Abstract
A method to optimize the topology of frame bracing system is presented. Firstly frame is filled by truss-like continuum uniformly. The truss-like continuum simulates the distributive bracing system. The frame combined with truss-like continuum is analyzed by finite element method. The densities and orientations of bracing system at nodes are taken as design variables. The distribution field of bracing system is optimized by the method of moving asymptotes (MMA) and the method of steepest descent. The frame bracing system is established according to the optimal distribution field of bracing system. The natural frequency of optimal braced frame increases to more than two times while material increases only 5%. For no intermediate densities being suppressed, there is no numerical instability, such as checkerboard patterns and one-node connected hinges. The expression of natural frequency and its sensitivities of truss-like continuum are derived.
Highlights
Frame is used widely in structural engineering
When frame is acted by wind and earthquake, increasing the later stiffness and natural frequency of frame become the most important design object [1]
An effective mean is to optimize the sectional sizes of members and the structural shapes. These optimization techniques are termed as size optimization and shape optimization, respectively. By these techniques structural performance is improved on the condition that the structural topology is prescribed
Summary
Frame is used widely in structural engineering. Its later stiffness of frame is more important design factor than its strength. An effective mean is to optimize the sectional sizes of members and the structural shapes (the positions of nodes, for example). It is effective to design the reinforcement material by topology optimization method [11, 12]. In these optimization methods, isotropic continua are taken as ground structures. Mijar and Qing used evolutionary structural optimization method to optimize the bracing system of frame to minimize structural compliance [2, 3]. The bracing system is expressed by a series of conjoint uniform isotropic elements remaining in structure. Michell's work has revealed the fact that topological optimal structures are truss-like continua generally [5]. The optimization method is applied to optimize the frame bracing system
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