Cosserat Spectrum of an Axisymmetric Elasticity Problem for a Finite-Length Solid Cylinder

ABSTRACTAn algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attention given to the effect of the cylinder aspect ratio.

L q-solutions to the Cosserat spectrum in bounded and exterior domains

SummaryIfλ = 1 is an eigenvalue of infinite multiplicity and λ = 2 is an accumulation point of eigenvalues of finite multiplicity. For the

The weak Lq-Cosserat spectrum for the first boundary value problem in the half-space. Applications to Stokes' and Lamé's system

SummaryIn the upper half-space

An operator related to the Cosserat spectrum. Applications

SummaryIf

Application of the Cosserat Spectrum Theory to Stokes Flow

This paper presents an application of the Cosserat spectrum theory in elasticity to the solution of low Reynolds number (Stokes flow) problems. The velocity field is divided into two components: a solution to the vector Laplace equation and a solution associated with the discrete Cosserat eigenvectors. Analytical solutions are presented for the Stokes flow past a sphere with uniform, extensional, and linear shear freestream profiles.