Numerical Recovery of Material Parameters in Euler-Bernoulli Beam Models

Abstract

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time dependent problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximate solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi- Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the methods are given for problems with both fixed and cantilever boundary conditions.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1991
Accession Number
ADA233128

Entities

People

  • C. R. Vogel
  • K. L. Bowers
  • R. C. Smith

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computers
  • Convergence
  • Data Sets
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of State
  • Galerkin Method
  • Inverse Problems
  • Partial Differential Equations
  • Time Intervals
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)