On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations
The paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjo...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2019-02-01
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| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/109459/PDF/08_069-076_00811_Bpast.No.67-1_06.02.20.pdf |
| _version_ | 1811314192262627328 |
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| author | L. Rybarska-Rusinek |
| author_facet | L. Rybarska-Rusinek |
| author_sort | L. Rybarska-Rusinek |
| collection | DOAJ |
| description | The paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjoin a singular line, and (ii) intermediate elements, which while not adjoining the line, are still under strong influence of the singularity. An efficient method to evaluate the influence coefficients and the field intensity factors is suggested for the both types of the elements. The method avoids time expensive numerical evaluation of singular and hypersingular integrals over the element surface by reduction to 1D integrals. The method being general, its details are explained by considering a representative examples for elasticity problems for a piece-wise homogeneous medium with cracks, inclusions and pores. Numerical examples for plane elements illustrate the exposition. The method can be extended for curvilinear elements. |
| first_indexed | 2024-04-13T11:07:43Z |
| format | Article |
| id | doaj.art-5e91476fd23446818c2ff990cd285fbe |
| institution | Directory Open Access Journal |
| issn | 2300-1917 |
| language | English |
| last_indexed | 2024-04-13T11:07:43Z |
| publishDate | 2019-02-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| spelling | doaj.art-5e91476fd23446818c2ff990cd285fbe2022-12-22T02:49:13ZengPolish Academy of SciencesBulletin of the Polish Academy of Sciences: Technical Sciences2300-19172019-02-0167No. 16976https://doi.org/10.24425/bpas.2019.125435On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrationsL. Rybarska-RusinekThe paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjoin a singular line, and (ii) intermediate elements, which while not adjoining the line, are still under strong influence of the singularity. An efficient method to evaluate the influence coefficients and the field intensity factors is suggested for the both types of the elements. The method avoids time expensive numerical evaluation of singular and hypersingular integrals over the element surface by reduction to 1D integrals. The method being general, its details are explained by considering a representative examples for elasticity problems for a piece-wise homogeneous medium with cracks, inclusions and pores. Numerical examples for plane elements illustrate the exposition. The method can be extended for curvilinear elements.https://journals.pan.pl/Content/109459/PDF/08_069-076_00811_Bpast.No.67-1_06.02.20.pdfboundary integral equationboundary element methodsingular elementhadamard finite part integral |
| spellingShingle | L. Rybarska-Rusinek On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations Bulletin of the Polish Academy of Sciences: Technical Sciences boundary integral equation boundary element method singular element hadamard finite part integral |
| title | On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations |
| title_full | On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations |
| title_fullStr | On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations |
| title_full_unstemmed | On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations |
| title_short | On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations |
| title_sort | on evaluation of influence coefficients for edge and intermediate boundary elements in 3d problems involving strong field concentrations |
| topic | boundary integral equation boundary element method singular element hadamard finite part integral |
| url | https://journals.pan.pl/Content/109459/PDF/08_069-076_00811_Bpast.No.67-1_06.02.20.pdf |
| work_keys_str_mv | AT lrybarskarusinek onevaluationofinfluencecoefficientsforedgeandintermediateboundaryelementsin3dproblemsinvolvingstrongfieldconcentrations |