An Optimum Design for Beams with Discrete and Continuous Variables.

This paper deals with an optimum design problem for beams subject to a moving load. The optimum design is classified into two types of problems. The first problem is a nonlinear optimization with discrete design variables, and the second one is the optimization with continuous variables. The optimization procedures consist of the dynamic programming with discrete variables and the penalty function method with continuous ones. The procedures are combined to a sequential form and applied to the problem. The optimum shapes of beams are obtained with the constraint of the conservation of total mass.