Abstract: Nonlocal operators are advantageous choices in modeling due to their flexibility in handling discontinuities, incorporating nonlocal effects, and modeling a range of interactions through different choices for kernels. Using these operators in models has several applications, notably peridynamics. The biharmonic operator appears in many models including deformations of beams and plates. The nonlocal biharmonic operator can be formulated in at least two ways: using a fourth difference operator or iterating the nonlocal Laplacian. In this talk, we discuss some similarities and differences between the two operators, as well as discuss nonlocal clamped and hinged boundary conditions.
Speaker’s Bio: Nicole Buczkowski is a postdoctoral scholar at Worcester Polytechnic Institute. She received her Ph.D. from the University of Nebraska-Lincoln in 2022, working with Professors Mikil Foss and Petronela Radu. Nicole's research interests include nonlocal models and fracture mechanics.
Last Updated: August 21, 2023 - 2:13 pm