M.E. Ergüven

Evaluation of sloshing problem by variational boundary element method

In this study, a Variational Boundary Element Method (VBEM) based on the Hamiltons principle that produces symmetric matrices is presented. The effect of a rigid baffle on the natural frequencies of the liquid in a cylindrical rigid container is then investigated by the use of VBEM. Boundary integral equations are regularized by moving the singular points outside the domain. Fluid motion is assumed to be irrotational, incompressible and inviscid. Linearized free surface conditions are taken into consideration.

On the penny-shaped crack in inhomogeneous elastic materials under normal extension

Abstract The solution of the problem of a penny-shaped crack in an inhomogeneous material with elastic coefficients which are varying continuously along the direction perpendicular to the crack is examined in this paper. We studied the problem for an inhomogeneous material which satisfies the conditions of either torsional deformation and normal extension. A series form solution to the problem is proposed and analytical expressions for the first two terms of the series are obtained by using a Hankel transform technique. In the solution a homogeneous body is chosen as the reference so that inhomogeneous quantities are treated as being perturbed from the zeros reference solutions. Closed form expressions for the relevant stress intensity factors and the crack energy are derived and specific cases of the problem are also considered.

An axisymmetric fundamental solution and the Reissner-Sagoci problem for an internally loaded non-homogeneous transversely isotropic half-space

Abstract This paper employs the concept of a ring of sources or forces using the Hankel transform and Fourier cosine transform to derive the axisymmetric fundamental solution for transversely isotropic nonhomogeneous materials in the case of torsional loads. These fundamental solutions determine the kernel functions used in the Boundary Integral Equation method and Body Force Method. Making use of the axisymmetric fundamental solution we consider the classical Reissner-Sagoci problem related to an elastic non-homogeneous transversely isotropic half-space region in which the rotation of the bonded circular disk is induced by a concentrated couple is located along the axis of symmetry and acts at a finite distance from surface. The rotation of bonded rigid disk due to the internally applied concentrated couple is evaluated. Special cases are examined.

A fundamental solution for transversely isotropic and nonhomogeneous media

Abstract The purpose of this paper is to consider the concept of a ring of sources or forces using the integral transform techniques to derive the axisymmetric fundamental solution for nonhomogeneous transversely isotropic elastic media. Firstly, the formulation of the problem in homogeneous media to derive the fundamental solutions is shown. In the case of a nonhomogeneous medium, the shear modulus of the material varies with the z-coordinate exponentially.

Container structures on a Vlasov foundation with variable soil characteristics

Abstract In this study container structures such as cylindrical vessels which have a flat or shallow spherical shell bottom on a Vlasov foundation with variable soil characteristics, are investigated. The variation of the soils elastic modulus is assumed exponential along the depth of soil layer. Interaction between superstructure, foundation and soil is taken into account. The loading is considered as axisymmetric relative to the center of the bottom. The solution is achieved using the flexibility method, in which the wall is represented by distributed loads and moments along the circumference of the bottom. Some parametrical results are obtained for various soil layer depth-to-bottom radius ratios and comparisons are made between exponential and the other variations of the soils elastic modulus.

Interaction between cylindrical and shallow spherical shells on the vlasov model foundation

Abstract In this study, the problems of shallow spherical shells on the Vlasov model and single-layer elastic foundations are investigated. The problems of axisymmetrical deformation of spherical shells on elastic single-layer foundations have also been considered. The external loads have been applied symmetrically relative to the shell centre. The differential equation of the shell has been solved according to the Bessel and Hankel functions, then constants of integration have been calculated from boundary and continuity conditions. This method has been applied to the analysis of the bottoms of cylindrical reservoirs. For the effect of the cylindrical reservoir walls on the strains of the bottom the method of flexibility has been used. Some of the results from the Vlasov model have been compared to the Winkler model and elastic half-space.

Torsion of a transversely isotropic elastic layer bonded to a transversely isotropic half-space

Abstract Torsional stresses and displacement of a transversely isotropic elastic layer of finite thickness for which torsional shearing forces are prescribed on its boundary surface are considered. The solutions are given for a few particular cases.