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Multi-domain BEM for two-dimensional problems of elastodynamics. (English) Zbl 0631.73067

An advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two-dimensional elastic or viscoelastic solids of arbitrary shape and connectivity is presented. For transient dynamic analysis the problem is first solved in the Laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions. The present analysis is capable of treating very large, multi-domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring capability, problems related to the layered media and soil-structure interaction can all be analyzed. This paper also introduces a new type of element called ‘enclosing element’, which has been developed and used to model the infinitely extending boundaries of a half-space or a layered medium. A number of numerical examples are presented, and through comparisons with available analytical and numerical results, the accuracy, stability and efficiency of the present analysis are established.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65R20 Numerical methods for integral equations
74H45 Vibrations in dynamical problems in solid mechanics
65R10 Numerical methods for integral transforms

Software:

LINPACK
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References:

[1] Banaugh, J. Appl. Mech. 30 pp 589– (1963) · Zbl 0134.44704
[2] Cruse, J. Math. Anal. Appl. 22 pp 244– (1968)
[3] Niwa, Memo Fac. Eng. Kyoto Univ. 37 pp 28– (1975)
[4] and , ’Application of integral equation method to some geomechanical problems’, Proc. 2nd Int. Conf. Numerical Methods and Geomechanics 1976, pp. 120-131.
[5] and , ’An analysis of transient stresses produced around a tunnel by the integral equation method’, Proc. Symp. Earthquake Engineering Japan, 1975, pp. 631-638.
[6] and , ’Transient stress analysis of tunnels and cavities of arbitrary shape due to travelling waves’, in and , (eds.), Developments in BEM–II. Applied Science Publishers, Barking, England. 1982, Chapt. 7.
[7] Manolis, Int. j. numer. methods eng. 17 pp 573– (1981)
[8] and , ’Elastodynamics’, in (ed.), Progress in Boundary Element Methods, Halstead Press, New York, 1981, Chapt. 7, pp. 213-257.
[9] and , ’Analysis of dynamic soil-structure interaction by boundary integral equation method’, Proc. 3rd Int. Symp. on Numerical Methods in Engineering, Vol 1, Paris, Pluralis Publ., 1983, pp. 353-362.
[10] and , ’Dynamic behavior of strip footings on nonhomogeneous visco-elastic soils’, in (ed.), Proc. Int. Symp. on Dynamic Soil-structure Interaction, Minneapolis, A. A. Balkema, 1984, pp. 25-35.
[11] and , ’Dynamic response of embedded strip foundation subjected to obliquely incident waves’, Proc. Seventh Int. Conf. on Boundary Element Methods, Lake Como, Italy, Springer-Verlag, Berlin, 1985, pp. 6-63 to 6-69.
[12] Graffi, Bologna Series 10 4 pp 103– (1947)
[13] ’Isoparametric finite elements in two and three-dimensional stress analysis’, Ph.D. Thesis, University of Wales, University College, Swansea, England, 1968.
[14] ’Further developments of the boundary integral technique for elasto-statics’, Ph.D. Thesis, Southampton University, England, 1975.
[15] ’Advanced implementation of the boundary element method for two and three-dimensional elastostatics’, in and , (eds.), Developments in BEM–, I Applied Science Publishers, Barking, England 1979, Chapt. 3.
[16] and , Boundary Element Methods in Engineering Science. McGraw-Hill, London, New York, 1981. · Zbl 0499.73070
[17] and , Gaussian Quadrature Formulas. Prentice-Hall, New York, 1966.
[18] , and , ’Boundary integral equation analysis for a class of earth-structure interaction problems’, Final Report to NSF, Grant No. CEE 80-13461, Department of Engineering Mechanics, University of Kentucky, Lexington 1985.
[19] ’Linear and nonlinear dynamic analysis by boundary element method’, Ph.D. Thesis, Department of Civil Engineering, State University of New York at Buffalo, 1986.
[20] and , ’Advanced three-dimensional dynamic analysis by boundary element’, ASME Conf. on Advanced Boundary Element Analysis, Florida, Nov. 1985.
[21] Banerjee, Earthquake eng. struc. dyn. 14 pp 933– (1986)
[22] LINPACK User’s Guide. SIAM, Philadelphia. PA, 1979.
[23] Ahmad, Comp. Mech. 2 pp 185– (1987)
[24] Gazetas, Methods Struct. Anal. ASCE 1 pp 115– (1976)
[25] Gazetas, J. Geotech. Eng. Div. ASCE 105 pp 1435– (1979)
[26] Hryniewicz, Comp. Methods Appl. Mech. Eng. 25 pp 355– (1981)
[27] and , ’Static and dynamic geometric and material nonlinear analysis’, Report No. UC SESM 74-4. Structural Engineering Laboratory, University of California, Berkeley, CA, 1974.
[28] and , ’A transmitting boundary for finite difference analysis of wave propagation in solids’, Project No. NR 064-183, University of Illinois, Urbana, 1975.
[29] and , ’Transient Elastodynamics’, in Topics in Boundary Element Research, Vol. 2, Springer-Verlag, Berlin, 1985, Chapt. 5. · Zbl 0591.73097
[30] Fu, J. Appl. Mech. ASME E37 pp 599– (1970) · Zbl 0201.26602
[31] Boley, J. Appl. Mech. ASME E25 pp 31– (1958)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.