Elastic Deformations of Constrained Cylinders

Abstract

The boundary-value problem for a constrained elastic cylinder under axial load is solved for the correct boundary conditions, in terms of set of infinite orthogonal Bessel and trigonometric functions. The orthogonality conditions are chosen on the basis of surface deformations noted during the experiments. Analysis is used in predicting apparent modulus for materials and compared with available experimental data. The agreement is found to be extremely good. The influence of Poisson’s ratio on apparent modulus is discussed.

Analytical Elastic Solution Based on Fourier Series for a Laterally Confined Granular Column

“…(14b). The stress and displacement fields of II S are derived from a potential approach whose derivation and various other applications are described extensively in previous contributions [see Love (1944); Timoshenko and Goodier (1970); Moghe and Neff (1971); and Little (1973)…”

Electroelastic field of a piezoelectric annular finite cylinder

“…An isotropic finite cylinder under axial compression was analyzed by Pickett (1944) by using a multiple Fourier-Bessel series solution. A similar analysis for a constrained cylinder under end compression was done by Moghe and Neff (1971). Power and Childs (1971) presented a solution for an isotropic circular bar of finite length subjected to axi-symmetric tractions and/or displacements on either or both ends.…”

Finite and transversely isotropic elastic cylinders under compression with end constraint induced by friction

“…Filon (1902) analyzed theoretically the non-uniform elastic stress distribution within a finite cylinder when the radial displacement of the two end surfaces is perfectly constrained. Since then the solution of non-uniform stress distribution has been improved by many researchers, including Pickett (1944), Balla (1960a,b), Peng (1971Peng ( , 1973, Al-Chalabi (1972), Brady (1971a,b), Moghe and Neff (1971), , , and Watanabe (1996). For more general cases of non-axisymmetric boundary conditions, Chau and Wei (2000) provided a general solution framework for finite isotropic cylinders.…”

“…Among previous theoretical studies, Filon (1902), Moore (1966), Edelman (1949), Moghe and Neff (1971), Nayak (1974) and Chau (1997) considered the correction factor for estimating the ''true Young's modulus" which is needed to multiply to the ''apparent Young's modulus" (which can be obtained by assuming a uniform stress distribution within a cylinder). Experimental studies by Gent and Lindley (1959) on highly elastic rubber blocks show that the apparent Young's modulus may differ significantly from the true Young's modulus, depending on the shape or aspect ratio of the blocks.…”