scholarly journals The transverse flexure of perforated isotropic plates

1946 ◽  
Vol 185 (1000) ◽  
pp. 35-49 ◽  
Keyword(s):  
General Solution ◽  
Isotropic Plate ◽  
Theoretical Solution ◽  
General Shape ◽  
Stress Couple ◽  
Isotropic Plates ◽  
Special Cases ◽  
Square Hole

A general theoretical solution is obtained for the problem of a large thin isotropic plate bent or twisted by couples at infinity, and containing a hole of fairly general shape. Certain known results for circular and elliptical boundaries are included in this general solution as special cases. Numerical values of the stress couple round the edge of a square hole with rounded comers are given when the plate is bent by all-round couples, or twisted or bent cylindrically about the diagonals or sides of the square. Results are also given for a triangular hole with rounded corners in a plate subject to the action of similar distributions of stress -couple at infinity.

scholarly journals Stress systems in isotropic and aeolotropic plates. V

1945 ◽  
Vol 184 (998) ◽  
pp. 231-252 ◽  
Keyword(s):  
Isotropic Plate ◽  
Elliptical Hole ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Stress Distributions ◽  
Isotropic Materials ◽  
Tension Member ◽  
Special Cases ◽  
Distribution Of Stress ◽  
Square Hole

A general theoretical solution is obtained for certain stress distributions in isotropic and aeolotropic plates containing holes of various types. The solution includes as special cases some well-known results for isotropic materials, and it is used here to obtain new results for both isotropic and aeolotropic plates. Numerical results are given for the distribution of stress round the edges of an elliptical hole in a spruce plank under tension, a square hole with rounded corners in an isotropic tension member and in an isotropic plate under shear, and a triangular hole with rounded comers in an isotropic tension member.

Green's functions for thin isotropic plates containing holes

1957 ◽  
Vol 53 (3) ◽  
pp. 755-763 ◽  
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Unit Circle ◽  
Isotropic Plate ◽  
Green’S Functions ◽  
Arbitrary Point ◽  
Outer Edge ◽  
Transverse Force ◽  
Closed Curve ◽  
Transverse Displacement ◽  
Isotropic Plates ◽  
Special Cases

ABSTRACTThis paper is concerned with the small transverse displacement of an infinite thin plane isotropic plate due to the application of a transverse force applied at an arbitrary point of the plate. The plate has its outer edge free, and is clamped along and bounded internally by a closed curve that can be mapped onto the unit circle by means of a polynomial. Three polynomials are considered and in each of these cases the deflexion is obtained in finite terms. Circular and elliptic holes as well as curvilinear polygonal holes are included as special cases.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

scholarly journals The elastic equilibrium of isotropic plates and cylinders

1949 ◽  
Vol 195 (1043) ◽  
pp. 533-552 ◽  
Keyword(s):  
Fourier Series ◽  
General Solution ◽  
Power Series ◽  
Elastic Equilibrium ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Isotropic Plates ◽  
First Approximation ◽  
Stress Components ◽  
Normal And Shear Stresses

A general solution of the elastic equations is obtained for problems of stress distributions in plates or cylinders when the bounding faces of the plates Z = ± h , or the flat ends of the cylinders, are free from applied normal and shear stresses. The solution is expressed either in the form of Fourier series in the co-ordinate Z , or in power series in Z , the coefficients of the series being certain functions of the x and y co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planes Z = ± h . The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variable z = x + iy . A first approximation to the part of the theory which deals with the bending of the plate yields a theory similar in character to that given recently by Reissner.

Helices of fractionalized Maxwell fluid

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Muhammad Jamil ◽  
Kashif Ali Abro ◽  
Najeeb Alam Khan
Keyword(s):  
Angular Velocity ◽  
General Solution ◽  
Circular Cylinder ◽  
Special Function ◽  
Fluid Model ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Initial Moment ◽  
Special Cases ◽  
In Series

AbstractIn this paper the helical flows of fractionalized Maxwell fluid model, through a circular cylinder, is studied. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Omegatp, and to slide along the same axis with linear velocity Utp. The solutions that have been obtained using Laplace and finite Hankel transforms and presented in series form in terms of the newly defined special function M(z), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluid obtained as special cases of the present general solution. Finally, the influence of various pertinent parameters on fluid motion as well as the comparison among different fluids models is analyzed by graphical illustrations.

Analysis of Stress Singularities at Bi-Material Corners in Reddy's Theory of Plate Bending

2006 ◽  
Vol 22 (1) ◽  
pp. 67-75 ◽  
Author(s):  
C. S. Huang
Keyword(s):  
Thick Plate ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Stress Singularity ◽  
Numerical Approach ◽  
Sharp Corner ◽  
Equilibrium Equations ◽  
Third Order ◽  
Isotropic Plates ◽  
Expansion Technique

AbstractThe order of stress singularity at a sharp corner of a plate needs to be known before a numerical approach can be taken to determine accurately the stress distribution of a plate with irregular geometry (such as a V-notch) under loading. This work analyzes the order of the stress singularity at a bi-material corner of a thick plate under bending, based on Reddy's third-order shear deformation plate theory. An eigenfunction expansion technique is used to derive the asymptotic displacement field in the vicinity of the sharp corner by solving the equilibrium equations in terms of displacement functions. This paper explicitly shows the first known characteristic equations for determining the order of the stress singularity at the interface corner of a bonded dissimilar isotropic plate. Moreover, the numerical results are given in graphic form for the order of stress singularity at the interface corner in bonded dissimilar isotropic plates and at the vertex of a bi-material wedge with free radial edges. The results presented herein fill some of the gaps in the literature

scholarly journals On Calculation of the First Integrals for Three-dimensional ODE Systems

2019 ◽  
pp. 11-21
Author(s):  
A. V. Kavinov
Keyword(s):  
Vector Field ◽  
General Solution ◽  
Nonlinear Dynamical Systems ◽  
First Integral ◽  
First Integrals ◽  
Third Order ◽  
The Third ◽  
Ode System ◽  
Special Cases ◽  
Ode Systems

The search for solutions of nonlinear stationary systems of ordinary differential equations (ODE) is sometimes very complicated. It is not always possible to obtain a general solution in an analytical form. As a consequence, a qualitative theory of nonlinear dynamical systems has been developed. Its methods allow us to investigate the properties of solutions without finding a general solution. Numerical methods of investigation are also widely used.In the case when it is impossible to find an analytically general solution of the ODE system, sometimes, nevertheless, it is possible to find its first integral. There is a number of known results that make it possible to obtain the first integral for certain special cases.The article deals with the method for obtaining the first integrals of ODE systems of the third order, based on the fact of integrability of the involutive distribution.The method proposed in the paper allows us to obtain the first integral of a nonlinear ODE system of the third order in the case when a vector field, which generates an involutive distribution of dimension 2 together with the vector field of the right-hand side of a given ODE system, is known. In this case, the solution of a certain sequence of Cauchy problems allows us to construct a level surface of the function of the first integral containing the given point of the state space of the system. Using the method of least squares, in a number of cases it is possible to obtain an analytic expression for the first integral.The article gives examples of the method application to two ODE systems, namely to a simple nonlinear third-order system and to the Lorentz system with special parameter values. The article shows how the first integrals can be obtained analytically using the method developed for the two systems mentioned above.

The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

2020 ◽  
Vol 87 (11) ◽  
Author(s):  
V. R. Feldgun ◽  
D. Z. Yankelevsky
Keyword(s):  
Analytical Solution ◽  
General Solution ◽  
Cylindrical Cavity ◽  
Constant Velocity ◽  
Present Model ◽  
Elastic Region ◽  
Cavity Expansion ◽  
Special Cases ◽  
Significant Difference ◽  
Cavity Boundary

Abstract A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

Displacement States for Isotropic Plates

2018 ◽  
Vol 16 (14) ◽  
pp. 64-67
Author(s):  
Carmen Popa ◽  
Violeta Anghelina ◽  
Octavian Munteanu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isotropic Plate ◽  
The Finite Element Method ◽  
Isotropic Plates ◽  
Deformation State ◽  
Element Method

Abstract In this paper the deformation state of a circular and isotropic plate is analyzed, using as methods of comparison the analytical, the finite element and the experimental element methods. In the finite element method, the plate is analyzed by several programmes, as well as assembled with the respective container.

Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling

2003 ◽  
Vol 125 (2) ◽  
pp. 169-177 ◽  
Author(s):  
M. M. Yovanovich
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Circular Disk ◽  
Spreading Resistance ◽  
Pin Fin ◽  
Special Cases ◽  
Extended Surface ◽  
The One ◽  
Circular Source ◽  
Special Case

General solution for thermal spreading and system resistances of a circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable for a general axisymmetric heat flux distribution which reduces to three important distributions including isoflux and equivalent isothermal flux distributions. The dimensionless system resistance depends on four dimensionless system parameters. It is shown that several special cases presented by many researchers arise directly from the general solution. Tabulated values and correlation equations are presented for several cases where the system resistance depends on one system parameter only. When the cylinder sides are adiabatic, the system resistance is equal to the one-dimensional resistance plus the spreading resistance. When the cylinder is very long and side cooling is small, the general relationship reduces to the case of an extended surface (pin fin) with end cooling and spreading resistance at the base. The special case of an equivalent isothermal circular source on a very thin infinite circular disk is presented.

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