SHAPE ESTIMATION OF A CAVITY BY INVERSE APPLICATION OF THE BOUNDARY ELEMENTS 2D ELASTOSTATICS PROBLEM

Abstract

The boundary elements method (BEM), manipulated genetic algorithm (MGA), conjugate gradient method (CGM), and cubic spline interpolation (CSI) are implemented to identify the shape of a cavity located inside a 2D solid body using displacements measured from a biaxial tension test. A fitness function which is defined as the squared differences between the computed and measured displacements is minimized. The BEM is used to solve the direct 2D elastostatics problem for the boundary displacements. The MGA is used as a robust explorer to find the best circular initial guess needed by the CGM to achieve convergence. The CSI is finally employed to draw the best curve through the points found by the CGM which depict the boundary of the cavity. Several example problems with different shapes of the cavity such as elliptic, pear, heart and egg shaped are solved. The effects of the size of cavity and measurement errors on the estimation process are investigated.