The modified Shanks transform for the solution of elastic problems by boundary integral equation (BIE) method

Abstract

SUMMARYA new approach which allows solving the elastic problems by the boundary integral equation (BIE) methods is presented. The solution of the integral equation is presented in the form of Neumann series and in order to accelerate its convergence the Shanks transform was applied in a modified form. Usage of this transform allows essentially the decrease of the number of Neumann series terms for complex geometrical forms of the bodies boundary. The BIE method to the class of problems characterized by mass potential forces (i.e. thermal, gravitational or centrifugal) is applied. The comparison with the known solution for the disturbed flow around a aerofoil shows good agreement. The method is demonstrated through an example of the stress analysis of a centrifugal high-speed compressor working wheel.