Analytical solutions and material tailoring for combined radial expansion and twisting of functionally graded orthotropic hollow cylinders

Abstract

Assuming that material properties are described by the same function of the radius, we first analytically find the displacement field in a functionally graded, orthotropic and linearly elastic hollow cylinder undergoing combined radial expansion and twisting. Subsequently, either for a desired axisymmetric displacement field or a stress distribution, we determine the required variations of the material properties to produce them in an inhomogeneous orthotropic cylinder. Numerical results presented for four example problems reveal the possibility of suitably varying material properties in the radial direction to simultaneously minimize the structural mass and the maximum circumferential stress on the inner surface of a hollow cylinder. It is found that out of the three heterogeneous cylinders of the same geometric and material parameters, the one having the least mass also has the smallest value of the maximum circumferential stress on the cylinder's inner surface. It occurs when the material moduli essentially vary affinely through the cylinder thickness. The analytical solutions presented here can serve as benchmarks for others to verify their numerical algorithms.