Elastic torsion of bars possessing regular polygon in cross-section using BCM

Kołodziej, Jan Adam; Fraska, Agnieszka

doi:10.1016/j.compstruc.2005.03.015

Cited by 19 publications

(15 citation statements)

References 31 publications

(42 reference statements)

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“…A particular case of the Trefftz method is the Trefftz method with the special purpose Trefftz functions in which the trial functions are chosen in such a way that they satisfy not only the governing equations but also some of the boundary conditions. It has been developed in some previous papers [25][26][27][28][29][30].…”

Section: The Trefftz Methodsmentioning

confidence: 99%

Determination of the Slip Constant in the Beavers‐Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method

Mierzwiczak

Fraska

Grabski

2019

Mathematical Problems in Engineering

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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.

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Section: The Trefftz Methodsmentioning

confidence: 99%

Determination of the Slip Constant in the Beavers‐Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method

Mierzwiczak

Fraska

Grabski

2019

Mathematical Problems in Engineering

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“…For tapered beam/column analysis, various taper functions [3,12,13] along the column axis, including linear, parabolic, sinusoidal, and exponential functions, have been considered. The effects of various cross-sectional shapes [14,15], including rectangular, circular, elliptical, and regular polygons, on the optimization of column buckling have been examined. Additionally, the initial imperfection affecting column behavior was discussed in the open literature [16,17].…”

Section: Introductionmentioning

confidence: 99%

Buckling of Tapered Heavy Columns with Constant Volume

Lee

2021

Mathematics

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This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

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“…He solved the problem numerically by the finite element method. The torsion problem is an important and basic subject and it is still a subject of research (Reagan and Pilkey, 2002;Sapountzakis and Mokos, 2004;Chen, 2004;Kolodziej and Fraska, 2005).…”

Section: Introductionmentioning

confidence: 99%