Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

Determination of shrinkage of weld

A calculation-experimental technique of determination of weld shrinkage is described in that work. Experimentally, with the help of strain gauges, residual stresses are determined at two points, which are at known distances from the weld. Shrinkages are found out from the theoretical solution of the plane elasticity theory about the insertion of bodies with interference. Calculations have been carried out for experimental studies of a weld 400 mm long for different thicknesses of metal. It is found that when the thickness of the metal increases, the shrinkage values also increase. This is due to the fact that as the thickness of the metal increases, the heat input required to penetrate it also increases.

Complete Williams Asymptotic Expansion near the Crack Tips of Collinear Cracks of Equal Lengths in an Infinite Plane

The present study is aimed at analytical determination of coefficients in crack tip expansion for two collinear finite cracks of equal lengths in an infinite plane medium. The study is based on the solutions of the complex variable theory in plane elasticity theory. The analytical dependence of the coefficients on the geometrical parameters and the applied loads for two finite cracks in an infinite plane medium is given. It is shown that the effect of the higher order terms of the Williams series expansion becomes more considerable at large distances from the crack tips. The knowledge of more terms of the stress asymptotic expansions allows us to approximate the stress field near the crack tips with high accuracy.

Free vibration analysis of functionally graded beams using an exact plane elasticity approach

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.