Certified solutions for hydraulic structures using the node‐based smoothed point interpolation method (NS‐PIM) |
| |
| Authors: | J Cheng X L Chang S C Wu G Y Zhang |
| |
| Institution: | 1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, People's Republic of China;2. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576 Singapore, Singapore;3. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430070, People's Republic of China;4. Centre for Advanced Materials Processing and Simulations (AMPS), School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, People's Republic of China |
| |
| Abstract: | A meshfree node‐based smoothed point interpolation method (NS‐PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node‐based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS‐PIM and the simulation results of NS‐PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS‐PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd. |
| |
| Keywords: | numerical methods meshfree method strain smoothing upper bound hydraulic structure engineering generalized smoothed Galerkin weak form |
|
|
