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Practical Application of the Stochastic Finite Element Method

Submitted by Lee Margetts on
research
Stochastic
FEA
random materials
random geometry
random loading
random signal

If you're interested in stochastic finite element analysis, you might like to know that we've just published a paper that reviews the "practical" application of the method. The paper first outlines the main methods of incorporating uncertainty into engineering computations. It then presents "practical" examples across a range of disciplines of where these methods have been used.

We hope that this paper is a good starting point for those looking to adopt stochastics in their work.

On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities

Submitted by arash_yavari on
research
Geometric elasticity
inclusions
Anisotropic eigenstrain
residual stresses
Stress singularity

The problems of singularity formation and hydrostatic stress created by an inhomogeneity with eigenstrain in an incompressible isotropic hyperelastic material are considered. For both a spherical ball and a cylindrical bar with a radially-symmetric distribution of finite possibly anisotropic eigenstrains, we show that the anisotropy of these eigenstrains at the center (the center of the sphere or the axis of the cylinder) controls the stress singularity.

Geometric nonlinear thermoelasticity and the time evolution of thermal stresses

Submitted by arash_yavari on
research
Geometric mechanics
nonlinear thermoelasticity
Thermal stresses

In this paper we formulate a geometric theory of nonlinear thermoelasticity that can be used to calculate the time evolution of the temperature and thermal stress fields in a nonlinear elastic body. In particular, this formulation can be used to calculate residual thermal stresses. In this theory the material manifold (natural stress-free configuration of the body) is a Riemannian manifold with a temperature-dependent metric. Evolution of the geometry of the material manifold is governed by a generalized heat equation.

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