Optimization of Functionally Graded Material Structures: Some Case Studies

Abstract

This chapter focuses on some of the most advances made in the field of stability, dynamic, and aeroelastic optimization of functionally graded composite structures. Practical realistic optimization models using different strategies for measuring structural performance are presented and discussed. The selected design variables include the volume fractions of the composite material constituents as well as geometrical and cross-sectional parameters. The mathematical formulation is based on dimensionless quantities; therefore, the analysis can be valid for different configurations and sizes. Such normalization has led to a naturally scaled optimization model, which is favorable for most optimization techniques. Case studies include structural dynamic optimization of thin-walled beams in bending motion, optimization of drive shafts against torsional buckling and whirling, and aeroelastic optimization of subsonic aircraft wings. Other stability problems concerning fluidstructure interaction has also been addressed. Several design charts that are useful for direct determination of the optimal values of the design variables are introduced. The proposed mathematical models have succeeded in reaching the required optimum solutions, within reasonable computational time, showing significant improvements in the overall structural performance as compared with reference or known baseline designs.