Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

High-resolution analysis of the complex wave spectrum in a cylindrical shell containing a viscoelastic medium. Part I. Theory and numerical results

Abstract: In this study the relation between frequency and complex wave number of axisymmetric wave modes in an isotropic, thin-walled, cylindrical shell containing a linear viscoelastic medium is derived. Shell wall bending and longitudinal motion are coupled in an empty cylindrical shell. When a viscoelastic medium is enclosed, the shell motion is affected by the complex bulk and shear modulus, as well as by the density of the medium enclosed. A Maxwell model is used for both complex Lame constants λ and μ to describe the constitutive equations of the medium. By varying the complex moduli, the medium can be modeled as an inviscid fluid, an elastic material, or anything between these two extremes. The interaction of the thin-walled linear elastic shell and the viscoelastic medium is discussed numerically by calculating the complex dispersion relation. Numerical results are presented for an empty shell and a shell filled with three types of core material: an inviscid fluid, a shear dissipative fluid, and a shear elastic fluid. In a companion paper [J. Vollmann et al., J. Acoust. Soc. Am. 102, 909–920 (1997)], the experimental setup and the signal processing used to perform the high-resolution measurement of the dispersion relation are described in detail. Theoretical and experimental results are compared.

A new nonconforming mixed finite element method for linear elasticity

Abstract: We have developed new nonconforming mixed finite element methods for linear elasticity with a pure traction (displacement) boundary condition based on the Hellinger–Reissner variational principle using rectangular elements. Convergence analysis yields an optimal (suboptimal) convergence rate of for the L2-error of the stress and for the displacement in the pure traction (displacement) boundary problem. However, numerical experiments have yielded optimal-order convergence rates for both stress and displacement in both problems and have shown superconvergence for the displacement at the midpoint of each element. Moreover, we observed that the optimal convergence rates are still valid for large λ.

Errors Associated with Flexure Testing of Brittle Materials

Abstract: : Requirements for accurate bend-testing of four-point and three-point beams of rectangular cross-section are outlined. The so-called simple beam theory assumptions are examined to yield beam geometry ratios that will result in minimum error when utilizing elasticity theory. Factors that give rise to additional errors when determining bend strength are examined, such as: wedging stress, contact stress, load mislocation, beam twisting, friction at beam contact points, contact point tangency shift, and neglect of corner radii or chamfer in the stress determination. Also included are the appropriate Weibull strength relationships and an estimate of errors in the determination of the Weibull parameters based on sample size. Such analyses and results provide guidance for the accurate determination of flexure strength of brittle materials within the linear elastic regime. Error tables resulting from these analyses are presented.