R.H. Gutierrez

Buckling of circular, solid and annular plates with an intermediate circular support

Abstract The title problem is solved in the case where uniform applied loading is present at the plate outer boundary. Two independent solutions are obtained: the optimized Rayleigh–Ritz method and the finite element algorithmic procedure. Good engineering agreement is shown to exist. The proposed analytical procedure is convenient from a designers viewpoint. Admittedly exact analytical solutions can be found in terms of Bessel functions, the procedure being rather complex from an engineering viewpoint.

Free vibrations of beams of bilinearly varying thickness

Free vibrations of Bernoulli beams of bilinearly varying thickness are studied using: (a) the optimized Rayleigh-Ritz method, (b) the differential quadrature technique and (c) the finite element approach. It is shown that the fundamental frequencies of vibration of the structural elements as determined by the methodologies (a) and (c) are in excellent agreement while rather considerable discrepancies are found when using the differential quadrature technique. The values of the second and third natural frequency coefficients determined via the finite element method are also presented.

Forced vibrations of rectangular plates subjected to harmonic loading distributed over a rectangular subdomain

Quite frequently naval and ocean structural designers confront the problem of a plate or slab which supports a motor or engine which excites, dynamically, the structural element. Very often the excitation is treated as a concentrated force but, obviously, it acts over a finite area. The present study deals with the title problem for several combinations of boundary conditions by means of a variational approach and also using the finite element method. Dynamic displacement and bending moment amplitudes are determined.

Analysis of vibrating circular plates of nonuniform thickness by the method of differential quadrature

The case of vibrating circular plates of linearly varying thickness is tackled using a method proposed by Bellman in the early 1970s.

Buckling of circular, annular plates of non-uniform thickness

Abstract This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly. An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.

Analysis of vibrating, thin, rectangular plates with point supports by the method of differential quadrature

The title problem is solved by an approach first suggested by Bellman early in the 1970s and which has recently been used in the solution of solid mechanics problems. It is shown that the methodology offers several important advantages from the point of view of naval analysts and designers.