Geometric uncertainties in finite element analysis |
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| Affiliation: | 1. GeM Institute UMR CNRS, Ecole Centrale Nantes 1 rue de la Noe, BP 92101, F-44321 Nantes cedex 3, France;2. ESI GROUP Chair & High Performance Computing Institute ECN, 1 rue de la Noe, BP 92101, F-44321 Nantes cedex 3, France;3. Notre Dame University, Louaize P.O. Box: 72, Zouk Mikael, Zouk Mosbeh, Lebanon;4. ESI GROUP Chair & PIMM Laboratory, ENSAM ParisTech 151 Boulevard de l’Hôpital, F-75013 Paris France;1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, Guangdong, 510641, China;2. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan, 410082, China |
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| Abstract: | This paper demonstrates the use of automatic differentiation in solving finite element problems with random geometry. In the area of biomechanics, the shape and size of the domain is often known only approximately. Stochastic finite element analysis can be used to compute the variability in the structural response as a result of variability in the shape of the structural domain. Automatic differentiation can be used to compute the shape sensitivites accurately and effortlessly. Unlike randomness in material properties, the response variability can be the same as or greater than the variability in the input. When both the Young's modulus and geometry are random, it is likely that randomness in geometry will dominate randomness in Young's modulus. |
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