Displacement-based optimization for truss structures subjected to static and dynamic constraints

The use of displacements as design variables for truss structure optimization is considered as an alternative to the conventional finite-element-analysis-based design approach. A two-level nested optimization has been developed; in an inner level, cross-sectional areas of truss members are designed for a given displacement field, and, at an outer level, optimal displacements corresponding to the minimum weight designs are searched through the use of sequential quadratic programming. The computational efficiency of the method is, demonstrated through three examples, and the evolutions of the cross-sectional areas and optimal weight as a function of the displacements are studied. Static, dynamic, and topology problems are considered. It is shown that the method is highly efficient compared to the conventional design approaches. It is also demonstrated that the weight is always continuous throughout the design history, although areas might exhibit large discontinuities.