Robert Napier Simpson

Lifetime prediction for solder joints with the extended finite element method

Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical methods are often used to predict the average lifetime of the critical joints. However, to get a reliable failure probability the standard deviation must also be addressed. The deviation of the lifetime from the mean value is a consequence of the variation in microstructure found in actual joints. We therefore propose a new methodology that calculates crack growth based on microstructural features of the joint. A series of random microstructures is generated. Crack growth calculations are performed for each of these structures. The structural problem is solved numerically with the extended finite element method which allows a complete automation of the process. The mean crack length and standard deviation are calculated from the crack growth simulations and the result is compared to experimental data.

An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

Abstract We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use Bezier extraction to accelerate the computation of NURBS and B-spline terms and employ H -matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.

A coupled isogeometric finite element and boundary element method with subdivision surfaces for structural -acoustic analysis of shell structures

We demonstrate a method for simulating medium-wave acoustic scattering over elastic thin shell structures. We propose a coupled approach whereby the finite element formulation is used to describe the dynamic structural response of the shell and the boundary element method models the acoustic pressure within the infinite acoustic domain. The two methods are coupled through the relationship between acoustic velocities on the structural-fluid interface. In our approach, a conforming subdivision discretization is generated in Computer Aided Design (CAD) software which can be used directly for analysis in keeping with the idea of isogeometric analysis whereby a common geometry and analysis model is adopted. The subdivision discretization provides C1 surface continuity which satisfies the challenging continuity requirements of Kirchhoff-Love shell theory. The new method can significantly reduce the number of elements required per wavelength to gain same accuracy as an equivalent Lagrangian discretization, but t...