1 / 76

Dual BEM since 1986 J T Chen ( 陳正宗特聘教授 )

Dual BEM since 1986 J T Chen ( 陳正宗特聘教授 ). National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering. Department of Harbor and River Engineering National Taiwan Ocean University, Keelung, Taiwan 8:30-9:50, Nov. 19, 2006. Outlines. Overview of BEM and dual BEM

dorothy-williamson
Download Presentation

Dual BEM since 1986 J T Chen ( 陳正宗特聘教授 )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dual BEM since 1986J T Chen (陳正宗特聘教授) National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering Department of Harbor and River Engineering National Taiwan Ocean University, Keelung, Taiwan 8:30-9:50, Nov. 19, 2006

  2. Outlines • Overview of BEM and dual BEM • Mathematical formulation Hypersingular BIE • Nonuniqueness and its treatments Degenerate scale True and spurious eigensolution (interior prob.) Fictitious frequency (exterior acoustics) • Conclusions

  3. Top ten countries of BEM and dual BEM • BEM USA (3423) , China (1288) , UK, Japan, Germany, France, Taiwan (551), Canada, South Korea, Italy (No.7) • Dual BEM (Made in Taiwan) UK (119), USA (90), Taiwan (69), China (46), Germany, France, Japan, Australia, Brazil, Slovenia (No.3) (ISI information Nov.06, 2006) 台灣加油 FEM Taiwan (No.9/1311)

  4. Top ten countries of FEM, FDM and Meshless methods • FEM USA, China, Japan, France, Germany, England, South Korea, Canada, Taiwan, Italy • Meshless methods USA, China, Singapore, Japan, Spain, Germany, Slovakia, England, France, Taiwan • FDM USA, Japan, China, England, France, Germany, Canada, Taiwan, South Korea, Italy (ISI information Nov.06, 2006)

  5. Top three scholars on BEM and dual BEM • BEM Aliabadi M H (UK, Queen Mary College) Mukherjee S (USA, Cornell Univ.) Chen J T (Taiwan, Ocean Univ.) 56 篇 Tanaka M (Japan, Shinshu Univ.) • Dual BEM (Made in Taiwan) Aliabadi M H (UK, Queen Mary Univ. London) Chen J T (Taiwan, Ocean Univ.) 43 篇 Power H (UK, Univ Nottingham) (ISI information Nov.06, 2006) NTOU/MSV 加油

  6. Overview of numerical methods Domain Boundary MFS Trefftz method MLS, EFG DE PDE- variational IE 6

  7. Number of Papers of FEM, BEM and FDM 6 2 1 (Data form Prof. Cheng A. H. D.)

  8. Growth of BEM/BIEM papers (data from Prof. Cheng A.H.D.)

  9. Advantages of BEM • Discretization dimension reduction • Infinite domain (half plane) • Interaction problem • Local concentration Disadvantages of BEM 北京清華 • Integral equations with singularity • Full matrix (nonsymmetric)

  10. NTUCE Ó BEM and FEM • 边界元法和各种无网格法等在许多工 • 程领域都属于有限元法的一个补充。 • (2)它的发展既受到有限元法的启发，又受到 • 有限元法的制约。只有在其优势领域，作 • 为补充才有实际意义。如果只是有限元能 • 计算的它也能算，而且结果吻合，那就这 • 种补充没有必要(Quoted from Prof. Yao) • Degenerate boundary(Crack growth) ! 第一場 • Fast multipole ! 第二場

  11. NTUCE Ó What Is Boundary Element Method ? • Finite element method Boundary element method 4 5 1 2 6 3 1 2 the Nth constant or linear element geometry node N

  12. NTUCE Ó Dual BEM Why hypersingular BIE is required (potential theory) Degenerate boundary 4 4 7 7 6 5 6 5 8 3 8 3 9 10 1 2 1 2 Artifical boundary introduced ! BEM Dual integral equations needed ! Dual BEM

  13. NTUCE Ó Some researchers on Dual BEM Chen(1986) Hong and Chen (1988） 71 citings ASCE Portela and Aliabadi (1992) 188 citings IJNME Mi and Aliabadi (1994) Wen and Aliabadi (1995) Chen and Chen (1995) 新竹清華 黎在良等---斷裂力學邊界數值方法(1996) 周慎杰(1999) Chen and Hong (1999) 76 citings ASME Niu and Wang (2001) Yu D H, Zhu J L, Chen Y Z, Tan R J …

  14. NTUCE Ó Dual Integral Equations by Hong and Chen(1984-1986) Singular integral equation Hypersingular integral equation Cauchy principal value Hadamard principal value Boundary element method Dual boundary element method 1969 2006 1986 normal boundary degenerate boundary

  15. Degenerate boundary geometry node (1,0.5) (-1,0.5) 4 7 the Nth constant or linear element N 6 5 8 3 (0,0) 1 2 (-1,-0.5) (1,-0.5) 5(+) 6(+) 5(+) 6(-) 5(+) 6(+) 5(+) 6(+) 5(+) 6(+) 5(+) 6(-) 5(+) 6(-) 5(+) 6(-)

  16. How to get additional constraints The constraint equation is not enough to determine coefficients of p and q, Another constraint equation is required

  17. BEM Cauchy kernel singular DBEM Hadamard kernel hypersingular crack 1888 Integral equation (1984) (2000) FMM Large scale Degenerate kernel Original data from Prof. Liu Y J Desktop computer fauilure

  18. Fundamental solution • Field response due to source (space) • Green’s function • Casual effect (time) K(x,s;t,τ)

  19. Green’s function, influence line and moment diagram Force Force s x s s=1/2 x=1/4 G(x,s) G(x,s) x s Moment diagram s:fixed x:observer Influence line s:moving x:observer(instrument)

  20. Two systems u and U U(x,s) u(x) Domain(D) s source Boundary (B) Infinite domain

  21. Dual integral equations for a domain point(Green’s third identity for two systems, u and U) Primary field Secondary field where U(s,x)=ln(r) is the fundamental solution.

  22. Dual integral equations for a boundary point(x push to boundary) Singular integral equation Hypersingular integral equation where U(s,x) is the fundamental solution.

  23. Potential theory • Single layer potential (U) • Double layer potential (T) • Normal derivative of single layer potential (L) • Normal derivative of double layer potential (M)

  24. Physical examples for potentials Moment Force U:moment diagram T:moment diagram L:shear diagram M:shear diagram

  25. Order of pseudo-differential operators • Single layer potential (U) --- (-1) • Double layer potential (T) --- (0) • Normal derivative of single layer potential (L) --- (0) • Normal derivative of double layer potential (M) --- (1) Pseudo differential operator Real differential operator

  26. Calderon projector

  27. How engineers avoid singularity BEM / BIEM Improper integral Singularity & hypersingularity Regularity Fictitious BEM Bump contour Limit process Fictitious boundary Achenbach et al. (1988) Null-field approach Guiggiani (1995) Gray and Manne (1993) Collocation point CPV and HPV Ill-posed Waterman (1965)

  28. NTUCE Ó Definitions of R.P.V., C.P.V. and H.P.V.using bump approach • R.P.V. (Riemann principal value) • C.P.V.(Cauchy principal value) • H.P.V.(Hadamard principal value)

  29. Principal value in who’s sense • Common sense • Riemann sense • Lebesgue sense • Cauchy sense • Hadamard sense (elasticity) • Mangler sense (aerodynamics) • Liggett and Liu’s sense The singularity that occur when the base point and field point coincide are not integrable. (1983)

  30. Two approaches to understand HPV Differential first and then trace operator (Limit and integral operator can not be commuted) Trace first and then differential operator (Leibnitz rule should be considered)

  31. Bump contribution (2-D) U T s s 0 x x 0 L s M s x x

  32. Bump contribution (3-D) 0` s s x x 0 s s x x

  33. Successful experiences since 1986

  34. Solid rocket motor (工蜂火箭)

  35. X-ray detection (三溫暖測試)

  36. FEM simulation

  37. Stress analysis

  38. BEM simulation

  39. Shong-Fon II missile

  40. IDF

  41. Flow field

  42. V-band structure (Tien-Gen missile)

  43. FEM simulation

  44. Seepage flow

  45. Meshes of FEM and BEM

  46. a t=0 t=0 t=0 c t=0 t=0 e b Screen in acoustics

  47. oblique incident water wave Top view y Free water surface S x O breakwater z breakwater z O x S Water wave problem with breakwater

  48. Reflection and Transmission

  49. Cracked torsion bar

More Related