Session: 03-02 Wave Propagation, Buckling, and Dynamic Response

Paper Number: 171917

171917 - Target Shape Matching of Non-Uniform Buckled Beams 

Compliant mechanisms designed to deform to pre-defined target shapes can be used in robotic end effectors to improve grip on contoured objects or other snap-through bistable mechanisms without hinges. One method to achieve shape change is by intentionally buckling slender beams. While buckling is traditionally avoided in engineering applications due to its association with failure under compressive loads, intentional buckling can be desirable in some applications because it can enable sudden and large shape changes when the deformation exceeds a critical value. We hypothesized that a broad range of post-buckled shapes could be achieved from an initially straight beam by locally changing the geometry, material properties, and boundary conditions of an initially straight beam. For example, locally increasing a beam’s thickness in a given section will intuitively reduce curvature in that section because a thicker beam will deform less than a thinner beam with the same load applied. However, designing a compliant beam to achieve a desired shape change is challenging when solely relying on a designer’s intuition or experience, particularly when considering complex target shapes that may require a large number of variables.

Our study focuses on developing an inverse design approach to design slender initially straight beams that deform to a pre-defined target shape when buckled. In this study, we investigate changes to the thickness along the beam’s length. We begin by discretizing the beam into equally sized sections along its length, where each section is assigned a thickness to influence the beam’s buckled shape. We can then find the buckled shape for a given design using finite element analysis (FEA). However, even with FEA, it would still be difficult to determine the required thickness of each section to achieve a target shape.

To enable inverse design, we use a genetic algorithm (GA) along with FEA to identify the design that most closely matches the target shape. First, the genetic algorithm generates the initial set of designs, and the design is constrained by a maximum and minimum thickness for each section. This set of designs is exported to and simulated in the finite element analysis model. The deformed shapes of these beams are used to calculate the shape error, which is returned to the genetic algorithm, which then returns the next generation of designs. The objective function is the shape error, which is defined as the relative distance between the beam’s post-buckled shape and the target shape. The designs which are most similar to our target shape are modified by the GA through arithmetic and heuristic crossover, as well as random mutation. Using this method, the designer specifies the target shape, and the genetic algorithm iteratively modifies the design space until it produces a design that deforms most similarly to the target shape.

Our results show that small changes in geometry can greatly affect the buckled shape of the beams. We have produced a beam that deforms into a bracket-like shape, with a flat midsection that shifts to the side, by increasing the thickness of the beam in its center. This method can be used to solve complex design problems and find optimal solutions for buckled beam deformation.

Presenting Author: Robert Chiccarine The Pennsylvania State University

Presenting Author Biography: Robert Chiccarine is a master's student in the additive manufacturing and design program at Penn State University working with Dr. Mary Frecker in the EDOG lab group. He previously received a Bachelor of Science in mechanical engineering from Penn State University. His research interests include additive manufacturing for biomedical application, engineering design optimization, and multi-material additive manufacturing.