Numerical evaluation of strain gradients in classical elasticity through the Boundary Element Method

2021 ◽  
Vol 86 ◽  
pp. 104178
Author(s):  
Dimitrios C. Rodopoulos ◽  
Theodore V. Gortsas ◽  
Stephanos V. Tsinopoulos ◽  
Demosthenes Polyzos
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Evaluation ◽  
Classical Elasticity ◽  
Strain Gradients ◽  
Element Method

scholarly journals Closed-Form Evaluation of Potential Integrals in the Boundary Element Method

2020 ◽  
Vol 28 (02) ◽  
pp. 1950014
Author(s):  
Michael Carley
Keyword(s):  
Boundary Element Method ◽  
Closed Form ◽  
Boundary Element ◽  
Numerical Evaluation ◽  
Singular Integrals ◽  
Machine Precision ◽  
Plane Element ◽  
Form Evaluation ◽  
Selection Of ◽  
Element Method

A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green’s function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

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