For a highly incompressible material the use of triangular elements in plane-strain finite-element analyses restricts the number of degrees of freedom. A computer programme is developed which uses quadrilateral elements, and various methods of reducing computation time are employed. A strain-energy function is proposed which will enable solutions to be obtained at strains well beyond those of linear classical elasticity theory.
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References
1.
LindleyP. B.‘Plane-stress analysis of rubber at high strains using finite elements’, J. Strain Analysis19716, 45–52.
2.
RivlinR. S.SaundersD. W.‘Cylindrical shear mountings’, Trans Instn Rubb. Ind.194924296–306.
3.
GentA. N.MeineckeE. A.‘Compression, bending and shear of bonded rubber blocks’, Polym. Engng Sci.197010, 48–53.
4.
GentA. N.LindleyP. B.‘The cómpression of bonded rubber blocks’, Proc. Instn mech. Engrs1959173, 111–23.
5.
WoodL. A.MartinG. M.‘Compressibility of natural rubber at pressures below 500 kg/cm2’J. Res. natn. Bur. Stand.196468A, 259–67.
6.
OdenJ. T.‘Finite plane strain of incompressible elastic solids by the finite element method’Aeronaut. Q.1968 (August), 254–64.
7.
HerrmannL. R.‘Elasticity equations for incompressible and nearly incompressible materials by a variational theorum’, A.I.A.A. JI19653, 1896–1900
8.
WilsonE. L.‘Finite element analysis of two-dimensional structures’, Report No. 63–2, Structure Engineering Laboratory, University of Californiia, 1963.
9.
ZienkiewiczO. C.CheungY. K.The finite element method in structural and continuum mechanics1967 (McGraw-Hill Book Co. Inc., New York and London).
10.
TreloarL. R. G.The physics of rubber elasticity 2nd edition 1958 Chapters 4 and 5 (Oxford University Press).
11.
TreloarL. R. G.‘Volume changes and mechanical anisotropy of strained rubbers’, Polymer196910, 279–89.
12.
LindleyP. B.‘Effect of Poisson's ratio on compression modulus’, J. Strain Analysis19683, 142–5.
