Stress and Strain Definition of an Open Profile Thin-Walled Beam at Constrained Torsion by Boundary Element Method

2012 ◽  
Vol 42 (2) ◽  
pp. 43-54
Author(s):  
Zlatko Zlatanov
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Stress And Strain ◽  
One Dimensional ◽  
Open Profile ◽  
Linear Algebraic Equations ◽  
Thin Walled ◽  
Definition Of ◽  
Constrained Torsion ◽  
Element Method

Stress and Strain Definition of an Open Profile Thin-Walled Beam at Constrained Torsion by Boundary Element Method Thin-walled beams with open profile at constrained torsion are investigated in this paper. A thin-walled beam loaded by an external bi-moment at constrained torsion is investigated in this paper. An analytical variant of the boundary element method (BEM) is presented, which is based on a new scheme of the integral ratios transformation of the initial parameters method in a system of linear algebraic equations. Only one dimensional integrals are used defining the one dimensional continuum.

Sound Radiation by a Point Source Near a Surface of Aircraft

2020 ◽  
pp. 17-25
Author(s):  
Natalia K. Musatova ◽  
Mezhlum A. Sumbatyan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Physical Theory ◽  
Acoustic Pressure ◽  
Sound Radiation ◽  
Hankel Function ◽  
Ray Theory ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Element Method

The problem of sound radiation by a source located in the tail of an aircraft is considered. Three methods of finding acoustic pressure are compared: the boundary element method, the Kirchhoff’s physical theory of diffraction and the ray theory. The simplest model in the form of two-dimensional problem and some thin long shape with acute angle is considered. The diffraction problem for an acoustically solid obstacle lay in the solving Fredholm’s integral equation of the second kind. Due to the boundary element method application, the equation along the entire region is reduced to the equation along the boundary. Discretization by grid nodes, selected on the boundary curve, using the collocation method is applied for numerical solution. A system of linear algebraic equations with real coefficients is formed, then the total acoustic pressure is found. The Kirchhoff’s physical theory of diffraction is based on the fact that on an arbitrary convex body in case of short-wave diffraction in the vicinity of each boundary point in the zone of light the boundary value of pressure is equal to twice pressures in the incident field. By the ray theory the modulus of the acoustic pressure in the scattering field is described by the Hankel function. Argument of this function is equal to the length of full path of the beam when it is reflected once from the border. In conclusion, the pressure in cases, when in the sharp edge there is a split node and when there isn’t, are compared. Also a scattering field calculated by three theories and scattering field in the far receiving point are built.

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