Shape sensitivity analysis of sequential structural–acoustic problems using FEM and BEM
Abstract A shape design sensitivity formulation for structural–acoustic problems using sequential finite element and boundary element methods is presented. Frequency-response analysis is used to obtain the dynamic behavior of the structure, while boundary element analysis is used to solve for the pressure response of the acoustic domain. It is shown that the adjoint method, which takes the reverse direction to response analysis, provides a very efficient way of sensitivity calculation. In addition, it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem. The only difference is the numerical integration that evaluates the sensitivity coefficient. The combination of the semi-analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation. The accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method.
Acoustic shape sensitivity analysis using the boundary integral equation
Boundary integral equations are formulated for the shape sensitivity analysis of the acoustic problems. The concept of the material derivative is employed in deriving the sensitivity equations. Since the equation is derived by the direct differentiation of the boundary integrals containing the field values, it is expected that the sensitivity would be computed more effectively and accurately than the conventional finite difference method. In addition, the equation has the potential to be applied to many complex acoustic problems, because the derived equation is regularized by using the integral identity that incorporates the one-dimensional propagating wave and its material derivative. The validity of the formulations is demonstrated through examples having regular shapes such as the three-dimensional pulsating sphere and the one-dimensional duct, for which the analytical solutions are available. As an example for an irregular domain, the two-dimensional model of an automotive interior cavity is dealt wit...
Review of Literature on Probability of Detection for Magnetic Particle Nondestructive Testing
Abstract : A critical review of the available literature concerning the minimum reliably detectable defect size aNDI for magnetic particle testing (MPT) in aerospace applications is presented. Four probability of detection (POD) studies relevant to detection of fatigue cracks in aircraft components were found over the period 1968 to 2011. As the statistical methods used in these four previous studies were either outdated or otherwise deficient, the original data were reanalysed using currently accepted techniques. A meta-analysis of the results is presented, with emphasis on statistical inferences for the defect size expected to be detected with 90% POD. It is shown that the minimum reliably detectable defect size aNDI = 2.0 mm currently specified by the Royal Australian Air Force for wet fluorescent magnetic particle inspection using the continuous method is consistent with estimates of the average performance of MPT derived from the reanalysis of the literature.