scholarly journals Influence of reinforcing ribs on the deformed state of ellipsoidal shells under distributed load

2021 ◽  
Author(s):  
Nataliia Maiborodina ◽  
Viacheslav Gerasymenko ◽  
Oleksandr Kovalov
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Discrete Location ◽  
Distributed Load ◽  
Reinforcing Ribs ◽  
Deformed State ◽  
Clamped Edges

Abstract This paper presents the problem about non-stationary oscillations of reinforced ellipsoidal shells, taking into account the discrete location of the ribs. Problem bases on a geometrically nonlinear variant of the Tymoshenko theory for shells and rods. A numerical method for solving problems of this class has been developed and substantiated. This article focuses on the location of the reinforcing ribs. On the basis of the developed numerical method the deformed state of discretely supported ellipsoidal shells for internal, external and internal-external placement of ribs is investigated. Boundary conditions for rigidly clamped edges of the shell were studied.

Bidimensional Fluid-Film Flows of Stokesian Fluids

1982 ◽  
Vol 104 (2) ◽  
pp. 227-233
Author(s):  
Patrick Bourgin ◽  
Bernard Gay
Keyword(s):  
Laminar Flow ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Differential System ◽  
Analytic Method ◽  
Shearing Stress ◽  
Flow Equations ◽  
Approximate Analytic Method ◽  
Film Flows

The bidimensional flow equations of a Stokesian fluid are solved for the case of steady, incompressible, and laminar flow between two arbitrary moving surfaces separated by a small gap. The stress T22 and the shearing stress at one of the walls are coupled through nonlinear integro-differential equations, depending on the viscous function only. The form of this differential system is specified for the equations derived from the theory of phenomenological macrorheology, as developed by Reiner and Rivlin. The solution is proved to be unique under certain conditions and for adequate boundary conditions. An example is worked out in the particular case of one single non-Newtonian parameter. The problem is solved in two different ways, using an approximate analytic method and a numerical method. The conception of the latter allows to generalize it by introducing only slight modifications into the program.

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

1953 ◽  
Vol 49 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Boundary Condition ◽  
Thermal Properties ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
The Moon ◽  
Non Linear

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

Parameter Estimation for an Imperfectly Clamped Plate: Numerical Examples

1995 ◽  
Author(s):  
H. T. Banks ◽  
R. C. Smith ◽  
Yun Wang
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Simple Zero ◽  
Numerical Examples ◽  
Vibrating Structures ◽  
Physical Experiments ◽  
Slight Rotation ◽  
Physical Manifestation ◽  
Clamped Edges

Abstract The problems associated with maintaining truly fixed (zero displacement and slope) or simple (zero displacement and moment) boundary conditions in applications involving vibrating structures have led to the development of models which admit slight rotation and displacement at the boundaries. In this paper, numerical examples demonstrating the dynamics of a model for a circular plate with imperfectly clamped boundary conditions are presented. The latitude gained when using the model for estimating parameters through fit-to-data techniques is also demonstrated. Through these examples, the manner in which the model accounts for the physical manifestation of imperfectly clamped edges is illustrated, and issues regarding the use of the model in physical experiments are defined.

scholarly journals Calculation of plates in a geometrically nonlinear setting with the use of generalized equations of finite difference method

2018 ◽  
Vol 196 ◽  
pp. 01024 ◽  
Author(s):  
Natalia Uvarova ◽  
Radek Gabbasov
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Generalized Equations ◽  
Nonlinear Formulation ◽  
First Derivative ◽  
Equation Solving ◽  
Flexible Plates ◽  
Minimum Number ◽  
The Right

The article proposes a numerical method and an algorithm for analysis rectangular flexible plates in a geometrically nonlinear formulation. The generalized equations of the method of finite differences (MD) are used to solve the problem within the integrable region taking into account the discontinuities of the desired function, its first derivative and the right part of the original differential equation. Solving differential equations of the problem, composed with respect to the desired functions of deflection and stress are reduced to the 4th differential equations of the second order, which are solved numerically. As an example, a square plate loaded with a uniformly distributed load is considered. The results of the calculation with a minimum number of partitions are compared with the known analytical solution of A. S. Volmir [1] and indicate the possibility of using the numerical method for solving problems in a nonlinear formulation.

scholarly journals A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Sachin Kumar ◽  
Jinde Cao ◽  
Xiaodi Li
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Research Work ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction

In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. For this, we developed a numerical scheme with the help of quasi-wavelets. The fractional term in the time direction is approximated by using the Crank–Nicolson scheme. The spatial term and the integral term present in integro reaction-diffusion are discretized and approximated with the help of quasi-wavelets. We study this model with Dirichlet boundary conditions. The discretization of these initial and boundary conditions is done with a different approach by the quasi-wavelet-based numerical method. The validity of this proposed method is tested by taking some numerical examples having an exact analytical solution. The accuracy of this method can be seen by error tables which we have drawn between the exact solution and the approximate solution. The effectiveness and validity can be seen by the graphs of the exact and numerical solutions. We conclude that this method has the desired accuracy and has a distinctive local property.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

A Nonlinear Shear Deformable Nanoplate Model Including Surface Effects for Large Amplitude Vibrations of Rectangular Nanoplates with Various Boundary Conditions

2015 ◽  
Vol 07 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Reza Ansari ◽  
Mostafa Faghih Shojaei ◽  
Vahid Mohammadi ◽  
Raheb Gholami ◽  
Mohammad Ali Darabi
Keyword(s):  
Boundary Conditions ◽  
Surface Stress ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Free Vibrations ◽  
Model Parameters ◽  
Geometrically Nonlinear ◽  
Residual Surface Stress ◽  
Various Boundary Conditions ◽  
Shear Deformable

In this paper, a geometrically nonlinear first-order shear deformable nanoplate model is developed to investigate the size-dependent geometrically nonlinear free vibrations of rectangular nanoplates considering surface stress effects. For this purpose, according to the Gurtin–Murdoch elasticity theory and Hamilton's principle, the governing equations of motion and associated boundary conditions of nanoplates are derived first. Afterwards, the set of obtained nonlinear equations is discretized using the generalized differential quadrature (GDQ) method and then solved by a numerical Galerkin scheme and pseudo arc-length continuation method. Finally, the effects of important model parameters including surface elastic modulus, residual surface stress, surface density, thickness and boundary conditions on the vibration characteristics of rectangular nanoplates are thoroughly investigated. It is found that with the increase of the thickness, nanoplates can experience different vibrational behavior depending on the type of boundary conditions.

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-driving System

2000 ◽  
Vol 122 (2) ◽  
pp. 213-218 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained. [S1050-0472(00)01102-8]

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