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DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
Optimization of Fundamental Frequency with Bidirectional Evolutionary Structural Method of Continuum Structures
Submission Author:
EDERVAL LISBOA , RS
Co-Authors:
EDERVAL LISBOA, João Baptista Dias Moreira, Emanuel Moutinho Cesconeto, José Evandro Garcez de Medeiros, Thomas S Ribeiro, Walter Jesus Paucar Casas
Presenter: EDERVAL LISBOA
doi://10.26678/ABCM.DINAME2017.DIN17-0202
Abstract
Hierarchical structures involve a structure which can be defined in scales of different length, where an structural element in a given scale is formed by smaller scale periodic substructures. Each hierarchical level can be assumed as a continuous medium formed by a homogeneous microstructure using the homogenization theory. The topology optimization aims to find the topology and shape of the structure, i.e. the material distribution of a structure where the structural performance must be optimized. The topology optimization of materials is involved with the microstructure design in a smaller scale focusing on the development of new periodical materials with predefined properties. Simultaneous design with multiple phases in materials and composite structures is limited because of the common separation between the material and the structure design. The design of composite materials aims to find the phase distribution of the base material in the microstructure of the material, while the topology optimization has been used to achieve the desired physical properties. Optimization of the frequency is essential in engineering, since it is desirable to modify the natural frequencies to avoid resonance responses produced by external excitations. This work aims the topology optimization of the dynamic behavior via natural frequency of the system through a hierarchical concurrent design in the macro and micro scales. The material distribution is hierarchically sought in both scales to maximize the natural frequency of the macro system. Based on the assumption that periodic materials behave as a homogeneous continuum, each phase of the macrostructure is composed of a periodic microstructure material. In the structural design of a system of two scales, two or more types of models are used to represent the macrostructure and the microstructure. The sensitivity analysis on both scales must be coupled with information of the other. The topological design of the macrostructure will be done in combination with that of the microstructure in the microscale. The bi-directional evolutionary optimization algorithm with binary design variables is implemented. Some numerical examples are developed to validate the proposed methodology and compared with the literature whenever possible.
Keywords
BESO, natural frequency, optimal design, SIMP
