.

[20]  G. Allaire,et al.  Coupled optimization of macroscopic structures and lattice infill , 2020, International Journal for Numerical Methods in Engineering.

[21]  H. Rodrigues,et al.  A material based model for topology optimization of thermoelastic structures , 1995 .

[22]  Amirhesam Amerinatanzi,et al.  Fabrication of NiTi through additive manufacturing: A review , 2016 .

[23]  Steve Marschner,et al.  Microstructures to control elasticity in 3D printing , 2015, ACM Trans. Graph..

[24]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[25]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[26]  D. Kinderlehrer,et al.  Homogenization and effective moduli of materials and media , 1986 .

[27]  W. Bangerth,et al.  deal.II—A general-purpose object-oriented finite element library , 2007, TOMS.

[28]  Ines Gloeckner,et al.  Variational Methods for Structural Optimization , 2002 .

[29]  Zhan Kang,et al.  Structural shape and topology optimization of cast parts using level set method , 2017 .

[30]  T. Ware,et al.  Voxelated Molecular Patterning in Three-Dimensional Freeforms , 2019 .

[31]  Mohammad Elahinia,et al.  Additive Manufacturing of Ni-Rich NiTiHf20: Manufacturability, Composition, Density, and Transformation Behavior , 2019, Shape Memory and Superelasticity.

[32]  G. Allaire,et al.  Shape optimization by the homogenization method , 1997 .

[33]  Cedric P. Ambulo,et al.  Four-dimensional Printing of Liquid Crystal Elastomers. , 2017, ACS applied materials & interfaces.

[34]  Grégoire Allaire,et al.  Structural optimization under overhang constraints imposed by additive manufacturing technologies , 2017, J. Comput. Phys..

[35]  Sung-Hoon Ahn,et al.  Fabrication of wrist-like SMA-based actuator by double smart soft composite casting , 2015 .