Applied and Computational Math Seminar: Non-Conforming FEM for Large Bending Deformations with Isometry Constraint

Speaker:Dimitris Ntogkas, Univeristy of Maryland, College Park
Title: Non-Conforming FEM for Large Bending Deformations with Isometry Constraint

Abstract: We propose a numerical method for the approximation of deformations $y:\Omega \subset \mathbb{R}^2 \to \mathbb{R}^3$ of a single-layer thin plate with mid-plane $\Omega$, under a non-linear isometry constraint. This deformation is the solution of a minimization problem under the isometry constraint and appropriate boundary conditions. We employ a discretization of the energy functional and the constraint using a space of fully discontinuous polynomials and introduce an appropriate discrete version of the Hessian that captures the discontinuities of the space. We prove the $\Gamma$- convergence of the discrete functional, as well as the convergence of discrete global minimizers to global minimizers of the continuous energy. We employ a simple extension of the model to account for the effect of a spontaneous curvature for a bi-layer plate and perform numerical simulations in order to explore the efficiency and the geometric flexibility of the method for both models. 

Time: Friday, January 26, 2018, 1:30-2:30pm

Place: Exploratory Hall, Room 4106