Rigid Boss Research Articles

Optimization of inelastic conical shells with cracks

Inelastic conical shells loaded by the central rigid boss with vertical load are studied. The thickness of the conical part of the structure is piecewise constant. The connection between the shell and the boss is weakened with a stable crack. The designs with the maximal load-carrying capacity are established under a given material consumption of the shell. Material of the shell wall obeys the von Mises yield condition.

Large deflection analysis of a pre-stressed annular plate with a rigidboss under axisymmetric loading

The large deflection analysis of a pre-stressed annularplate with a central rigid boss subjected to axisymmetric loading ispresented. The factors affecting the transition from plate behaviourto membrane behaviour (e.g. thickness, in-plane tension and materialproperties) are studied. The effect of boss size and pre-tension onthe effective stiffness of the plate are investigated. The extent ofthe bending boundary layers at the edges of the plate are quantified.All results are presented in non-dimensional form. The designimplications for microelectromechanical system components areassessed.

Optimization of plastic conical shells loaded by a rigid central boss

Simply supported conical shells loaded by the central rigid boss with vertical load are considered. The thickness of the shell wall is assumed to be piece-wise constant with a finite number of jumps. The minimum weight design of the shell is established under the condition that the load carrying capacity of the shell is given. The shell material is assumed to be an ideal rigid-plastic one obeying the generalized diamond yield condition and associated flow law.

Coherent response to a point source irradiating a rough plane

We consider a point source above a rough surface, and write the coherent response as the Sommerfeld–Weyl–Noether integral in terms of the coherent plane-wave reflection coefficient R for correlated distributions of bosses on rigid or free planes. The uniform asymptotic development of the integral (a generalization of the original Sommerfeld approximation based on the error function complement) is applied to near-grazing for a rigid base, and graphical results and simple analytical approximations are presented to exhibit the essentials for data inversion programs. The coefficient R and the associated angle-dependent impedance (determined by the ensemble-averaged multiple scattering amplitude for one fixed boss) are specified by the single scattered amplitude and the statistical-mechanics pair distribution function. Low-frequency illustrations for rigid bosses delineate multipole-coupling and packing effects on propagation and on attenuation arising from incoherent scattering, as functions of the packing fraction and of the shapes of the bosses and their exclusion regions.

Plastic analysis of thick circular plates

The von Mises yield criterion is used to study circular plates including the effect of transverse shear. The deformation rate caused by the shear force is assumed to be uniform through the thickness. The appropriate relations among the generalized strain-rate variables and the normal velocity are developed. A piecewise linear approximation inscribing the von Mises yield surface is chosen for the limit load analysis of plates. The problem of a simply supported circular plate loaded by a rigid boss is solved. Below a critical radius of the loaded boss, shear through failure is predicted for non-hardening materials.

A new finite element method for analysing symmetrically loaded thin shells of revolution

AbstractAn essential feature of finite element methods of analysis for symmetrically loaded shells of revolution is the setting up of equations representing the response of a short ‘ring’ element to edge loading.In this paper the axisymmetric behaviour of a short elastic cylindrical shell element under edge loading is described in a new way by means of a matrix which is a combination of stiffness, flexibility and ‘neutral’ sub‐matrices. The coefficients of the matrix are derived direct from the equations of the problem, which involves a trivial amount of work in comparison with conventional methods.The corresponding matrix for a short section of an arbitrary shell of revolution is set up with little additional effort, and its use is described for calculation of edge response coefficients for portions of spherical shells.Finally, the method is used to study by iteration the behaviour of a thin spherical shell of viscous material containing a rigid boss which is loaded radially inwards: changes in meridional profile are followed as deformation proceeds. Results are presented for both linear and non‐linear viscous material.

Simple upper-bound calculations for the indentation of cylindrical shells

An analytical study is made of the behaviour of a thin cylindrical shell subjected to two equal loads acting radially inward in opposite directions across the diameter of the shell and applied through two rigid bosses. A simple sequence of upper-bound calculations is performed, which makes possible a study of the effects of changing geometry on the capacity of the shell to carry applied loads.The interaction of elastic and plastic effects is analysed with the aid of some experimental results. The paper concludes with the observation that this type of structure and loading configuration do not exhibit any snap-through phenomena if plastic effects predominate, in contrast to the behaviour of the corresponding spherical shell.

Non‐linear programming for the plastic analysis of local deformations in shell structures

AbstractThe paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load‐deflection behaviour of these structures after the application of the yield‐point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non‐linear programming routine.The results of this analysis are correlated with a non‐dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.

Experimental Investigation into the Effects of Indenting a Cylindrical Shell by a Load Applied through a Rigid Boss

A series of tests has been performed on thin unpressurized cylinders loaded by two equal and opposite forces applied across a diameter. Special emphasis was laid on elucidating the response of the specimens to large displacements in order to check the possible appearance of any snapping action. Tests were performed on cylinders both with and without edge constraints and the experimental procedure was devised in order to isolate, as far as possible, the effects of plastic strains. No actual strains were measured and the results presented all correlate the variation of displacements with variations in the applied loads.