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