Quasi-weak and weak formulation of stochastic finite elements on static and dynamic problems—a unifying framework |
| |
| Affiliation: | 1. Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu City, 30013, Taiwan;2. Department of Mechanical Engineering, National Cheng Kung University, Tainan City, 70101, Taiwan;1. Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, 16801, USA;2. Department of Material Science and Engineering, University of Florida, Gainesville, FL, 32611, USA;3. Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA;1. Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;2. GE Global Research Center, Schenectady, NY 12309, USA;3. Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan |
| |
| Abstract: | To model uncertainty of spatial and/or temporal variations widely present in synthetic and natural media, a variety of displacement-based stochastic finite element methods (SFEMs) have been formulated using the standard displacement-based finite elements. In this paper, by distinguishing a quasi-weak form from a weak form in both real and random space, a unifying framework of variational formulation is presented covering both the displacement-based SFEMs and the recently proposed Green-function-based (GFB) SFEM. The study shows that Monte Carlo, perturbation, and weighted integral SFEMs correspond to the quasi-weak form, while the weak form results in spectral SFEM, pseudo-spectral SFEM, and GFB-SFEM. Within the unifying framework, dynamic problems are further addressed especially to demonstrate the unique feature of GFB-SFEM on problems with inputs characterized as random fields or random processes. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
