Conservation laws for 3-dimensional equations of anisotropic elasticity

В работе найдены законы сохранения для трехмерных стационарных уравнений упругости в случае общей анизотропии. Conservation Laws for 3-dimensional Stationary Equations in the Case of General Anosotropy are obtained in the work.

Determination of the anisotropic elasticity tensor by mechanical spectroscopy

A method is proposed to identify the fully anisotropic elasticity tensor by applying the impulse excitation technique. A specially designed batch of several differently oriented bar-shaped specimens with rectangular cross section is analyzed with respect to the eigenfrequencies of their fundamental flexural and torsional modes. Estimations based on the equations for the calculation of the isotropic Young’s modulus and the shear modulus from the ASTM standard allow a first approximation of the elasticity tensor from a selected subset of the measured eigenfrequencies. Subsequently, a more precise determination of the elasticity tensor is achieved by a numerical modal analysis using the finite element method. In this course, a Newton–Raphson optimization method is applied to solve the inverse problem. The proposed approach is demonstrated on a batch of specimen fabricated from the nickel-base alloy IN718 by selective laser melting.

Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism

The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out.

Calculation method of belt material parameters for finite element tire model

The radial tire belt is composed of multi-layered fiber-reinforced cords with a very complex structure. Restricted by the computing speed, the simplified finite element (FE) tire model with equivalent belt is usually applied in the vehicle dynamic simulation. However, it is always difficult to obtain the material parameters of the equivalent belt. In this paper, a calculation method of equivalent belt material parameters for the simplified FE tire model is proposed based on the three-dimensional (3-D) anisotropic elasticity of the cord reinforced composites. The simulation results of the static radial stiffness, modal characteristics, and dynamic responses for the simplified FE tire model with parameters obtained by the calculation method were compared with experiment results. The results show that the deviation between the experiment and simulation is acceptable, and the validity of the calculation method is verified.

On Eshelby’s inclusion problem in nonlinear anisotropic elasticity

In this paper, the recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby’s inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of combined finite radial, azimuthal, axial and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed. The same problem for a finite circular cylindrical bar is revisited. The stress and deformation fields of an orthotropic incompressible solid circular cylinder with distributed eigentwists are analyzed.