TY - GEN
T1 - Efficiency of the fast multipole BEM with quadratic elements for 3D linear elasticity
AU - Ptaszny, Jacek
AU - Swinka, Pawe L.
N1 - Publisher Copyright:
copyright © Crown copyright (2018).All right reserved.
PY - 2020
Y1 - 2020
N2 - A Fast Multipole Boundary Element Method (FMBEM) and a computer code for 3D elasticity is developed. Higher order boundary elements with quadratic shape functions, i.e. 8-node Serendipity elements, are applied to the discretization of geometry and boundary quantities. The numerical integration of boundary integrals, depending on Kelvin solutions, involves an adaptive subdivision of elements to provide a high accuracy of the calculations. The efficiency of the method is evaluated in terms of the model size, accuracy and execution time by a comparison with Finite Element Method (FEM) models, with quadratic shape function elements. Models of selected machine components, with stress concentration, are analysed. For the analysed structures, both methods provide results with similar accuracy. However, the FMBEM models have by an order of magnitude lower number of Degrees of Freedom (DOF) compared to the FEM, and can be analysed within time comparable to the FEM with a direct solver. Thus, the FMBEM can be competetive to the widely used FEM.
AB - A Fast Multipole Boundary Element Method (FMBEM) and a computer code for 3D elasticity is developed. Higher order boundary elements with quadratic shape functions, i.e. 8-node Serendipity elements, are applied to the discretization of geometry and boundary quantities. The numerical integration of boundary integrals, depending on Kelvin solutions, involves an adaptive subdivision of elements to provide a high accuracy of the calculations. The efficiency of the method is evaluated in terms of the model size, accuracy and execution time by a comparison with Finite Element Method (FEM) models, with quadratic shape function elements. Models of selected machine components, with stress concentration, are analysed. For the analysed structures, both methods provide results with similar accuracy. However, the FMBEM models have by an order of magnitude lower number of Degrees of Freedom (DOF) compared to the FEM, and can be analysed within time comparable to the FEM with a direct solver. Thus, the FMBEM can be competetive to the widely used FEM.
KW - 3D Elasticity
KW - Efficiency
KW - Fast Multipole Boundary Element Method
KW - Finite Element Method
KW - Quadratic Elements
UR - https://www.scopus.com/pages/publications/85081051200
M3 - Conference contribution
AN - SCOPUS:85081051200
T3 - Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
SP - 2889
EP - 2900
BT - Proceedings of the 6th European Conference on Computational Mechanics
A2 - Owen, Roger
A2 - de Borst, Rene
A2 - Reese, Jason
A2 - Pearce, Chris
PB - International Centre for Numerical Methods in Engineering, CIMNE
T2 - 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
Y2 - 11 June 2018 through 15 June 2018
ER -