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Dynamic programming and the solution of the biharmonic equation
Author(s) -
Distéfano Néstor
Publication year - 1971
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620030206
Subject(s) - biharmonic equation , mathematics , riccati equation , mathematical analysis , context (archaeology) , domain (mathematical analysis) , matrix (chemical analysis) , stiffness matrix , variational principle , partial differential equation , stiffness , boundary value problem , physics , paleontology , materials science , composite material , biology , thermodynamics
The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton‐Jacobi‐Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.