Optimal topology design using linear programming

Abstract

The topology design problem is formulated as a general optimization problem and is solved by sequential linear programming. Two objectives are considered: one is to maximize the stiffness of the structure and the other is to maximize the lowest eigenvalue. A total material usage constraint is imposed for both cases. The density of each finite element is chosen as the design variable and its relationship with Young's modulus is expressed by an empirical formula. Typically, the number of design variables is large, as the finite element mesh must be fine enough to represent the shape of the structure. To handle the large number of design variables, an efficient strategy for sensitivity analysis and optimization must be established. In this research, the adjoint variable is used for sensitivity analysis and the linear programming method is used to obtain the optimal topology. The advantage of this approach is its generality as opposed to the optimality criteria method; it can handle various problems, for example, multiple objective functions and multiple design criteria. Several two- and three-dimensional examples are presented to demonstrate the use of this approach.