Invitation: PhD Dissertation Defense of Jingkun Gao
Hello ME Community,
You are invited to join the PhD Dissertation Defense of Jingkun Gao, on Monday, October 19, beginning at 10:00am. The defense will be presented in person in the Mechanical Engineering Conference Room. Interested parties may also attend via webex
Advisor: Dr. Weidong Zhu
Title: Deployability and Multistability of Jessen's Icosahedron Tensegrity Structure
Abstract:
Tensegrity structures can undergo substantial shape changes through interactions among geometry, self-stress, and member deformation. Deployability and multistability are related aspects of this capability. A central question is how initial self-stress, cable slackening, and member flexibility influence equilibrium paths, stability, and deployment behavior under different geometric and joint conditions. This dissertation addresses this question for Jessen'sicosahedron tensegrity structure through three investigations: static folding and multistability, dynamic deployment, and static bistability with initially curved rod members.
First, static folding and multistability are investigated using anaxial-member model combining a complementarity description of tension-only cables with arc-length continuation and a load-increment strategy for nonsmooth slack–tension switching. The equilibrium paths characterize the stability, elastic energy, and overall stiffness of self-equilibrated states. A second stable self-equilibrated state occurs only within an intermediate range of initial self-stress, contains no slack cables, and exhibits nonmonotonic variation in overall stiffness with initial self-stress. At lower self-stress, cable switching is closely associated with load extrema and stability transitions. Geometric perturbations complicate equilibrium branches while leaving the principal stability domain largely unchanged.
Second, dynamic deployment after release from a constrained folded configuration is investigated using gradient-deficient beam elements in the absolute nodal coordinate formulation to represent flexible rods and cables. The model reproduces the deployment path, overshoot, and decay trend measured by high-speed three-dimensional digital image correlation more closely than the axial-member model. The two-stage process involves initial upper-rod unfolding and cable re-tensioning, followed by overall height adjustment and residual vibration. Initial self-stress governs the tangent modal characteristics throughout deployment. Higher self-stress reduces cable vibration amplitudes following the re-tensioning of slack cables and increases the dominant frequencies of residual vibration. Within the investigated range, folding ratio mainly modifies post-deployment oscillations, while damping affects the later response more strongly than initial unfolding.
Third, static bistability with initially curved rods and rigid joint connections is investigated using a geometrically exact beam formulation. For straight rods, the beam and axial-member models give similar responses when stretching dominates but differ appreciably at lower shear-to-axial stiffness ratios. Within the adopted sectional model, local analysis identifies a nonzero-shear branch above a critical stretch ratio, while rigid joint constraints can induce shear below this threshold. For curved rods, initial self-stress and reference curvature reshape stability domains and elastic-energy distribution. In representative comparisons, increasing curvature reduces the inter-state elastic-energy difference while increasing its relative bending contribution. Under geometrically similar section scaling, increasing cable area or reducing rod area restricts the sampled parameter region, admitting the second stable self-equilibrated state.