Abstract
A closed form solution to the second order clasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed normal load, is presented. The method of integral transform is emploved and the case when loading is distributed, in accordance with Hertz's law, is discussed. The limiting solution for mcompressible isotropic clastic material is also derived. Numerical calculattons for the second order clastic material for the displacement and the normal stress in the z-direction are carried out. It is found that, in comparison to the linear elastic case, the displacement increases and the normal stress decreases in the second order clastic matierial.
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Rivlin, R. S., The solution of problems in second order elasticity theory.J. Ration. Mech. Analysis,2 (1953). 52.
Green, A. E. and E. B. Spratt. Second order effect in the deformation of clastic solids.Proc. R. Soc. London.A224 (1954). 347.
Truesdell, C. A. and W. Noll. The nonlinear field theories of mechanics.Handbuch der Physik (Ed. S. Flugge), Vol. III/3, Springer-Verlag, Berlin (1965).
Green, A. E. and J. E. Adkins,Large Elastic Deformations (2nd ed.). Oxford University Press (1970).
Goodman, W. H. and P. M. Naghdi. The use of displacement potentials in second order elasticity.J. Elasticity. 22 (1989), 25.
Chan, C. and D. F. Carlson. Second order incompressible elastic torsion.Int. J. Engrg. Sci.,8 (1970), 415.
Selvadurai, A. P. S. and A. J. M. Spencer. Second-order elasticity with axial symmetry-I. General theory,Int. J. Engrg. Sci. 10 (1972), 97.
Carroll, M. M. and F. J. Rooney. Simplification of the second-order problem for incompressible clastic solids.Q. J. Mech. Appl. Math.,37 (1984), 261.
Choi, I. and R. T. Shield, Second-order effects in problems for a class of elastic materials.Z. Angen. Math. Phys.,32 (1981), 361.
Signorni, A., Transformazioni termoelastiche finite.Annali Mat. Pure Appl.,30 (1949). 10.
Stoppeli, F., Un teorema di esistenza e di unicita relativo alle equazioni dell'elastostatica isoterma per deformazioni finite.Ricerche Mat.,3 (1954), 247–267.
Stoppeli, F., Sulla svilluppabilita in serie di potenze di un parametro delle soluzioni delle equazioni dell'elastostatica isoterma.Ric. Mat.,4 (1955), 58–73.
Sneddon, I. N.,The Use of Transform Methods in Elasticity. Tech. Report.AFOSR 64-1789, North Carolina State University. Rayletgh. N. C. (1964).
Cerruti, V., Rierehe intono all equilibrie de corpi elastici isotropi.Atti. Accord. Nazl. Lincet. Mc Classe. Sct. Fis. Met. Nat.,13 (1882), 81.
Gradshteyn, I. S. and I. M. Ryzhik.Tables of Integrals, Series and Products, Academic Press. New York (1965).
Guo, J., Second order effects in an elastic half-space acted upon by non-uniform loads. Master thesis. Department of Mathematics and Statistics. University of Windsor (1992).
Sneddon, I. N., On Muki's solutions of the equation of linear elasticity.Int. J. Engrg. Sci.,30 (1992), 1237.
Murnaghan, F. D., Finite deformation of an elastic solid.Amer. J. Math.,59 (1937). 235.
Foux, A., An experimental investigation of the poynting effect.Second-Order Effects in Elasticity. Plasticity and Fluid Dynamics. International Symposium. Haifa, Israel. April 23–27 (1962).
Haines, D. W. and W. D. Wilson. Strain-energy density function for rubber like material.J. Math. Phys. Solids. 27 (1979). 345.
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Communicated by Fan Ta-chung
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You-wen, L., Jian-lin, G. Second order effects in an elastic half-space acted upon by a non-uniform normal load. Appl Math Mech 15, 1149–1168 (1994). https://doi.org/10.1007/BF02451986
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DOI: https://doi.org/10.1007/BF02451986