Numerical Solutions Using Adjoint Variational Formulation to Stress Wave Problems.
Abstract
This report deals with the numerical implementation of an involved analysis in conjunction with cubic Hermite polynomials as the approximate functions. The specific example used for numerical results is the longitudinal stress wave of a uniform bar. First, the adjoint principle associated with this problem is stated. It is followed by the discretized counterparts in spatial and temporal dimensions. The procedures involving the assemblage of the 'mass' and 'stiffness' matrices in the two dimensions are described. Due to the null variations of some adjoint variables, certain rows of the matrices are eliminated. Because certain variables are known at the boundaries, the unknown variables for the next interval of time can be computed by inversion of a band matrix in terms of their present values.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1982
- Accession Number
- ADA122257
Entities
People
- C. N. Shen
- J. J. Wu
Organizations
- United States Army Armament Research, Development and Engineering Center