Optimization of a Ribbed Table for Minimum Weight and Minimum Deflection

Abstract

This paper demonstrates a method for the optimization of a ribbed table, such as a machine tool base. Although the particular structure considered has been idealized so that the shapes of only five members are developed, the method is applicable to very complex structures. This technique utilizes energy methods to synthesize mathematical models and the Euler-Lagrange Equation to find the best shape. In this way the optimization of each individual member is separated from the rest of the problem causing great simplification in the mathematics involved.