GENERALIZED FINITE ELEMENT METHODS FOR MULTISCALE STRUCTURAL DYNAMICS AND WAVE PROPAGATION
Abstract
n this research, we propose to address the limitations of existing Finite Element Methods (FEMs) for the solution of nonlinear structural dynamics problems subjected to high-frequency loading and wave propagation problems in the presence of singularities and discontinuities. This overarching multiscale model problem shares many of the features and challenges of other hyperbolic problems of relevance to the United States Air Force. The proposed multiscale Generalized FEM (GFEM) adopts shape functions that are on-the-fly numerically computed in parallel. If successful, this GFEM will be able to capture high-frequency responses using structural-scale meshes that are much coarser than those required by the FEM. A novel strategy for the computation of block-diagonal mass matrices applicable to high-order GFEMs will also be investigated. This approach is not limited to polynomial shape functions like in the FEM and can be used with any element topology. The time steps required for stability of the proposed GFEM are expected to be significantly larger than in the FEM, in particular in problems with singularities and discontinuities. Preliminary numerical experiments with 1-D model problems confirm this hypothesis. Another unique feature of this GFEM is its ability to adopt different time-marching schemes and time steps at the structural scale and in the computation of GFEM shape functions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010296
Entities
People
- C. Armando Duarte
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Illinois Urbana–Champaign