Green's function based finite element formulations for isotropic seepage analysis with free surface
Abstract A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steady-state seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the ove...
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Marcílio Alves
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doaj-a2ca49819ca046ccbc334c7c80759e052020-11-25T01:32:29ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782512101991200510.1590/1679-78251726S1679-78252015001001991Green's function based finite element formulations for isotropic seepage analysis with free surfaceHui WangYa-Ting GaoQing-Hua QinAbstract A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steady-state seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the over-specified free surface problem to a regular partial differential equation problem. Then, at each iteration step, the Green's function for isotropic linear seepage partial differential equation is employed to construct the element interior water head field, while the conventional shape functions are used for the independent element frame water head field. Then these two independent fields are connected by a double-variable hybrid functional to produce the final solving equation system. By means of the physical definition of Green's function, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals, so that versatile multi-node element is constructed to simplify mesh reconstruction during iteration. Finally, numerical results from the present Green's function based FEM with isotropic Green's function kernels are compared with other numerical results to verify and demonstrate the performance of the present method.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015001001991&lng=en&tlng=enSeepagefree surfaceisotropic damhybrid finite element methodGreen's function |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hui Wang Ya-Ting Gao Qing-Hua Qin |
spellingShingle |
Hui Wang Ya-Ting Gao Qing-Hua Qin Green's function based finite element formulations for isotropic seepage analysis with free surface Latin American Journal of Solids and Structures Seepage free surface isotropic dam hybrid finite element method Green's function |
author_facet |
Hui Wang Ya-Ting Gao Qing-Hua Qin |
author_sort |
Hui Wang |
title |
Green's function based finite element formulations for isotropic seepage analysis with free surface |
title_short |
Green's function based finite element formulations for isotropic seepage analysis with free surface |
title_full |
Green's function based finite element formulations for isotropic seepage analysis with free surface |
title_fullStr |
Green's function based finite element formulations for isotropic seepage analysis with free surface |
title_full_unstemmed |
Green's function based finite element formulations for isotropic seepage analysis with free surface |
title_sort |
green's function based finite element formulations for isotropic seepage analysis with free surface |
publisher |
Marcílio Alves |
series |
Latin American Journal of Solids and Structures |
issn |
1679-7825 |
description |
Abstract A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steady-state seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the over-specified free surface problem to a regular partial differential equation problem. Then, at each iteration step, the Green's function for isotropic linear seepage partial differential equation is employed to construct the element interior water head field, while the conventional shape functions are used for the independent element frame water head field. Then these two independent fields are connected by a double-variable hybrid functional to produce the final solving equation system. By means of the physical definition of Green's function, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals, so that versatile multi-node element is constructed to simplify mesh reconstruction during iteration. Finally, numerical results from the present Green's function based FEM with isotropic Green's function kernels are compared with other numerical results to verify and demonstrate the performance of the present method. |
topic |
Seepage free surface isotropic dam hybrid finite element method Green's function |
url |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015001001991&lng=en&tlng=en |
work_keys_str_mv |
AT huiwang greensfunctionbasedfiniteelementformulationsforisotropicseepageanalysiswithfreesurface AT yatinggao greensfunctionbasedfiniteelementformulationsforisotropicseepageanalysiswithfreesurface AT qinghuaqin greensfunctionbasedfiniteelementformulationsforisotropicseepageanalysiswithfreesurface |
_version_ |
1725081846981591040 |