Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl
by Jorge M. Pérez Zerpa (Instituto de Estructuras y Transporte, Facultad de Ingeniería, UdelaR, Montevideo, Uruguay), Marcelo Forets (Depto. de Matemática y Aplicaciones, CURE, UdelaR, Maldonado, Uruguay) and Daniel Freire Caporale (Instituto de Física, Facultad de Ciencias, UdelaR, Montevideo, Uruguay).
Presentation
Extended Abstract
During the review process, the pdf is automatically generated by whedon, see: https://github.com/JuliaCon/proceedings-review/issues/95
Publication
See Forets, Marcelo, Daniel Freire Caporale, and Jorge M. Pérez Zerpa. "Combining set propagation with finite element methods for time integration in transient solid mechanics problems." Computers & Structures 259 (2022): 106699.
The pre-print is available here: https://arxiv.org/abs/2105.05841
Implementation
See https://github.com/JuliaReach/ReachabilityAnalysis.jl
Examples repository
See https://github.com/JuliaReach/SetPropagation-FEM-Examples
Minimal example
We solve the system of two degrees of freedom loaded with a Heaviside step function subject to Rayleigh damping shown in the diagram below.
Given the FEM assembled matrices, the range of variation of the external loads is 10\% around the nominal value 1.
Initial displacements and velocities for both masses belong to the interval [-0.5, 0.5].
The initial-value problem is instantiated and homogeneized as described in [1].
To illustrate the flexibility of our approach, two algorithm choices are considered, both relying on support functions [7] (LGG09 algorithm). solA contains the flowpipe efficiently computed along box directions. To improve the accuracy, solB is computed using octagonal template directions.
References
See https://github.com/JuliaCon/proceedings-review/issues/95