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The coupling of the finite element method and boundary solution procedures. (English) Zbl 0347.65048

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] and , ’Numerical Solutions of Free-Surface and Flow Problems’, 10th Symposium in Naval Hydrodynamics, 1974. Office of Naval Research.
[2] Banaugh, J. Acoust. Soc. Am. 35 pp 1590– (1963)
[3] ’A Contribution to the Study of Axially Loaded Pile Foundations’, Ph.D. Thesis, Southampton University.
[4] ’Foundations with a Finite Elastic Layer: Application of the Integral Equation Method’, Civil Engineering, 1197-1202, November 1971.
[5] ’Integral Equation Methods for Analysis of Three Dimensional Elastic Solids of Arbitrary Shape’, unpublished Work, Dept. of Civil and Structural Eng., University College, Cardiff, Wales.
[6] ’Kombination eines Integralgleichungs verfahrens mil Methode der Finiten Elementen zur berechnung ebener Spennungs Konzentrations probleme’, Ph.D. Thesis. University of München, 1974.
[7] ’Linear Wave Propagation Problems and the Finite Element Method’, Ch. 13, Finite Element Methods in Fluid Mechanics (Ed.) R. H. Gallagher, J. T. Oden, C. Taylor and O. C. Zienkiewicz 1975.
[8] Berkhoff, Proc. 13th Coastal Eng. Conference I pp 471– (1973)
[9] Boissenot, Revue de Physique Appliquee 9 pp 611– (1974)
[10] ’Wave Action on Large Offshore Structures’, Conference on Offshore Structures, I.C.E. 7-14, 7-8 Oct., 1974.
[11] ’The application of Integral Equation Methods to Continuum Problems in Soil Mechanics’, Roscoe Memorial Symposium, Cambridge, 573-587, 1971.
[12] Butterfield, Geotechnique 21 pp 43– (1971)
[13] Butterfield, Geotechnique 21 pp 135– (1971)
[14] Butterfield, Geotechnique 20 pp 100– (1970)
[15] Butterfield, Geotech. Eng., Jn. S. E. Asian Soc. Soil Eng. U2 pp 35– (1971)
[16] Butterfield, International Conference on Variational Methods in Engng II (1972)
[17] Chang, J. Heat and Mass Trans. 16 pp 1905– (1973)
[18] and , ’Oscillations and Wave Forces in a Man-Made Harbor in Open Sea’, (Presented 10th Naval Hydrodynamics Symposium, June 1974). Dept. of Civil Eng., Mass. Inst. Tech., Cambridge, Mass.
[19] and , ’Oscillations and Wave Forces in an Offshore Harbor; Applications of Hybrid Finite Element Method to Water-Wave Scattering’, Ralph M. Parsons Laboratory for Water Resources & Hydrodynamics, Rep. No. 190, Cambridge, Mass. August 1974.
[20] Courant, Bull. Am. Maths. Soc. 49 pp 1– (1943)
[21] ’The Direct Potential Method in Three-dimensional Elasto-statics’, SM-13, Dept. of Mech. Eng., Carnegie-Mellon University, 1968.
[22] Cruse, J. Math. Anal. Appl. 22 pp 341– (1968)
[23] Cruse, Int. J. Solids Struct. 5 pp 1259– (1969)
[24] Chapter 4 (unpublished book). Two Dimensional Anisotropic Boundary-Integral Equation Method.
[25] ’Some Classical Elastic Sphere Problems Solved Numerically by Integral Equations’, J. Appl. Mech. 272-274 March 1972.
[26] private correspondence, Pratt & Whitney Aircraft, 9 Dec. 1974.
[27] Cruse, J. Comp. & Struct. 3 pp 509– (1973)
[28] ’Application of the Boundary-Integral Equation Method in Solid Mechanics’, Variational Methods in Engineering Vol. II. Proceedings of an International Conference on Variational Methods in Engineering, Southampton, Sept. 1972.
[29] Cruse, J. Math. Anal. Appl. 22 pp 244– (1968)
[30] Cruse, ASME Proc. AMD 11 (1975)
[31] and , ’Interactive Program for Analysis and Design Problems in Advanced Composites Technology’, AFML-TR-71-268, 1971.
[32] Cruse, Int. J. Fract. Mech. 7 pp 1– (1971)
[33] and , ’The Care and Treatment of Singularities in the Finite-Element Method’,
[34] and , Introduction to the Finite Element Method: A Numerical Method for Engineering Analysis, Van Nostrand Reinhold Co., New York, 1972.
[35] and , ’The Integral Formulation of Boundary Value Problems’, Variational Methods in Engineering Vol. II, Proc. Int. Conf. Variational Meth. Engng, Southampton, Sept. 1972.
[36] Finite Element Analysis of Prob. Formulated by an Integral Equation; Application to Potential Flow, Institut für Statik & Dynamik der Luft-und Raumfahrtkonstruktionene, Universität Stuttgart, Oct. 1968.
[37] ’F.E.M. In Fluid Dynamics and Heat Transfer’, ISD-Report 38, April, 1967.
[38] Garrison, Proc. ASCE 98 pp 375– (1972)
[39] and , ’Stress Intensity Factors by Boundary Collocation for Single-Edge-Notch Specimens subject to Splitting Forces’, NASA TN D-2395, 1966.
[40] Hess, Computer Methods in Applied Mech. & Eng. 2 pp 1– (1973)
[41] Hess, Comp. Meth. Appl. Mech. and Eng. 5 pp 145– (1975)
[42] Jaswon, Proc. Roy. Soc., Series A. 275 pp 23– (1963)
[43] Jaswon, Proc. Roy. Soc. Series A 273 pp 237– (1963)
[44] ’Calculation of Pressure Distribution on Airship Hulls’. NACA TM 574 (1930).
[45] and , ’On Boundary Value Problems of Elasticity’, Res. Rep. Fac. Eng. Meiji Univ. No. 8, 1956.
[46] Kikuchi, Nuclear Eng. and Design 21 pp 95– (1972)
[47] Potential Methods in the Theory of Elasticity, Davey, New York, 1965.
[48] Kupradze, Usp. Matem. Nauk 8 (1953)
[49] and , ’A Second Generation Boundary Integral Equation Program for three-dimensional elastic analysis’, ASME Conf. on Integral Equation Methods, New York, 23-25, June, 1975.
[50] Lachat, ASME Proc. AMD 11 (1975)
[51] ’A Further Development of the Boundary-Integral Technique for Elastostatics’, Ph.D. thesis, University of Southampton, 1975.
[52] Lachat, Int. J. num. Meth. Engng 10 pp 991– (1976)
[53] and , ’Analysis of Shallow Shells by the Method of Point Matching’, Tech. Rep. AFFDL-TR-69-71, Air Force Flight Dynamics Lab., Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, 1971.
[54] Leissa, AIAA J. 7 pp 920– (1969)
[55] and , ’Further Studies in the Application of the Point Matching Technique to Plate Bending and other Harmonic and Biharmonic Boundary Value Problems’, Tech. Rep. AFFDL-TR-65-117, Air Force Flight Dynamics Lab., Research and Technology Div., Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, 1965.
[56] ’Numerical Use of Integral Procedures’, Stress Analysis. (Ed.) and Wiley, London, 1965.
[57] McDonald, IEEE Transactions on Microwave Theory and Techniques MTT-20 (1972)
[58] ’Boundary Integral Methods in Elasticity and Plasticity’, NASA Technical Note, NASA TN D-7418, 1973.
[59] Variational Methods in Mathematical Physics, MacMillan, New York, 1964. · Zbl 0119.19002
[60] and , Approximate Methods for Solution of Differential and Integral Equation, Elsevier, New York, 1967.
[61] Mindlin, J. Physics 77 pp 195– (1936)
[62] Mote, Int. J. num. Meth. Engng 3 pp 565– (1971)
[63] and , ’Plane Stress Analysis by a General Integral Method’, J. Eng. Mechanic Div. of Proc. of ASCE, 79-101, Feb. 1968.
[64] Papamechael, Comp. Meth. Appl. Mech. and Eng. 6 pp 175– (1975)
[65] Pian, Int. J. num. Meth. Engng 6 pp 3– (1969)
[66] The edge function method in elastostatic studies in numerical analysis, SCAIFE University Press, 1974.
[67] Quinlan, Proc. Roy. Soc. A 282 pp 208– (1964)
[68] Rizzo, Quart. Appl. Math. 25 pp 83– (1967)
[69] Rizzo, Int. J. Solids Struct. 5 pp 1161– (1968)
[70] Rizzo, AIAA J. 8 pp 2004– (1970)
[71] Silvester, Proc. IEE 118 pp 1743– (1971)
[72] Silvester, J. Comp. Phys. 8 pp 73– (1971)
[73] and , An Analysis of the Finite Element Method, Prentice-Hall Inc. Englewood Cliffs, New Jersey, 1973.
[74] Swedlow, Int. J. Solids Struct. 7 pp 1673– (1971)
[75] Symm, Proc. Roy. Soc. A 275 pp 33– (1963)
[76] ’Integral Equation Methods in Elasticity and Potential Theory’, NPL Report Ma51 (1964).
[77] Symm, Nuclear Instruments and Meth. 118 pp 605– (1974)
[78] ’Treatment of Singularities in the Solution of Laplace’s Equation by an Integral Equation Method’, NPL Report NAC 31 (1973).
[79] and , ’Solution of Laplace’s Equation in Two Dimensions’, NPL Report NAC 44 (1974).
[80] ’Numerical Analysis of Continuum Problems in Zoned Anisotropic Media’, Ph.D. thesis, Southampton University, 1972.
[81] Tong, Int. J. num. Meth. Engng 7 pp 297– (1973)
[82] ’The Indirect Potential Method for Three Dimensional Boundary Value Problems of Classical Elastic Equilibrium’, Res. Rpt. 68-1D7-MEKMA-R2 Westinghouse Research Laboratories, Pittsburg, 1968.
[83] ’A finite element method for the determination of non stationary temperature distribution and thermal deformation’, Proc. Conf. Matrix methods in Stationary Mechanics, Wright-Patterson Air Force Base, Ohio, 1965.
[84] Walsh, Int. J. Solids Struct. 7 pp 1333– (1971)
[85] Variational Methods in elasticity and plasticity, 2nd edn., Pergamon Press, Oxford, 1975.
[86] ’The Analysis of 3-D Problems of Elasticity by Integral Representation of Displacements’, Variational Methods in Eng. Vol. II, International Conference, Southampton, September, 1972.
[87] ’An Integral Representation of the Displacement of an Elastic Body’, Rpt. CE/18/1968, Southampton University, 1968.
[88] ’Analysis of Thick Shells with Holes by Using Integral Equation Method’, Ph.D. thesis, Southampton University, 1973.
[89] Winslow, J. Comp. Physics 1 pp 149– (1966)
[90] Wood, Int. J. num. Meth. Engng 10 pp 885– (1976)
[91] and , ’Finite Elements in the Solution of Field Problems’, The Engineer, 507-510, September, 1965.
[92] The Finite Element Method in Engineering Science, McGraw-Hill, London, 1971.
[93] Zienkiewicz, Finite Elements in Fluids 1 (1975)
[94] and , ’A Direct Coupling Scheme for the Boundary Integral Equation and Finite Element Methods’, Additional references.
[95] and , ’Wave Forces on Piles: A Diffraction Theory’, Inst. Eng. Res., Waves Investigation Lab., Series 3, Issue 334, Berkeley, California (1952).
[96] Numerical Methods that Work, Harper and Row, New York, 1970, pp. 410-430.
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