EFFICIENT COMPUTING OF POTENTIAL FIELDS INDUCED BY POINT SOURCES IN THIN PERFORATED SHELL STRUCTURES

Abstract

Potential fields of various physical nature might significantly affect viability of structures in automobiles, aircraft, and other areas of contemporary engineering. That is why accurate analysis of potential fields, occurring in elements of structures, is required for the exploration of conditions of their predetermined functioning. Thermoelasticity, for example, is a specific branch of natural sciences where information about thermal fields is especially critical. Fields induced by point sources represent an important particular case quite often occurring in reality.

The present project aims at the investigation of potential fields in thin shell structures made of conductive materials. Our manual is conditionally viewed as consisting of three segments, the first of which deals with point sources in single shell fragments of standard geometry (cylindrical, spherical, toroidal, etc.). The second segment is devoted to joint shell structures composed of fragments of different geometries, whilst single fragments and joint structures weakened with apertures are considered in the last segment.

The Green's function formalism constitutes theoretical background of our work. Exploring potential fields generated by point sources in single shell fragments, we use the Green's function method, possibility of which implementation had been advocated, for this class of problems, a few decades ago. We have further developed this approach by obtaining computer-friendly representations of Green's functions for a broad variety of boundary-value problems stated for the Laplace equation written in geographical coordinates.

In approaching solid joint shell structures, the classical Green's function formalism fails. We turn therefore to the matrix of Green's type notion also introduced awhile ago, and our focus is on obtaining readily computable matrices for a score of structures.

A Green's function-based algorithm, that allows an accurate computation of potential fields induced in shell structures weakened with apertures, is developed.