On Non-Linear Transformations for the Integration of the Singular Kernels in the Boundary Element Method

2009 ◽  
Author(s):  
M. Doblare ◽  
L. Gracia
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Transformations ◽  
Non Linear ◽  
Singular Kernels ◽  
Element Method

A Boundary Element Method Formulation for Design Sensitivities in Steady-State Conduction-Convection Problems

1992 ◽  
Vol 59 (1) ◽  
pp. 182-190 ◽  
Author(s):  
Abhijit Chandra ◽  
Cho Lik Chan
Keyword(s):  
Steady State ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Machining Processes ◽  
Convection Diffusion ◽  
Design Sensitivities ◽  
Singular Kernels ◽  
Method Formulation ◽  
Diffusion Problems ◽  
Element Method

A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes.

On the Solution of the 3D Crack Surface Contact Problem Using the Boundary Element Method

2010 ◽  
Vol 454 ◽  
pp. 11-29 ◽  
Author(s):  
Wilhelm Weber ◽  
Karsten Kolk ◽  
Kai Willner ◽  
Günther Kuhn
Keyword(s):  
Boundary Element Method ◽  
Contact Problem ◽  
Boundary Element ◽  
Crack Surface ◽  
Load Cycle ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Non Linear ◽  
Surface Contact ◽  
Element Method

The efficient solution of the 3D crack surface contact problem utilizing the boundary element method (BEM) is presented. The dual discontinuity method (DDM), a special formulation of the BEM, is applied. This method deals directly with the relative displacements and the discontinuities of the tractions at the crack. For the normal behavior a unilateral contact is assumed and for the description of the tangential behavior Coulomb’s frictional law is utilized. The hard contact formulation is regularized by the application of the penalty method. An incremental iterative procedure based on a radial return mapping algorithm is applied for the solution of this non-linear problem. Based on the stress field the fracture mechanical parameters are determined by an extrapolation method for all increments of a characteristic load cycle. By the analysis of this load cycle the cyclic fracture mechanics values are obtained. Due to the non-linear nature of crack growth the simulation is implemented in the framework of a predictor-corrector scheme. For the investigation of the influence of the crack surface roughness on the behavior of cracks two numerical examples are presented.

Sign in / Sign up

Export Citation Format

Share Document