Augmentation of Doubly Asymptotic Approximations in Underwater Shock Problems for Singular Structural Mass Matrices

摘要

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 Doublv Asvmptotic Approximations (DAA). Practical implementation of the method has relied on the so-called augmentation of the .UAA 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 exists 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.