scholarly journals A stochastic collocation approach for parabolic PDEs with random domain deformations

2021 ◽  
Vol 93 ◽  
pp. 32-49
Author(s):  
Julio E. Castrillón-Candás ◽  
Jie Xu
Keyword(s):  
Stochastic Collocation ◽  
Parabolic Pdes ◽  
Collocation Approach

scholarly journals Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis

2018 ◽  
Vol 371 ◽  
pp. 732-750 ◽  
Author(s):  
Anindya Bhaduri ◽  
Yanyan He ◽  
Michael D. Shields ◽  
Lori Graham-Brady ◽  
Robert M. Kirby
Keyword(s):  
Uncertainty Analysis ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Parametric Uncertainty ◽  
Adaptive Mesh ◽  
Stochastic Collocation ◽  
Collocation Approach

scholarly journals Cylindrical Shell with Junctions: Uncertainty Quantification of Free Vibration and Frequency Response Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Harri Hakula ◽  
Vesa Kaarnioja ◽  
Mikael Laaksonen
Keyword(s):  
Free Vibration ◽  
Frequency Response ◽  
Response Analysis ◽  
Stochastic Collocation ◽  
Frequency Response Analysis ◽  
Shells Of Revolution ◽  
Sources Of Uncertainty ◽  
Elasticity Problems ◽  
Collocation Approach ◽  
3D Elasticity

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.

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