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MECSOL 2022
8th International Symposium on Solid Mechanics
Topology Optimization with Volume and Natural Frequency Constraints by Using the TOBS Method.
Submission Author:
Lucas Oliveira Siqueira , SP
Co-Authors:
Lucas Oliveira Siqueira, Emilio Carlos Nelli Silva, Renato Picelli
Presenter: Lucas Oliveira Siqueira
doi://10.26678/ABCM.MECSOL2022.MSL22-0067
Abstract
A challenge for topology optimization methods is to incorporate multiple constraints into the structural design. This type of problems can be important for the design of vibrating structures, allowing to change the structural layout so that the natural frequencies of the structure deviates from the operating frequency while maintaining the structural stiffness. In this paper, it is proposed to perform topology optimization with volume and natural frequency constraints to obtain a stiff design. The Topology Optimization of Binary Structures (TOBS) method is employed. The equilibrium equations are solved by using finite element method. The modified SIMP model is used as a material interpolation model to obtain the natural frequency sensitivities. The first four natural frequencies for each case are observed using the Modal Assurance Criterion (MAC)-based mode-tracking seeking to evaluate mode crossing. The algorithm is tested and verified for two bidimensional problems, the biclamped beam and the tower subjected to a horizontal load. Different values of natural frequency constraints are tested, looking at the final topology and mode crossing. The penalty variation effect in final topology is verified. This is the first time a binary topology optimization method is employed to incorporate multiple volume and natural frequency constraints.Numerical results show that the TOBS method suits well the present problem, providing optimum layouts for structures subjected to vibrations maintaining the natural frequency in levels established in the optimization process.
Keywords
Topology optimization, Integer Linear Programming, natural frequency, Modified SIMP model
