scholarly journals An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

2002 ◽  
Vol 24 (1) ◽  
pp. 1-9 ◽  
Author(s):  
R. B. V. Pessolani
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Two Dimensions ◽  
Element Method

Design of Tools for Electrochemical Machining by the Boundary Element Method

1986 ◽  
Vol 200 (3) ◽  
pp. 195-205 ◽  
Author(s):  
O H Narayanan ◽  
S Hinduja ◽  
C F Noble
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Electrochemical Machining ◽  
Two Dimensions ◽  
Different Boundary Conditions ◽  
Work Surface ◽  
Tool Profile ◽  
Tool Profiles ◽  
Element Method

Techniques for modelling electrochemical machining are briefly reviewed before concentrating on the boundary element method for computing the shape of tool profiles. The model described caters for problems which can be represented geometrically in two dimensions; it is iterative in nature and uses the approximate cos θ method to initiate the procedure. Subsequent iterations employ one of three formulations developed for correcting the tool profile to obtain workpiece equilibrium. Linear and quadratic isoparametric elements have been used and their relative accuracy is assessed. Special emphasis is placed on the design of tools expected to need sharp profile discontinuities and the merits of specifying different boundary conditions on the known work surface are examined.

Design sensitivity analysis using the boundary element method

1993 ◽  
Vol 28 (4) ◽  
pp. 283-291 ◽  
Author(s):  
A Tafreshi ◽  
R T Fenner
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Optimization Problems ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Optimum Shape ◽  
Shape Design ◽  
Design Algorithm ◽  
Wide Range ◽  
Element Method

A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities. This allows the coupling of an optimizing technique and a boundary element elastic stress analyser to form an optimum shape design algorithm in two dimensions. Hermitian cubic spline functions used to represent boundary shapes offer considerable advantages in fitting a wide range of curves, and in the automatic remeshing process. They also reduce the need for optimization constraints to avoid impractical designs during the optimization procedure. The boundary element method offers advantages over the finite element method, and is applicable to a wide range of shape optimization problems.

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