OPTIMAL TOPOLOGY DESIGN USING LINEAR-PROGRAMMING

The topology design problem is formulated as a general optimization pr oblem and is solved by sequential linear programming. Two objectives a re considered: one is to maximize the stiffness of the structure and t he other is to maximize the lowest eigenvalue. A total material usage constraint is imposed for both cases. The density of each finite eleme nt 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 en ough to represent the shape of the structure. To handle the large numb er of design variables, an efficient strategy for sensitivity analysis and optimization must be established. In this research, the adjoint v ariable is used for sensitivity analysis and the linear programming me thod is used to obtain the optimal topology. The advantage of this app roach is its generality as opposed to the optimality criteria method; it can handle various problems, for example, multiple objective functi ons and multiple design criteria. Several two- and three-dimensional e xamples are presented to demonstrate the use of this approach.