Accession Number:

ADA564655

Title:

Novel Discretization Schemes for the Numerical Simulation of Membrane Dynamics

Descriptive Note:

Doctorial thesis

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH GRADUATE SCHOOL OF ENGINEERING AND MANAGEMENT

Personal Author(s):

• Kolsti, Kyle F.

Report Date:

2012-09-13

Pagination or Media Count:

160.0

Abstract:

Motivated by the demands of simulating flapping wings of Micro Air Vehicles, novel numerical methods were developed and evaluated for the dynamic simulation of membranes. For linear membranes, a mixed-form time-continuous Galerkin method was employed using trilinear space-time elements, and the entire space-time domain was discretized and solved simultaneously. For geometrically nonlinear membranes, the model incorporated two new schemes that were independently developed and evaluated. Time marching was performed using quintic Hermite polynomials uniquely determined by end-point jerk constraints. The single-step, implicit scheme was significantly more accurate than the most common Newmark schemes. For a simple harmonic oscillator, the scheme was found to be symplectic, frequency-preserving, and conditionally stable. Time step size was limited by accuracy requirements rather than stability. The spatial discretization scheme employed a staggered grid, grouping of nonlinear terms, and polygon shape functions in a strong-form point collocation formulation. Validation against existing experimental data showed the method to be accurate until hyperelastic effects dominate.

Descriptors:

• *NONLINEAR SYSTEMS
• *NUMERICAL ANALYSIS
• EXPERIMENTAL DATA
• MATHEMATICAL MODELS
• MEMBRANES
• NUMERICAL METHODS AND PROCEDURES

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE