Second Variations for the Stress Wave Problem Using the Euler-Lagrange and Adjoint Formulations
Final technical rept.
ARMY ARMAMENT RESEARCH AND DEVELOPMENT CENTER WATERVLIET NY LARGE CALIBER WEAPON SYSTEMS LAB
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The adjoint system can be arranged in a manner so it is a reflected mirror of the original system in time. Generalized boundary conditions employ many types of springs relating the various spatial partial derivatives. They are defined to satisfy the boundaries of the original and adjoint system relationship for the bilinear expression. Algorithms for use in the finite element method are simplified since the adjoint system gives exactly the same solutions as those of the original system. The second necessary condition for an extremum is satisfied by showing that the second variation of the functional is positive semi-definite.
- Theoretical Mathematics