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Stochastic Mechanics
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Professor Roger Ghanem, Dr. Jianxu Shi, and other colleagues at Johns Hopkins University and University of Southern California have been conducting pioneering researches and successfully applied stochastic mechanics method in various applications.
The spectral version of the stochastic finite element method can be viewed as an extension of the deterministic finite element method to situations involving random material properties. The consistency in this extension stems from the functional analysis basis of the representation of stochastic processes and the projection-based definition of best approximations with respect to basis sets. In the context of stochastic finite element analysis, two particular Hilbert spaces are of singular interest: one each for the system input and output. The former can be described as the span of the random entities that are ultimately described by the data; while the latter refers to the Hilbert space spanned by all the random variables defining information generated by the process of filtering the data through the model.
Figure 1: Karhunen-Loeve representation of random material
In particular, the system input is represented by the Karhunen-Loeve (KL) expansion and the solution is represented by a mean-square convergent series expansion, e.g., the polynomial chaos expansion. This expansion essentially consists of all multidimensional Hermite polynomials in the set of random variables generated by the Karhunen-Loeve representation.
Figure 2: Polynomial chaos representation of random response
Figure 3: SFEM toolkit for Stochastic FEM analysis
Funded by ONR, our R&D objective is to develop general purpose formalism for treating uncertainty in physical systems and to develop a software product to enable ABAQUS to quantify uncertainties in their predictions that are consistent with model parameters, such as material properties and geometry.
Figure 4: 3D shell barge SFEM analysis
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GEM Capabilities
Computational Mechanics
Composite Mechanics
Fatigue and Fracture
Probabilistic Mechanics and Reliability Engineering
Stochastic Mechanics
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