Augmentation of DAA staggered – solution equations in underwater shock problems for singular structural mass matrices

Issue title: Dedicated to Eugene Sevin

Article type: Research Article

Authors: DeRuntz, Jr., John A.

Affiliations: Unique Software Applications, 4172 Hampshire Place, Colorado Springs, CO 80906, USA. Tel.: +1 719 540 0864; E-mail: [email protected]

Abstract: The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA). Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equations, and the total pressure applied to the structural equations on its right hand side. By formally solving for the acceleration vector from the structural system and substituting it into its place in the DAA equations, the augmentation introduces a term involving the inverse of the structural mass matrix. However there exist at least two important classes of problems in which the structural mass matrix is singular. This paper develops a method to carry out the augmentation for such problems using a generalized inverse technique.

Keywords: underwater shock, doubly asymptotic approximation, augmentation, singular structural mass matrix, generalized inverse

Journal: Shock and Vibration, vol. 12, no. 1, pp. 25-35, 2005