A bottom‐up optimization method for inverse design of two‐dimensional clamped‐free elastic rods

• Published in: International journal for numerical methods in engineering Vol. 123; no. 11; pp. 2556 - 2572
• Main Authors: Qin, Longhui, Zhu, Jianxiong, Huang, Weicheng
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.06.2022; Wiley Subscription Services, Inc
• Subjects: Bending; bottom‐up design method; Boundary conditions; Cables; Clamping; Design optimization; discrete elastic rods; Elastic deformation; Free boundaries; global searching algorithm; Inverse design; Inverse problems; Numerical methods; Rods; Search algorithms; solid mechanics
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6950

Rod‐like structures, such as DNA, climbing plants, and cables, pervade the nature and our daily life and also belong to a frequently encountered engineering problem, which usually assume a deformed shape based on the competition between elasticity (stretching, bending, twisting) and external forces (e.g., gravity). These structures often undergo geometrically nonlinear deformation under its own weight. Computing the natural (undeformed) shape of a rod from the observed deformed configuration is a nonlinear inverse problem. Here we introduce a numerical method to solve this problem in case planar (2D) rods, that is, beams, under a clamped‐free boundary condition. A simulation model is developed based on the discrete elastic rods (DER) algorithm to address the forward deformation process from natural to deformed shapes under gravity. Based on the internal mechanical link among the nodes on the discretized elastic rod, a bottom‐up optimization method is proposed in this article for an efficient inverse solution. Associated with it, a global searching algorithm is developed to search for the optimal bending curvature along the arc length of the rod. The method is numerically validated for accuracy and sheds light on the inverse design of rod‐like structures for various applications, for example, soft robots and tails of animated characters.