Optimization of Functionally Graded Material Structures: Some Case Studies

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 fluid-structure 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

Structural Optimization of Wind Turbine Blades for Improved Dynamic Performance

The design of the main structure of a wind turbine blade is optimized aiming at the improvement of the overall dynamic performance. Three optimization strategies are developed and tested. The first fundamental one is based on minimizing the total structural mass of the blade spar under frequency and strength constraints. The second and third strategies are concerned with the reduction of the overall vibration level by either minimizing a frequency-placement index or maximizing the natural frequencies and placing them at their target values to avoid large amplitudes and resonance occurrence. Design variables include cross-sectional dimensions and material properties along the spanwise direction of the blade spar. The optimization problem is formulated as a nonlinear constrained problem solved by sequential quadratic programming (SQP) technique. Two specific layup configurations, namely, circumferentially asymmetric stiffness ( CAS ) and circumferentially uniform stiffness ( CUS ), are analyzed. Exact analytical methods are applied to calculate the natural modes of vibration of a composite, thin-walled, tapered blade spar. The influence of coupling on the vibration modes is identified, and the functional behavior of the frequencies with the lamination parameters is thoroughly investigated and discussed. Finite element modeling using NX Nastran solver is performed in order to validate the analytical results. As a case study, optimized blade spar designs of a 750-kW horizontal axis wind turbine are given. The attained solutions show that the approach used in this study enhances the dynamic characteristics of the optimized spar structures as compared with a known baseline design of the wind turbine blade

Efficient algorithms and models for mechanical and structural design optimization

In the present work, different algorithms and penalty methods for design optimization of mechanical elements and structures are applied. Seven robust optimization techniques and seven penalty methods are thoroughly investigated and implemented in MATLAB codes. In addition, different optimization models are compared using two benchmark problems, namely, the minimal cost design of a welded beam structure and the optimal buckling design of a functionally graded material column. A performance measure factor is defined to determine the best technique among the implemented optimization algorithms. The results are arranged and nested to make it easy for the reader to figure out each technique characteristics, and hence choose the suitable one for a specific design problem and/or application. Comprehensive computer experimentations were performed, and the best optimization techniques and models have been thoroughly demonstrated. The attained optimal solutions show that, in general, the hybrid algorithms worked better than the stand-alone ones and the sequential quadratic programming (SQP) with global search indicates a superior performance than other techniques. Finally, based on the present study, the adaptive and dynamic penalties need further investigation to become more consistent with the implemented optimization algorithms

Optimum Composite Structures

The subject of optimum composite structures is a rapidly evolving field and intensive research and development have taken place in the last few decades. Therefore, this book aims to provide an up-to-date comprehensive overview of the current status in this field to the research community. The contributing authors combine structural analysis, design and optimization basis of composites with a description of the implemented mathematical approaches. Within this framework, each author has dealt with the individual subject as he/she thought appropriate. Each chapter offers detailed information on the related subject of its research with the main objectives of the works carried out as well as providing a comprehensive list of references that should provide a rich platform of research to the field of optimum composite structures