High-Order Numerical Scheme for Vortex Layer Intensity Computation in Two-Dimensional Aerohydrodynamics Problems Solved by Vortex Element Method

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy, and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique. The scaled boundary finite element equations are formulated within a general framework integrating the influence of the distributed body source, mixed boundary conditions, contributions the side face with either prescribed surface load or prescribed displacement. The position of scaling center is considered for modeling problem. The proposed method is evaluated by solving two-dimensional linear problem. A selected set of results is reported to demonstrate the accuracy and convergence of the proposed method for solving problems in general boundary conditions.

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Reduction of stress concentration around a hole in a uniaxially loaded plate

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247v182135 ◽

1983 ◽

Vol 18 (2) ◽

pp. 135-141 ◽

Cited By ~ 22

Author(s):

U C Jindal

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Stress Concentration ◽

Circular Hole ◽

High Order ◽

Two Dimensional ◽

The Finite Element Method ◽

Loaded Plate ◽

Hole Geometry ◽

Element Method

The stress concentration around a circular hole in a plate can be reduced by up to 21 per cent by introducing auxiliary holes on either side of the original hole. But this approach of auxiliary holes creates two more regions of stress concentration in the plate. In the present study, the hole geometry has been modified to effect stress reductions as high as 22 per cent. The problem has been analysed numerically by the finite element method and experimentally by two-dimensional photoelasticity. It has been observed that by making the hole oblong in the direction of loading, a high order of reduction in stress concentration around the hole can be obtained.

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A high-order numerical scheme using orthogonal spline collocation for solving the two-dimensional fractional reaction–subdiffusion equation

Advances in Difference Equations ◽

10.1186/s13662-019-2022-7 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 2

Author(s):

Xiaoyong Xu ◽

Da Xu

Keyword(s):

Numerical Scheme ◽

High Order ◽

Two Dimensional ◽

Spline Collocation ◽

Orthogonal Spline Collocation ◽

Subdiffusion Equation ◽

Fractional Reaction

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Development of a Virtual Two-Dimensional Wind Tunnel Using a Vortex Element Method

Volume 2: Symposia, Parts A, B, and C ◽

10.1115/fedsm2003-45446 ◽

2003 ◽

Author(s):

Hideaki Shono ◽

Akira Ojima ◽

Kyoji Kamemoto

Keyword(s):

Wind Tunnel ◽

Numerical Procedure ◽

Numerical Data ◽

Bluff Bodies ◽

Two Dimensional ◽

Mathematical Basis ◽

Vortex Element ◽

Unsteady Characteristics ◽

Lift And Drag ◽

Element Method

This paper describes the work of development of a virtual two-dimensional wind tunnel using a vortex element method carried by the authors group, explaining the mathematical basis of the method and structure of the virtual wind tunnel. Following the development of an advanced vortex element method, the authors proceeded to development of a virtual wind tunnel, which provides a useful tool for researchers, designers and teaching staffs in the field of fluid dynamics. As the first step of the development, construction of a two-dimensional wind tunnel has been studied. The 2-D wind tunnel works on a PC, and it has such attractive features that once a user prepares a set of numerical data of two-dimensional bodies, he or she can begin immediately unsteady calculation of a flow around either an isolated body or multiple bodies in a uniform flow without any grid-generation work. The calculation provides unsteady characteristics of lift and drag coefficients acting on each body and instantaneous flow patters visualized by distribution of vortex elements. In this paper, the numerical procedure of the vortex element method and structure of the virtual wind tunnel are briefly explained. And typical results of two-dimensional and unsteady calculation of flows around bluff bodies will be demonstrated.

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