Transverse decay of solutions in an elastic cylinder
The authors consider a semi-infinite cylinder of bounded cross-section of anisotropic, inhomogeneous and linearized elastic material. The lateral surface is clamped, and a load is prescribed pointwise on the base. The stresses and strains are assumed to be bounded at asymptotically large axial distances. The authors investigate the transverse radial decay of the solution as measured by the strain energy in a region close to the cylinder's axis compared to the strain energy in a region near the lateral surface where the energy vanishes. An estimate is obtained for the strain energy contained in an annulus at a given distance from the base and of variable radius, the outer boundary of which lies on the lateral surface of the cylinder. It is shown that the strain energy decays at most algebraically to zero as the inner radius of the annulus tends to the radius of the cylinder. The validity of this result is illustrated by the example of simple torsion in an isotropic elastic material. The results obtained by the authors are shown to be in a good agreement with available explicit solutions for the torsion problem.
scientific article; zbMATH DE number 1323042