Optimality Criteria Optimization of Truss Structures Under Multiple Frequency Constraints by the Linear Approximation Resizing Rule

Abstract

The optimization of structures requires an efficient method to minimize weight, while satisfying multiple types of constraints. This approach generalizes the optimality criteria for the specific type of constraints in the frequency. Equations of motion for truss structures are considered to obtain the derivatives of the constraints required by the optimality criterion. Exponential and linear resizing optimization rules for the design variables are described. In the first, the optimized areas are compared with the analytical solution for a continuous rod. As a second example the optimized frequencies, weights and areas obtained by the linear resizing rule are compared to reference values. Both examples demonstrate the validity and effectiveness of the optimality criteria approach for the frequency constraints in truss structures.