Analysis and optimum design of structures under static and dynamic loads

This thesis deals with the development of reliable, and efficient computational tools for the linearly elastic analysis and optimum design of 2D and 3D discrete structures under static, free vibration and dynamic loads. Structural optimization procedures considered in this thesis involve the efficient integration of computer aided geometry modeling, automatic mesh generation, structural analysis and genetic algorithm. The procedures for structural shapes and thickness definition using parametric cubic splines for complex discrete structures are developed. A versatile, efficient and inexpensive algorithm for mesh generation, which is integrated with the shape definition is implemented. Finite element formulations for the static and free vibration analysis of 2D and 3D trusses, beams, arches and frame structures are developed and implemented. The use of a reliable and competitive procedure for finding the optimum solutions for problems involving discrete and continuous design variables based on genetic algorithms is demonstrated. A reliable finite element formulation for the transient analysis of 2D and 3D beams, arches and frame structures is implemented and the dynamic characteristics of various optimized beam and frame structure are considered. The validity of the formulations and programs is verified by comparing with literature, commercial software and analytical solution whenever possible. Key words: Finite element, geometric modeling, mesh generation, static analysis, free vibration analysis, transient dynamic analysis, structural shape optimization, genetic algorithm. m