Large Axisymmetric Deformations of Elastic/Plastic Perforated Circular Plates

2003 ◽  
Vol 125 (4) ◽  
pp. 357-364 ◽  
Author(s):  
D. Wu ◽  
J. Peddieson ◽  
G. R. Buchanan ◽  
S. G. Rochelle
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Circular Plate ◽  
Numerical Solutions ◽  
Outer Edge ◽  
Plate Bending ◽  
Large Deflections ◽  
Circular Plates ◽  
Elastic Plastic ◽  
Thickness Variations

A mathematical model of axisymmetric elastic/plastic perforated circular plate bending and stretching is developed which accounts for through thickness yielding, through thickness variations in perforation geometry, elastic outer edge restraint, and moderately large deflections. Selected numerical solutions of the resulting differential equations are presented graphically and used to illustrate interesting trends.

scholarly journals Memory effects on the proliferative function in the cycle-specific of chemotherapy

2021 ◽  
Author(s):  
Najma Ahmed ◽  
Dumitru Vieru ◽  
Fiazud Din Zaman
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Classical Model ◽  
Cell Mass ◽  
Time Derivative ◽  
Fractional Model ◽  
Fractional Differential ◽  
Mathcad Software

A generalized mathematical model of the breast and ovarian cancer is developed by considering the fractional differential equations with Caputo time-fractional derivatives. The use of the fractional model shows that the time-evolution of the proliferating cell mass, the quiescent cell mass, and the proliferative function are significantly influenced by their history. Even if the classical model, based on the derivative of integer order has been studied in many papers, its analytical solutions are presented in order to make the comparison between the classical model and the fractional model. Using the finite difference method, numerical schemes to the Caputo derivative operator and Riemann-Liouville fractional integral operator are obtained. Numerical solutions to the fractional differential equations of the generalized mathematical model are determined for the chemotherapy scheme based on the function of "on-off" type. Numerical results, obtained with the Mathcad software, are discussed and presented in graphical illustrations. The presence of the fractional order of the time-derivative as a parameter of solutions gives important information regarding the proliferative function, therefore, could give the possible rules for more efficient chemotherapy.

Large Deflections of Circular Plates of Variable Thickness

1982 ◽  
Vol 49 (1) ◽  
pp. 243-245 ◽  
Author(s):  
B. Banerjee
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Deflection ◽  
Numerical Results ◽  
Large Deflections ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

Large Deflections of Circular Plates

1952 ◽  
Vol 19 (3) ◽  
pp. 287-292
Author(s):  
M. Stippes ◽  
A. H. Hausrath
Keyword(s):  
Circular Plate ◽  
Critical Values ◽  
Graphical Form ◽  
Series Expansions ◽  
Large Deflections ◽  
Circular Plates ◽  
Simply Supported ◽  
Perturbation Procedure

Abstract This paper contains a solution of von Kármán’s equations for a uniformly loaded, simply supported circular plate. The method used to obtain the solution is the perturbation procedure. Series expansions for the deflection and stresses in the plate are obtained. The legitimacy of these expansions is demonstrated in the Appendix. Critical values of stress and deflection are presented in graphical form. Furthermore, tables of coefficients for the afore-mentioned series are presented if anyone desires to extend the results which are presented here.

Deflection of Uniformly Loaded Circular Plates

1943 ◽  
Vol 10 (4) ◽  
pp. A181-A182
Author(s):  
F. C. W. Olson
Keyword(s):  
General Theory ◽  
Circular Plate ◽  
Elastic Constants ◽  
Energy Method ◽  
Plate Thickness ◽  
Large Deflections ◽  
Bending Moments ◽  
Circular Plates ◽  
Boundary Parameter ◽  
Center Deflection

Abstract The equation for small deflections of a uniformly loaded and supported circular plate is rewritten so that the two constants of integration are interpreted as the center deflection ω0 and a boundary parameter α. Stresses and bending moments are given in terms of ω0 and α. A particular advantage of this treatment is that the nature of the support may be found experimentally even if the elastic constants, plate thickness, and load are unknown. The energy method is used to develop a more general theory of large deflections, valid for any condition of uniform support at the edge.

Bending of Circular Plates Under a Uniform Load on a Concentric Circle—Part II

1968 ◽  
Vol 90 (2) ◽  
pp. 279-293
Author(s):  
J. C. Heap
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Concentric Circle ◽  
Outer Edge ◽  
Circular Plates ◽  
Uniform Load ◽  
Simply Supported ◽  
Basic Equations

The basic equations of deflection, slope, and moments for a thin, flat, circular plate subjected to a uniform load on a concentric circle were derived for four generalized cases. From these generalized cases, six simplified cases were deduced. The four generalized cases have the uniform load acting on a concentric circle of the plate between the inner and outer edges, with the following boundary conditions: (a) Outer edge supported and fixed, inner edge fixed; (b) outer edge simply supported, inner edge free; (c) outer edge simply supported, inner edge fixed; and (d) outer edge supported and fixed, inner edge free.

scholarly journals A mathematical model of serious and minor criminal activity

2016 ◽  
Vol 27 (3) ◽  
pp. 403-421 ◽  
Author(s):  
A. A. LACEY ◽  
M. N. TSARDAKAS
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Criminal Activity ◽  
Specific Area ◽  
Actual Data ◽  
Mathematical Methods ◽  
Diffusion Type ◽  
Recent Idea

Using mathematical methods to understand and model crime is a recent idea that has drawn considerable attention from researchers during the last five years. From the plethora of models that have been proposed, perhaps the most successful one has been a diffusion-type differential equations model that describes how the number of criminals evolves in a specific area. We propose a more detailed form of this model that allows for two distinct criminal types associated with major and minor crime. Additionally, we examine a stochastic variant of the model that represents more realistically the ‘generation’ of new criminals. Numerical solutions from both models are presented and compared with actual crime data for the Greater Manchester area. Agreement between simulations and actual data is satisfactory. A preliminary statistical analysis of the data also supports the model's potential to describe crime.

A semi-analytic finite-element analysis of circular plate bending problems

1980 ◽  
Vol 15 (2) ◽  
pp. 75-82 ◽  
Author(s):  
T H Richards ◽  
B Delves
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Circular Plate ◽  
Plate Bending ◽  
Circular Plates ◽  
Element Analysis ◽  
Bending Problems ◽  
Design Analyses ◽  
Axisymmetric Structures

Semi-analytic formulations have previously been used for a number of stressing problems wherein axisymmetric structures have supported non-axisymmetric loads. The approach is here shown to be very useful for circular plates, and to have especial value for design analyses using desk top computers in which the main store is relatively small.

scholarly journals Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

2021 ◽  
Vol 6 (7 (114)) ◽  
Author(s):  
Volodymyr Zelenyak ◽  
Myroslava Klapchuk ◽  
Lubov Kolyasa ◽  
Oksana Oryshchyn ◽  
Svitlana Vozna
Keyword(s):  
Mathematical Model ◽  
Stress Intensity ◽  
Integral Equations ◽  
Circular Plate ◽  
Singular Integral ◽  
Numerical Solutions ◽  
Thermal Power ◽  
Singular Integral Equations ◽  
Two Dimensional ◽  
Curvilinear Inclusion

A two-dimensional mathematical model of the thermoelastic state has been built for a circular plate containing a curvilinear inclusion and a crack, under the action of a uniformly distributed temperature across the entire piece-homogeneous plate. Using the apparatus of singular integral equations (SIEs), the problem was reduced to a system of two singular integral equations of the first and second kind on the contours of the crack and inclusion, respectively. Numerical solutions to the system of integral equations have been obtained for certain cases of the circular disk with an elliptical inclusion and a crack in the disk outside the inclusion, as well as within the inclusion. These solutions were applied to determine the stress intensity coefficients (SICs) at the tops of the crack. Stress intensity coefficients could later be used to determine the critical temperature values in the disk at which a crack begins to grow. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of those engineering structures with cracks that are operated in the thermal power industry and, therefore, is relevant. Graphic dependences of stress intensity coefficients on the shape of an inclusion have been built, as well as on its mechanical and thermal-physical characteristics, and a distance to the crack. This would make it possible to analyze the intensity of stresses in the neighborhood of the crack vertices, depending on geometric and mechanical factors. The study's specific results, given in the form of plots, could prove useful in the development of rational modes of operation of structural elements in the form of circular plates with an inclusion hosting a crack. The reported mathematical model builds on the earlier models of two-dimensional stationary problems of thermal conductivity and thermoelasticity for piece-homogeneous bodies with cracks.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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