Optimal Finite Element Discretization - A Dynamic Programming Approach,

Abstract : An investigation from the topological aspect of the optimal finite element idealization is carried out for the liner elastic system. The criterion for the topological optimization is based on the minimization of the total potential energy, the Rayleigh quotient, and the energy quotient for the static equilibrium, free vibration, and Euler buckling problems, respectively. Firstly, in order to clarify the relation between the functional to be minimized and the discretization topology, the dynamic programming approach proposed by Distefano et al. is extended to the two kind of eigenvalue problems, that is, the free vibration and the Euler buckling analysis.