Abstract
Numerical simulation of thin solids remains one of the challenges in computational mechanics. The 3D elasticity problems of shells of revolution are dimensionally reduced in different ways depending on the symmetries of the configurations resulting in corresponding 2D models. In this paper, we solve the multiparametric free vibration of complex shell configurations under uncertainty using stochastic collocation with the p‐version of finite element method and apply the collocation approach to frequency response analysis. In numerical examples, the sources of uncertainty are related to material parameters and geometry representing manufacturing imperfections. All stochastic collocation results have been verified with Monte Carlo methods.
Highlights
Numerical simulation of thin solids remains one of the challenges in computational mechanics. e advent of stochastic finite element methods has led to new possibilities in simulations, where it is possible to replace isotropy assumptions with statistical models of material parameters or incorporate manufacturing imperfections with parametrized computational domains and derive statistical quantities of interest such as expectation and variance of the solution
The sources of uncertainty relate to materials and geometry
Possible to construct similar interpolation operators even if the point set is limited to some subset of the parameter space, or, crucially, points are added to the sparse grid
Summary
Numerical simulation of thin solids remains one of the challenges in computational mechanics. e advent of stochastic finite element methods has led to new possibilities in simulations, where it is possible to replace isotropy assumptions with statistical models of material parameters or incorporate manufacturing imperfections with parametrized computational domains and derive statistical quantities of interest such as expectation and variance of the solution. We discuss two special classes of such uncertainty quantification problems: free vibration of shells of revolution and directly related frequency response analysis. Sparse grids are designed to satisfy given requirements for quadrature rules It is, possible to construct similar interpolation operators even if the point set is limited to some subset of the parameter space (partial sparse grids), or, crucially, points are added to the sparse grid.
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