An Improvement to the Fourier Series Method for Inversion of Laplace Transforms Applied to Elastic and Viscoelastic Waves

Abstract

A parametric study of composite strips leads to systems of partial differential equations, coupled through interface conditions, that are naturally solved in Laplace transform space. Because of the complexity of the solutions in transform space and the potential variations due to geometry and materials, a systematic approach to inversion is necessarily numerical. The Dubner-Abate-Crump (DAC) algorithm is the standard in such problems and is implemented. The presence of discontinuous wavefronts in the problems considered leads to Gibbs phenomenon; which, in turn, overestimates the values of maximum stress. These errors are mitigated by use of Lanczos' sigma-factors, which combine naturally with the DAC algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA463526

Entities

People

  • George A. Gazonas
  • Richard R. Laverty

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Advanced Electronics
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Composite Materials
  • Computational Science
  • Differential Equations
  • Equations
  • Fourier Series
  • Geometry
  • Integrals
  • Inversion
  • Materials
  • Materials Science
  • Military Research
  • Partial Differential Equations
  • Standards
  • United States
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space