Abstract
Herein, to improve the dynamic performance of continuum structures, their fundamental frequency is optimized using the topology optimization method. This helps to obtain the best material distribution in the design space and increases the fundamental frequency of the structure higher than the disturbance frequency. Using the variable density method, the dynamic topology optimization model of a long-span continuum structure is built based on the density interpolation model of a solid isotropic material with penalization (SIMP). The goal of this optimization is to maximize the first-order eigenvalue, and the optimization constraint is that the total volume of the structure is smaller than the given value. To improve the efficiency and accuracy of the model, sensitivity filtering is adopted to avoid numerical instability during calculation. Moreover, the optimization criterion method is used to iteratively solve the optimization results. Finally, the structural topology optimization method is implemented on the long-span single beam of a bridge crane at a construction site. The results show that the natural frequency of the structure is increased and the modal characteristics are improved, which lays the foundation for further optimization and dynamic-response analysis.
Highlights
In comparison to static topology optimization, research on the dynamic topology optimization of engineering structures is still limited owing to the difficulty in setting up a model for continuum topology optimization, along with the large computational cost of using numerical algorithms in engineering applications
Yang et al [13] proposed a structural topology optimization method with regular geometric constraints in combination with a method based on the changes in material properties and the bidirectional evolutionary structural optimization method, aimed at solving the structural optimization problem in the design of fuselage flutter models, which takes the modal values as the goal
The topology optimization calculation of a large-span continuum structure of construction machinery is implemented to improve the natural frequency and modal characteristics, which lays the foundation for further optimization design and dynamic-response analysis. e innovation of this paper is the presentation of an optimization criterion method by constructing the Lagrange function by introducing Lagrange multiplier based on Kuhn–Tucker condition to overcome the large computational cost and cope with the implicit nonlinear objective function in topology optimization of large-span engineering structures
Summary
In comparison to static topology optimization, research on the dynamic topology optimization of engineering structures is still limited owing to the difficulty in setting up a model for continuum topology optimization, along with the large computational cost of using numerical algorithms in engineering applications. En, the relationship between the subdomains and the optimization domain was constructed to establish a mathematical model for the periodic topology optimization of the girder In this optimization problem, the relative density of the elements in the optimization domain was taken as the design variable and the minimum compliance under the volume constraint as the objective function. A topology optimization model is established by combining the topology optimization method and finite element theory In this model, maximizing the firstorder eigenvalue is the goal, the total volume of the structure is the constraint, and the relative density of the elements is the design variable. E innovation of this paper is the presentation of an optimization criterion method by constructing the Lagrange function by introducing Lagrange multiplier based on Kuhn–Tucker condition to overcome the large computational cost and cope with the implicit nonlinear objective function in topology optimization of large-span engineering structures The topology optimization calculation of a large-span continuum structure of construction machinery is implemented to improve the natural frequency and modal characteristics, which lays the foundation for further optimization design and dynamic-response analysis. e innovation of this paper is the presentation of an optimization criterion method by constructing the Lagrange function by introducing Lagrange multiplier based on Kuhn–Tucker condition to overcome the large computational cost and cope with the implicit nonlinear objective function in topology optimization of large-span engineering structures
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