Abstract
Chapter 3 presents the fundamentals of the Stochastic Finite Element Method in the framework of the stochastic formulation of the virtual work principle. The resulting stochastic partial differential equations are solved with either non-intrusive Monte Carlo simulation methods, or intrusive approaches such as the versatile spectral stochastic finite element method. Additional approximate methodologies such as the Neumann and Taylor series expansion methods are also presented together with some exact analytic solutions that are available for statically determinate stochastic structures. The concept of the variability response function is then developed and generalized for general stochastic finite element systems.
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Notes
- 1.
The Dirichlet boundary condition specifies the values that the solution needs to take on along the boundary of the domain.
- 2.
Neumann boundary condition specifies the values that the derivative of the solution needs to take on the boundary of the domain.
- 3.
I.e. it spans a Hilbert space which is defined as a vector space possessing an inner product as measure. Named after David Hilbert (1862–1943).
- 4.
This is a simple 1D implementation of the Latin Hypercube Sampling methodology.
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Papadopoulos, V., Giovanis, D.G. (2018). Stochastic Finite Element Method. In: Stochastic Finite Element Methods. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-64528-5_3
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DOI: https://doi.org/10.1007/978-3-319-64528-5_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-64528-5
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