Impact force and moment problems on random fields with fractal and hurst effects

Wave propagation through random heterogeneous media is an important research area due to its significance in engineering and science applications. This dissertation focuses on the investigation of dynamical responses of Lamb’s wave propagation through random media with fractal and Hurst effects. Inspired by nature, we use fractal and Hurst parameters to characterize the spatial randomness. Two random field models, namely, Cauchy and Dagum models, have been employed to model both mass density and stiffness tensor fields. Since there exists no closed solution for transient waves in random media, we adopt and generalize a numerical scheme called cellular automata (CA) to simulate the dynamical responses. We first investigate cellular automata’s response to an anti-plane, impulse line load on a half-space on random mass density random fields. In this study, we validate our numerical solver by comparing simulated responses on white noise with the homogeneous results and the theoretical, analytical solution from classical elasticity theory. Evaluation of stochastic imperfection sensitivity has shown that the shear wave is less sensitive to spatial fluctuations compared with pressure and Rayleigh waves. We then generalize the cellular automata to in-plane force and moment problems on random mass density fields. We find out that the responses are more sensitive to Hurst parameter than the fractal dimension for all loading scenarios. The sensitivity for all loading cases are also presented and compared with one another both qualitatively and quantitatively. To fully capture the complexity of material spatial randomness requires the consideration of both mass density and stiffness tensor. In the last part of this thesis, we adopt a novel second-rank anti-plane stiffness tensor random field (TRF) model by taking the dyadic product of two scalar random fields. This model allows us to represent full anisotropy with heterogeneity. With the introduction of random mass density field, a comparion study for anti-plane Lamb's problem is conducted among three stiffness tensor models: (1) a deterministic stiffness tensor; (2) a locally isotropic stiffness tensor with heterogeneity; (3) a second-rank tensor admitting full anisotropy and heterogeneity. The simulation results show that the fluctuation of displacement reponses on model (3) is the strongest, followed by model (2), and then by model (1). in general, this thesis has made contributions in areas of random field modeling, numerical scheme for elastodynamics and sensitivity analysis for wave propagations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical & Applied Mechans

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Zhang, Xian

Contributors dc:contributor

• Ostoja-Starzewski, Martin
• Fischer, Paul
• Matlack, Kathryn
• Elbanna, Ahmed Ettaf

• Mechanical science

Statement dc:rights

• N/A

Language dc:language

en, eng

Handle dc:identifier

http://hdl.handle.net/2142/113807

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F113807