Shells Of Rectangular Planform Research Articles

Proof of convergence for a set of admissible functions for the Rayleigh–Ritz analysis of beams and plates and shells of rectangular planform

This work presents a discussion on the characteristics of sets of admissible functions to be used in the Rayleigh–Ritz method (RRM). Of particular interest are sets that can lead to converged results when penalty terms are added to model constraints and interconnection of elements in vibration and buckling problems of beams, as well as plates and shells of rectangular planform. The discussion includes the use of polynomials, trigonometric functions and a combination of both. In the past, several sets of admissible functions that have a limit on the number of terms that can be included in the solution without producing ill-conditioning were used. On the other hand, a combination of trigonometric and low order polynomials have been found to produce accurate results without ill-conditioning for any number of terms and any number of penalty parameters that can be accommodated by the computer memory.

Non-linear dynamic response of a doubly curved shallow shell on an elastic foundation

This paper deals with the moderately large dynamic response of a doubly curved shallow spherical shell of rectangular plan form, supported on a two parameter elastic subgrade and subjected to uniformly distributed step and sinusoidal loadings. Von Kármán-Donnell type non-linear partial differential equations of motion are employed and solved by using finite difference and Houbolt time marching techniques. Two boundary conditions are considered. The influence of stiffnesses and mass of the elastic subgrade on the moderately large amplitude of response of the shell has been investigated.

Vibration of a Cracked Cylindrical Shell of Rectangular Planform

Harmonic vibrations of a circular, cylindrical shell of rectangular planform and with an arbitrarily located crack, are investigated. The problem is described by Donnell’s equations and solved using triple finite Fourier transformation of discontinuous functions. The unknowns of the problem are the discontinuities of the slope and of three displacement components across the crack. These last quantities are replaced, using constitutive equations, by curvatures and strain in order to improve convergence and to represent explicitly the singularities at the tips. The formulas for differentiation of discontinuous functions are derived using Green-Gauss theorem. Application of the boundary conditions at the crack leads to a homogeneous system of linear algebraic equations. The frequencies are obtained from the characteristic equation resulting from this system. Numerical results for special cases are provided.