The Earthquake Engineering Online Archive

Dynamic programming and the solution of the biharmonic equation

Distefano, J. Nestor

UCB/EERC-69/05, Earthquake Engineering Research Center, University of California, Berkeley, 1969-03, 28 pages (555/D551/1969)

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. Several examples are presented to show the feasibility and accuracy of the method.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-69-05.pdf (2 MB)