Open Access
Pontecorvo, Michael Eugene
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Farhan Gandhi, Thesis Advisor
  • Farhan S Gandhi, Thesis Advisor
  • cellular structure
  • elastic arch
  • bistable
  • hexagonal cell
  • internal features
  • cell modulus
In classical cellular structures the unit cells have typically not had any inclusions. In the current research, unit cells with various types of inclusions or internal features are envisaged. Different types of internal features such as linear springs or dashpots, and a wide variety of nonlinear elements (buckling beams which display softening behavior, mechanical stops or contact elements which display stiffening behavior, and bistable elements which display negative stiffness or snap-through behavior) can be introduced into the unit cell. These internal features will strongly impact the behavior of the unit cell. Unit cells with different types of inclusions can then be thought of as ``Lego blocks'. A structure can be assembled using specific types of ``blocks' in specific arrangements, to provide desired system level behavior. The current study is based on the concept of a two-dimensional cellular structure with hexagonal cells made of pinned-pinned rigid links. Since such a cell has no stiffness of its own, the behavior of the internal feature dominates. The study presents the necessity to include three constraints within the hexagonal cell for its stability. Of the different elements/inclusions that can be used, this thesis focuses on two: a linear spring, and a bistable elastic arch. The selection of the linear spring is based on its being the simplest possible inclusion. For different spring arrangements, closed-form analytical expressions are derived for the in-plane modulus and Poisson's ratio of the hexagonal cell (and by extension, of a cellular structure with that unit cell repeated). The analytical expressions are validated using NASTRAN finite element simulations, as well as against tensile/compressive tests of unit cells with internal springs in an Instron machine. When the spring stiffness exceeds certain values, the rigid cell wall assumption is no longer valid, and these bounds are established. The validated analysis is used to conduct design studies on how the cell modulus (nondimensionalized by the spring stiffness) would vary with cell geometric parameters such as cell angle and cell wall length ratio. An in-plane cell modulus as high as 1.15 GPa was calculated using springs that were stiff but yet compliant enough so as not to violate the rigid cell wall assumption. The second part of the study focused on a bistable elastic arch. This is of interest because of the negative stiffness or snap-through behavior it can display. The large stroke and velocity of the arch, when transitioning from one stable equilibrium condition to the other, can be exploited for enhanced energy dissipation when coupled to a damping element. In the present study a finite element model of the arch is developed and its bistable behavior examined. Experiments on Nitinol and Delrin arches are used to validate the finite element analysis. The analysis is further used to conduct a parametric study on how variation in arch height, thickness or restraining spring stiffness influences the critical snap-through force, the stroke, and the maximum strains. This thesis lays the framework for cellular structures with diverse inclusions in the unit cells, and the study can be extended to other inclusions such as buckling beam elements, dashpots, etc., in the future.