311 research outputs found
On Stability of Non-inflectional Elastica
This study considers the stability of a non-inflectional elastica under a
conservative end force subject to the Dirichlet, mixed, and Neumann boundary
conditions. It is demonstrated that the non-inflectional elastica subject to
the Dirichlet boundary conditions is unconditionally stable, while for the
other two boundary conditions, sufficient criteria for stability depend on the
signs of the second derivatives of the tangent angle at the endpoints
Uniformly Loaded Rectangular Thin Plates with Symmetrical Boundary Conditions
In the article the Fourier series analytical solutions of uniformly loaded
rectangular thin plates with symmetrical boundary conditions are considered.
For all the cases the numerical values are tabulated
On Jacobi's condition for the simplest problem of calculus of variations with mixed boundary conditions
The purpose of this paper is the extension of Jacobi's criteria for positive
definiteness of second variation of the simplest problems of calculus of
variations subject to mixed boundary conditions. Both non constrained and
isoperimetric problems are discussed. The main result is that Jacobi's
condition remains valid also for the mixed boundary conditions
A Closed Form Solution for Reissner's Planar Finite-Strain Beam Using Jacobi Elliptical Functions
In the article we introduce an analytical solution for Reissner's
large-deflection finite-strain planar beam subject to an end force and a
bending moment. The solution is given in terms of Jacobi elliptical functions.
The obtained analytical solution is enhanced with numerical examples. A
buckling and post buckling behavior of a beam under axial compressive load
applied at the end and subject to various boundary conditions is also discussed
in some details. In particular, the buckling factor is derived for each case of
the boundary conditions
A Note on a Generalization of Sherman-Morrison-Woodbury formula
The article presents a generalization of Sherman-Morrison-Woodbury (SMW)
formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).Comment: 3 page
A Note On Steady Flow of Incompressible Fluid Between Two Co-rotating Disks
The article provides an analytical solution of the Navier-Stokes equations
for the case of the steady flow of an incompressible fluid between two
uniformly co-rotating disks. The solution is derived from the asymptotical
evolution of unknown components of velocity and pressure in a radial
direction--in contrast to the Briter-Pohlhausen analytical solution, which is
supported by simplified Navier-Stokes equations. The obtained infinite system
of ordinary differential equations forms recurrent relations from which unknown
functions can be calculated successively. The first and second approximations
of solution are solved analytically and the third and fourth approximations of
solutions are solved numerically. The numerical example demonstrates agreements
with results obtained by other authors using different methods.Comment: 19 pages, 3 tables, 6 figure
Solution of a Class of the Riemann-Papperitz Equation with Two Singular Points
This paper provides the solution of the Riemann-Papperitz equation with
singular points at z=-i,i.This solution is obtained by mapping the singular
points into points 0,infinity. The solution is then obtained in terms of the
Gauss hypergeometric function.Comment: 5 page
Large deflections and stability of spring-hinged cantilever beam
In the article, we investigate the influence of spring on the large
deflections and stability of a spring-hinged cantilever subject to conservative
tip force. Using the closed form solution of the equilibrium equation and
closed form solution of Jacobi accessory equation, we determine the beam
equilibrium forms and their stability. Also, the solution for spring-hinged
cantilever bema subject to a follower force is given. Results are present in
the graphical and the tabular form
Large Deflections of Beam Subject to Three-points Bending
In the paper a solution for equilibrium configurations of an elastic beam
subject to three points bending is given in terms of Jacobi elliptical
functions. General equations are derived and the domain of solution is
established. Several examples that illustrate a use of the solution are
discussed. The obtained numerical results are compared with results of other
authors. Approximation formula by which the beam load is given as polynomial
function of beam deflection is also derived. The range of applicability of the
approximation is illustrated by numerical example.Comment: 11 figures, 4 table
Stability of Vertical Steady Rotation of an Ellipsoid On a Smooth Horizontal Plane
The article treats the classical problem of stability of steady rotation of a
rigid homogeneous ellipsoid on a rigid smooth plane which rotates about its
vertical axis. The condition for the steady rotation is derived from the
Euler-Poisson equations.Comment: 11 page
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