Determining the stress state of shells of revolution with complex boundary conditions

1989 ◽  
Vol 25 (2) ◽  
pp. 127-132
Author(s):  
A. T. Vasilenko ◽  
Ya. M. Grigorenko
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Shells Of Revolution ◽  
Complex Boundary

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

Effects of complex boundary conditions on natural convection of a viscoplastic fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2792-2808 ◽  
Author(s):  
Behnam Rafiei ◽  
Hamed Masoumi ◽  
Mohammad Saeid Aghighi ◽  
Amine Ammar
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Heated Wall ◽  
Uniform Heating ◽  
Content Type ◽  
Yield Stress Fluids ◽  
Complex Boundary

Purpose The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides. Design/methodology/approach The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid. Findings Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number. Originality/value Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

Unsteady Flow Calculations by Numerical Methods

1972 ◽  
Vol 94 (2) ◽  
pp. 457-465 ◽  
Author(s):  
V. L. Streeter
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Various Boundary Conditions ◽  
Flow Problems ◽  
Velocity Flow ◽  
Compressed Gas ◽  
Order Of Magnitude ◽  
Metal Pipes ◽  
Complex Boundary

A review of methods of handling unsteady flow problems in metal pipes by numerical methods is undertaken. The characteristic method, typifying explicit methods, and the centered implicit method are developed, including the manner various boundary conditions are introduced into the solutions. High velocity flow is briefly reviewed, i.e., flow cases with the velocity of flow of the same order of magnitude as the pulse wave speed. Three complex boundary conditions are examined: turbomachinery, column separation, and the compressed gas accumulator.

Numerical Simulation of Levee Breach Flows Under Complex Boundary Conditions

2009 ◽  
Vol 21 (5) ◽  
pp. 633-639 ◽  
Author(s):  
Ming-hui Yu ◽  
Yin-ling Deng ◽  
Lian-chao Qin ◽  
Dang-wei Wang ◽  
Ya-ling Chen
Keyword(s):  
Numerical Simulation ◽  
Boundary Conditions ◽  
Levee Breach ◽  
Complex Boundary
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