caa a22 4500 397572492 CHVBK 20180308164845.0 cr unu---uuuuu 161202e199602 xx s 000 0 eng 10.1093/qjmam/49.1.19 doi (NATIONALLICENCE)oxford-10.1093/qjmam/49.1.19 ON AXIALLY SYMMETRIC DEFORMATIONS OF PERFECTLY ELASTIC COMPRESSIBLE MATERIALS [Elektronische Daten] [JAMES M. HILL, DANIEL J. ARRIGO] The governing partial differential equations for static deformations of homogeneous isotropic compressible hyperelastic materials (sometimes referred to simply as perfectly elastic materials) are highly nonlinear and consequently only a few exact solutions are known. For these materials, only one general solution is known which is for plane deformations and is applicable to the so-called harmonic materials originally introduced by John. In this paper we extend this result to axially symmetric deformations of perfectly elastic harmonic materials. The results presented hinge on a reformulation of the equilibrium equations and a similar procedure can be exploited to derive the known solution due to John. It is shown that axially symmetric deformations of a harmonic material can be reduced to two linear equations whose coefficients involve the partial derivatives of an arbitrary harmonic function ω(R, Z). For any harmonic material, this linear system admits a simple general solution for the two special cases ω = ω(R) and ω = ω(Z). For the ‘linear-elastic' strain-energy function, the linear system is shown to admit a general solution for the two harmonic functions which, in spherical polar coordinates, arise from the assumptions of spherical and radial symmetry. © Oxford University Press Articles nationallicence HILL JAMES M. Department of Mathematics, University of Wollongong, Wollongong, NSW 2500, Australia aut ARRIGO DANIEL J. Department of Mathematics, University of Wollongong, Wollongong, NSW 2500, Australia aut The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 49/1(1996-02), 19-28 0033-5614 49:1<19 1996 49 qjmamj https://doi.org/10.1093/qjmam/49.1.19 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1093/qjmam/49.1.19 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- HILL JAMES M. Department of Mathematics, University of Wollongong, Wollongong, NSW 2500, Australia aut NATIONALLICENCE 700 1- ARRIGO DANIEL J. Department of Mathematics, University of Wollongong, Wollongong, NSW 2500, Australia aut NATIONALLICENCE 773 0- The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 49/1(1996-02), 19-28 0033-5614 49:1<19 1996 49 qjmamj Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford