Buradasınız

SKALAR DALG A PROBLEMLERİNİN ÇÖZÜMÜNDE ZAMAN-DOMENİ SINIR ELEMANI METODU

THE TIME DOMAIN BOUNDARY ELEMENT METHOD FOR SCALAR WAVE PROBLEMS

Journal Name:

Publication Year:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
This paper deals with the stability of the boundary element method. The effects of various element sizes and time increments on the internal solution are analyzed. To this end, a time domain boundary element method is used. To achieve this, an existing BEM code for the boundary nodes is modified to optional internal nodes. Using appropriate time and spatial variations for the field variables, some observations on the numerical stability are reported. The internal solutions are presented for different p values and discussed the reasons of unstable cases appeared.
Abstract (Original Language): 
Bu makale Sınır Elemanı Metodunun (SEM) kararlılığını konu edinir. Farklı boyutlardaki elemanların ve değişik zaman artımlarının dahili çözüm üzerindeki etkileri analiz edilmiştir. Bunun yapılabilmesi için, bir zaman-domeni sınır elemanı metodu kullanılmıştır. Bu çalışma, sınır noktaları için mevcut olan bir SEM programının keyfi sayıdaki dahili noktalara modifiye edilerek başarıya ulaştırılmıştır. Alan değişkenlerinin nümerik hesaplanmasında benimsenen uygun zaman ve geometrik değişimler gözönünde tutularak nümerik kararlılık konusundaki bazı gözlemler kaleme alınmaktadır. Farklı p değerleri için dahili çözümler sunularak ve ortaya çıkan kararsız çözümlerin nedenleri irdelenmiştir.
129
136

REFERENCES

References: 

Antes, H. 1985. A Boundary Element Procedure For Transient Wave Propagation in Two-Dimensional Isotropic Elastic Media, Finite Element Analysis and Design, Vol. 1, pp. 313-322.
Arai, M., Adachi, T. and Matsumoto, H. 1999. Boundary Element Analysis For Unsteady Elastodynamic Problems Based on The Laplace Transform, JSME International Journal Series A, Vol. 42, No. 4, pp. 507-514.
Banerjee, P. K. 1994. The Boundary Element Methods in Engineering, McGraw-Hill, London.
Birgisson, B., Siebrits, E. and Peirce, A. P. 1999. Elastodynamic Direct Boundary Element Methods With Enhanced Numerical Stability Properties,
International Journal For Numerical Methods in Engineering, Vol. 46, pp. 871-888.
Cole, D. M., Kosloff, D. D. and Minster, J. B. 1978. A Numerical Boundary Integral Equation Method For Elastodynamics I, Bulletin of the Seismological Society of America, Vol. 68, No. 5, pp. 1331-1357.
Dominguez, J. and Gallego, R. 1991. The Time Domain Boundary Element Method For Elastodynamic Problems, Mathematical and
Computer Modelling, Vol. 15, No, 3-5, pp. 119-129.
Dominguez, J. 1993. Boundary Elements in Dynamics, CMP, Southampton, UK.
Eringen, A. C. and Şuhubi, E. S. 1975.
Elastodynamics, Vol. II, Linear Theory, Academic Press, New York.
Gilbert, J. E. and Knobs, R. J. 1967. Stability of General Systems, Archive For Rational Mechanics
and Analysis, Vol. 25, pp. 271-284.
Graff, K. F. 1975. Wave Motion in Elastic Solids, Oxford: Clarendon Press.
Mansur, W. J. 1983. A Time-Stepping Technique To Solve Wave Propagation Problems Using the Boundary Element Method, Ph.D. Thesis, 1983, University of Southampton, UK.
Morse, P. M. and Feshbach, H.1953. Methods of Theoretical Physics, McGraw-Hill.
Peirce, A. and Siebrits, E. 1996. Stability Analysis Of Model Problems For Elastodynamic Boundary Element Discretizations, Numerical Methods for Partial Differential Equations, Vol. 12, pp. 585-613.
Peirce, A. and Siebrits, E. 1997. Stability Analysis And Design of Time-Stepping Schemes For General Elastodynamic Boundary Element Models,
International Journal For Numerical Methods in Engineering, Vol. 40, pp. 319-342.
Richter, C. 1997. Topics in Engineering: A Green's Function Time-Domain BEM of Elastodynamics, Brebbia, C. A. and Connor, J. J. (Eds.), Vol. 31,
CMP, Southampton, Uk.
Sari, M. 2000. Seismic Wave Modelling Using The
Boundary Element Method, Ph.D. Thesis, University of Glamorgan, UK.
Siebrits, E., Birgisson, B., Peirce, A. P. and Crouch, S. L. 1997. On the Numerical Stability of The Time Domain Boundary Element Methods, International Journal of Blasting and Fragmentation, Vol. 1, pp.
305-316.
Siebrits, E. and Peirce, A. P. 1995. The Stability Properties Of Time Domain Elastodynamic Boundary Element Methods, in Boundary Element Methods XVII, Southampton, pp. 45-53.
Mühendislik Bilimleri Dergisi 2003 9 (1) 129-136
135
Journal of Engineering Sciences 2003 9 (1) 129-136
The Time Domain Boundary Element Method For Scalar Wave Problems, M. Sarı
Spyrakos, C. C. and Antes, H. 1986. Time-Domain Boundary Element Method Approaches in Elastodynamics: A Comparative Study, Computers and Structures, Vol. 24, No. 4, pp. 529-535.
Tian, Y. 1990. Boundary Element Methods In
Elastodynamics
, Ph.D. Thesis. University of Minnesota, USA.
Yu, G., Mansur, W. J. and Carrer, J. A. M. 1999.
The Linear 6 Method For 2D Elastodynamic BE Analysis, Computational Mechanics, Vol. 24, p. 2,
pp. 82-89.
Yu, G., Mansur, W. J., Carrer, J. A. M. and Gong, L. 2000. Stability of Galerkin and Collocation Time Domain Boundary Element Methods As Applied to the Scalar Wave Equation, Computers and Structures, Vol. 74, pp. 495-506.

Thank you for copying data from http://www.arastirmax.com