On the surface displacement of an isotropic elastic halfspace containing an inextensible membrane reinforcement. (English) Zbl 1257.74035
Summary: This paper examines the axisymmetric problem of the uniform circular surface loading of an isotropic elastic halfspace, which is internally reinforced with an inextensible membrane of finite extent.
Keywords:
reinforced halfspace; elastic deformations; inextensible reinforcement; mixed boundary value problem; dual integral equations; Fredholm integral equations; surface displacementReferences:
| [1] | Westergaard, H.M. A problem of elasticity suggested by a problem in soil mechanics: soft material reinforced by numerous strong horizontal sheets, in Contributions to the Mechanics of Solids, dedicated to Stephen Timoshenko by his Friends on the Occasion of his Sixtieth Birthday Anniversary, MacMillan, New York , pp. 268-277, 1938. |
| [2] | Wieghardt, K., Zeitschrift für Angewandte Mathematik und Mechanik 2 pp 165– (1922) · JFM 48.0930.04 · doi:10.1002/zamm.19220020301 |
| [3] | Vlazov, V.Z., Structural Mechanics of Thin-Walled Three-Dimensional Systems (1949) |
| [4] | Selvadurai, A.P.S., Developments in Geotechnical Engineering 17 (1979) |
| [5] | Spencer, A.J.M., Deformations of Fibre Reinforced Materials (1972) · Zbl 0238.73001 |
| [6] | Barnett, D.M., Journal of Space-crafts and Rockets 38 pp 226– (2001) · doi:10.2514/2.3674 |
| [7] | Davis, R.O., Elasticity and Geomechanics (1996) |
| [8] | Selvadurai, A.P.S., Applied Mechanics Reviews 60 pp 87– (2007) · doi:10.1115/1.2730845 |
| [9] | Truesdell, C., Archive for Rational Mechanics and Analysis 4 pp 1– (1960) · doi:10.1007/BF00281376 |
| [10] | Gurtin, M.E., Linear Theory of Elasticity, in Handbuch der Physik, Vol. VIa/2, Mechanics of Solids II (1972) |
| [11] | Gladwell, G.M.L., Contact Problems in the Classical Theory of Elasticity (1980) · Zbl 0431.73094 · doi:10.1007/978-94-009-9127-9 |
| [12] | Barber, J.R., Elasticity (1992) · doi:10.1007/978-94-011-2454-6 |
| [13] | Green, A.E., Theoretical Elasticity (1968) · Zbl 0155.51801 |
| [14] | Sneddon, I.N., Fourier Transforms (1951) · Zbl 0038.26801 |
| [15] | Sneddon, I.N., Mixed Boundary Value Problems in Potential Theory (1966) · Zbl 0139.28801 |
| [16] | Baker, C.T.H., The Numerical Treatment of Integral Equations (1977) · Zbl 0373.65060 |
| [17] | Delves, L.M., Computational Methods for Integral Equations (1985) · Zbl 0592.65093 · doi:10.1017/CBO9780511569609 |
| [18] | Atkinson, K.E., The Numerical Solution of Integral Equations of the Second Kind (1997) · Zbl 0899.65077 · doi:10.1017/CBO9780511626340 |
| [19] | Selvadurai, A.P.S., Journal of Engineering Mathematics 37 pp 155– (2000) · Zbl 0973.74013 · doi:10.1023/A:1004782110718 |
| [20] | Selvadurai, A.P.S., Mathematics and Mechanics of Solids 5 pp 483– (2000) · Zbl 1169.74360 · doi:10.1177/108128650000500406 |
| [21] | Selvadurai, A.P.S., International Journal of Geomechanics 1 pp 149– (2001) · doi:10.1061/(ASCE)1532-3641(2001)1:2(149) |
| [22] | Selvadurai, A.P.S., Journal of Applied Mechanics, Transactions of the ASME 58 pp 362– (1991) · Zbl 0756.73043 · doi:10.1115/1.2897194 |
| [23] | Timoshenko, S.P., Theory of Elasticity (1970) · Zbl 0266.73008 |
| [24] | Westergaard, H.M., Theory of Elasticity and Plasticity (1952) · Zbl 0048.42103 · doi:10.4159/harvard.9780674436923 |
| [25] | Selvadurai, A.P.S., Partial Differential Equations in Mechanics. Vol. 2, The Biharmonic Equation and Poisson’s Equation (2000) · Zbl 0967.35002 · doi:10.1007/978-3-662-09205-7 |
| [26] | Selvadurai, A.P.S., International Journal of Engineering Science 39 pp 317– (2001) · Zbl 1210.35193 · doi:10.1016/S0020-7225(00)00043-4 |
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