Annular Dome Subjected to Uniform Load Over an Eccentric Circular Area

1978 ◽  
Vol 45 (4) ◽  
pp. 845-851
Author(s):  
H. Ainso
Keyword(s):  
General Solution ◽  
Shallow Shell ◽  
Outer Boundary ◽  
Uniform Load ◽  
Circular Area ◽  
Distributed Load ◽  
Load Effects ◽  
Particular Solution ◽  
Shell Equations ◽  
General Method

A general method is presented for solving shallow shell problems with finite boundaries and with an arbitrarily placed load that is uniformly distributed over a circular area of radius r0. A known solution for the distributed load on an unbounded shell is used to describe the load effects, and this particular solution is combined with Reissner’s general solution of the shallow shell equations in such a manner that all the boundary conditions are satisfied. Numerical results have been obtained for a shallow shell, clamped at the outer boundary and having a circular polar aperture free of tractions and support.

scholarly journals General solution of second order fractional differential equations

2018 ◽  
Vol 7 (2) ◽  
pp. 56 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Second Order ◽  
Conformable Fractional Derivative ◽  
High Importance ◽  
Particular Solution ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations ◽  
General Method

Fractional differential equations are often seeming perplexing to solve. Therefore, finding comprehensive methods for solving them sounds of high importance. In this paper, a general method for solving second order fractional differential equations has been presented based on conformable fractional derivative. This method realizes on determining a general solution of homogeneous and a particular solution of a second order linear fractional differential equations. Furthermore, a general solution has been developed for fractional Euler’s equation. For more explanation of each part, some examples have been solved. 

Pressurized Cylindrical Shell With a Rigid Circular Inclusion

1978 ◽  
Vol 100 (2) ◽  
pp. 158-163 ◽  
Author(s):  
D. H. Bonde ◽  
K. P. Rao
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Shallow Shell ◽  
Circular Inclusion ◽  
Hankel Functions ◽  
Curvature Parameter ◽  
Shell Equations ◽  
Limiting Case ◽  
Rigid Circular Inclusion ◽  
Good Agreement

The effect of a rigid circular inclusion on stresses in a cylindrical shell subjected to internal pressure has been studied. The two linear shallow shell equations governing the behavior of a cylindrical shell are converted into a single differential equation involving a curvature parameter and a potential function in nondimensionalized form. The solution in terms of Hankel functions is used to find membrane and bending stressses. Boundary conditions at the inclusion shell junction are expressed in a simple form involving the in-plane strains and change of curvature. Good agreement has been obtained for the limiting case of a flat plate. The shell results are plotted in nondimensional form for ready use.

scholarly journals An application of Ritt’s low power theorem

1977 ◽  
Vol 68 ◽  
pp. 17-19 ◽  
Author(s):  
Michihiko Matsuda
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Low Power ◽  
Singular Solution ◽  
Algebraic Differential Equation ◽  
Classical Concept ◽  
First Order ◽  
Particular Solutions ◽  
Rigorous Definition ◽  
Particular Solution

AbstractConsider an algebraic differential equation F = 0 of the first order. A rigorous definition will be given to the classical concept of “particular solutions” of F = 0. By Ritt’s low power theorem we shall prove that a singular solution of F = 0 belongs to the general solution of F if and only if it is a particular solution of F = 0.

An Exact Modal Analysis of the Static Deformation of Long Cylinders and Rings

1984 ◽  
Vol 106 (4) ◽  
pp. 348-353 ◽  
Author(s):  
H. D. Fisher
Keyword(s):  
Continuous Function ◽  
General Solution ◽  
Cross Section ◽  
Thin Shell ◽  
Present Theory ◽  
Angular Variable ◽  
Arbitrary Angle ◽  
Shell Equations ◽  
Modal Solution ◽  
Long Cylinder

This paper presents a static, modal solution of Flugge’s thin shell equations for the cases of a ring or a long cylinder in a state of plane strain. The solution derived here enables the design analyst to compute the deflection resulting from concentrated loads applied in the plane of the cross section at an arbitrary angle to the circumference of the shell and to eliminate the error which results, in certain cases, from employing a previously derived inextensional analysis. A general solution is given for the case of any number of concentrated radial, tangential, and moment loads. The method of analysis for loadings that are a continuous function of the angular variable is also illustrated via a specific example. Numerical results compare solutions obtained with the present theory with those computed by invoking the assumption of inextensional deformation.

A General Solution for the Elastoplastic Thermal Stresses in a Strain-Hardening Plate With Arbitrary Material Properties

1962 ◽  
Vol 29 (1) ◽  
pp. 151-158 ◽  
Author(s):  
A. Mendelson ◽  
S. W. Spero
Keyword(s):  
Thermal Expansion ◽  
General Solution ◽  
Strain Hardening ◽  
Material Properties ◽  
Thermal Stresses ◽  
Coefficient Of Thermal Expansion ◽  
Stress And Strain ◽  
Linear Strain ◽  
Hardening Material ◽  
General Method

A general method is presented for obtaining the elastoplastic stress and strain distributions in a thermally stressed plate of a strain-hardening material with temperature-varying modulus, yield point, and coefficient of thermal expansion. It is shown that for linear strain-hardening the solution can often be obtained in closed form. It is indicated that the error due to neglecting strain-hardening may sometimes be appreciable. The assumption that the total strain remains the same as that computed elastically (strain invariance) often leads to smaller errors than the neglect of strain-hardening.

scholarly journals On shallow shell equations

2009 ◽  
Vol 2 (3) ◽  
pp. 697-722 ◽  
Author(s):  
Peng-Fei Yao ◽  
Keyword(s):  
Shallow Shell ◽  
Shell Equations

scholarly journals The Laplace transform as an alternative general method for solving linear ordinary differential equations

2021 ◽  
Vol 1 (4) ◽  
pp. 309
Author(s):  
William Guo
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Laplace Transform ◽  
Ordinary Differential Equations ◽  
Case Studies ◽  
Initial Conditions ◽  
Linear Ordinary Differential Equations ◽  
The Laplace Transform ◽  
Linear Odes ◽  
General Method

<p style='text-indent:20px;'>The Laplace transform is a popular approach in solving ordinary differential equations (ODEs), particularly solving initial value problems (IVPs) of ODEs. Such stereotype may confuse students when they face a task of solving ODEs without explicit initial condition(s). In this paper, four case studies of solving ODEs by the Laplace transform are used to demonstrate that, firstly, how much influence of the stereotype of the Laplace transform was on student's perception of utilizing this method to solve ODEs under different initial conditions; secondly, how the generalization of the Laplace transform for solving linear ODEs with generic initial conditions can not only break down the stereotype but also broaden the applicability of the Laplace transform for solving constant-coefficient linear ODEs. These case studies also show that the Laplace transform is even more robust for obtaining the specific solutions directly from the general solution once the initial values are assigned later. This implies that the generic initial conditions in the general solution obtained by the Laplace transform could be used as a point of control for some dynamic systems.</p>

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

2019 ◽  
Vol 968 ◽  
pp. 475-485 ◽  
Author(s):  
Stanislav Koval’chuk ◽  
Alexey Goryk
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Theory Of Elasticity ◽  
Transverse Shear Deformation ◽  
Uniform Load ◽  
Principle Of Superposition ◽  
Elastic Bending ◽  
Transverse Bending

An exact solution of the theory of elasticity is presented for the problem of a narrow multilayer bar section transverse bending under the action of a normal uniform load on longitudinal faces. The solution is built using the principle of superposition, by imposing common solutions to the problems of bending a multilayer cantilever with uniform loads on the longitudinal faces and an arbitrary load on the free end, and allows to take into account the orthotropy of the materials of the layers, as well as transverse shear deformation and compression. On the basis of a built-in general solution, a number of particular solutions are obtained for multi-layer beams with various ways of the ends fixing.

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