The torsion of a prismatic beam has been a classic problem of structural mechanics since the famous works of Saint-Venant. In this paper, an analysis is extended on a composite beam with elliptical cross-section. We consider a beam in which the elliptical cross-section is split into sectors in which two materials, one of which is auxetic, are distributed alternately. The influence of auxetic phase on the total elastic strain energy is analyzed as well as geometrical parameters representing both the shape of the cross-section, and the arrangements of sectors. An unexpected behavior of a beam with strong auxetic phase is presented as, in the case of selected parameters, the beam with elliptical crosssection is more rigid than the beam with a circular one.
In the paper, a numerical simulation of the Beavers-Joseph experiment is presented. The simulation is based on a meshless method which is called the Trefftz method with the special purpose Trefftz functions. The porous medium is modeled as a regular array of fibers. Three kinds of arrays are taken under consideration: triangular, square, and hexagonal. Firstly, the permeability of the fibrous porous medium is determined by consideration of flow between an infinite array of fibers. In the next step the considered region is divided into two parts. The first half of the channel is a porous medium modeled by a regular array of fibers and the second part which is a free fluid flow region. In the paper, the slip constant existing in the Beavers-Joseph boundary condition is determined in terms of the volume fraction of fibers.
This paper considers the torsional stiffness of long bones. The phenomenon of long-bone twisting is a boundary value problem. We propose to solve the problem by a numerical procedure based on a meshfree method, the method of fundamental solutions.
The aim of this study is implementation of the Homotopy Analysis Method (HAM) and the Method of Fundamental Solution (MFS) for solving a torsion problem of functionally graded orthotropic bars. The boundary value problem is formulated for the Prandtl's stress function, described by partial differential equation of second order with variable coefficients and appropriate boundary conditions. In the solving process the HAM is used to convert nonlinear equation into a linear one with known fundamental solutions. The Method of Fundamental Solutions supported by Radial Basis Functions and Monomials is suggested for calculate this linear boundary value problem. The numerical experiment has been performed to check the accuracy and the convergence of the presented method.
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