Stochastic analyses of mechanical and biomedical structures with uncertainties

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Copyright: Yang, Ji
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Abstract
Stochastic models are developed to investigate mechanical and biomedical structures with uncertainties. The natural frequencies and frequency statistics of a plate randomised by point masses or with variation in its thickness are initially examined experimentally as well as numerically using a range of techniques corresponding to direct Monte Carlo simulations, proper orthogonal decomposition, random matrix theory and the polynomial chaos expansion method. Hybrid techniques combining finite element analysis and Galerkin projection polynomial chaos expansion with either deterministic or stochastic model order reduction are then developed. For deterministic model order reduction, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. In the stochastic model order reduction, the stochastic reduced basis method is implemented in which the modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. Furthermore, the deterministic and stochastic model order reduction techniques are combined to accelerate the pre-processing of the basis vectors in the stochastic model order reduction. To demonstrate the performance of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate with uncertainties in its geometrical and material parameters is examined. By using the proposed model order reduction methods, the computational efficiency of the stochastic model is significantly increased while the physical content of the original system is preserved. Polynomial chaos expansion is also implemented to examine a bone implant healing process with uncertainties. To investigate the effects of uncertain mechanical and biochemical parameters on the bone implant healing process, stochastic models using both Galerkin projection and collocation based polynomial chaos expansion are proposed. Results from the numerical models of the homogeneous healing of the bone implant are initially validated by canine experiments from literature. Results from the stochastic models are compared with Monte Carlo simulations, showing high accuracy with significantly improved computational cost. This thesis demonstrates that the polynomial chaos expansion method is applicable to a range of problems with uncertainties ranging from linear dynamics to nonlinear biomechanics.
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Author(s)
Yang, Ji
Supervisor(s)
Kessissoglou, Nicole
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Publication Year
2016
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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