Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency

Niu, Bin; Yan, Jun; Cheng, Gengdong

doi:10.1007/s00158-008-0334-4

Cited by 196 publications

(61 citation statements)

References 43 publications

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“…Again homogenization is used to bridge the scales and the derivatives of macroscale objective and constraint functions with respect to the microscale design variables are obtained by differentiating the homogenization equations. It is thus straightforward to solve for many structural design problems beyond compliance and has been used to solve for natural frequency (Niu et al 2009) and multiobjective thermoelastic problems (Deng et al 2013). However, this approach does not allow local tailoring of material properties and cannot explore the full structurematerial design space, thus limiting the potential performance gains that may otherwise be possible.…”

Section: Figure 1 Multiscale Topology Optimizationmentioning

confidence: 99%

Simultaneous material and structural optimization by multiscale topology optimization

Sivapuram

Dunning

Kim

2016

Struct Multidisc Optim

255

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This paper introduces a new approach to multiscale optimization, where design optimization is applied at two scales: the macroscale, where the structure is optimized, and the microscale, where the material is optimized. Thus, structure and material are optimized simultaneously. We approach multiscale design optimization by linearizing and formulating a new way to decompose into macro and microscale design problems in such a way that solving the decomposed problems separately lead to an overall optimum solution. In addition, the macro and microstructural designs are coupled tightly through homogenization and inverse homogenization. This approach is generic in that it allows any number of unique microstructures and can be applied to a wide range of design problems. An advantage of decomposing the problem in this physical way is that it is potentially straight forward to specify additional design requirements at a specific scale or in specific regions of the design domain. The decomposition approach also allows an easy parallelization of the computational methodology and this enables the computational time to be maintained at a practical level. We demonstrate the proposed approach using the level-set topology optimization at both scales, i.e. macrostructural topological design and microstructural topology of architected material. A series of optimization problems, minimizing compliance and compliant mechanism are solved for verification and investigation of potential benefits.

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Section: Figure 1 Multiscale Topology Optimizationmentioning

confidence: 99%

Simultaneous material and structural optimization by multiscale topology optimization

Sivapuram

Dunning

Kim

2016

Struct Multidisc Optim

255

View full text Add to dashboard Cite

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“…In buckling optimization and other eigenvalue problems for plate structures, user defined reinforcements are often used as non-design domains to create acceptable load-paths (Bendsoe and Sigmund 2003;Niu et al 2009). It is evident that the present proposed connectivity coefficient can also be effective to serve the purpose of ensuring load-path continuity.…”

Section: Optimal Buckling Design For a Relatively-narrow Plate And Comentioning

confidence: 99%

“…When eigenvalue λ 1 is repeated, the correct eigenvector may not be selected owing to multiple eigenvectors, which leads to mode switching and subsequently slows down convergence or even causes iterative divergence. A linear combination of eigenvalues or average-mean eigenvalues can be used as an objective function to prevent the mode switch in optimization to maximize a specific eigenvalue (Ma et al 1995;Neves et al 2002;Du and Olhoff 2007;Niu et al 2009). A mode tracking technique can also be used (Eldred et al 1995;Bruyneel et al 2008) to monitor the mode switch and it will be used in the present MIST computing.…”

Section: Introductionmentioning

confidence: 99%

Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

Luo

Tong

2015

Struct Multidisc Optim

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This paper investigates topology design optimization for maximizing critical buckling loads of thin-walled structures using a moving iso-surface threshold (MIST) method. Formulation for maximizing linear buckling loads with additional constraints on load-path continuity and lower bound of eigenvalue is firstly presented. New physical response functions are proposed and expressed in terms of the strain energy densities determined in the two-steps of finite element buckling analysis. A novel approach by introducing a connectivity coefficient is developed to ensure continuity of effective load-path in optimum topology. The lower bound of eigenvalue is defined to eliminate spurious localized buckling modes. The MIST algorithm and its interfaces with commercial finite element (FE) software are given in detail. Numerical results are presented for topology optimization of plate-like structures to maximize critical buckling forces or displacements considering in-plane and out-of-plane buckling respectively. The FE analyses of the re-meshed final solid topologies with and without void material reveal that the presence of the void material has a significant effect on the out-of-plane buckling loads and a minor influence on the in-plane buckling loads.

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“…The problem of design optimization of various types of structures for maximum value of a natural frequency or maximum gap between two adjacent natural frequencies is extensively studied, see, e.g., [23][24][25][26][27] for shape optimization of beam structures, and reference may be given to, e.g., [12,15,16,28,29] for topology optimization of continuum structures, and to [30] for two-scale topology optimization of continuum structures with microstructures. An abundance of other references is available in the exhaustive textbook [31].…”

Section: Introductionmentioning

confidence: 99%

On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. A band-gap structure usually consists of a periodic distribution of elastic materials or segments, where the propagation of waves is impeded or This paper extends earlier optimum shape design results for transversely vibrating Bernoulli-Euler beams by determining new optimum band-gap beam structures for (i) different combinations of classical boundary conditions, (ii) much larger values of the orders n (n>1) and n-1 of adjacent upper and lower eigenfrequencies of maximized band-gaps, and (iii) different values of a minimum beam cross-sectional area constraint. In the present paper, instead of maximizing band-gaps between frequencies of propagating waves or forced vibrations excited by external time-harmonic loads, the closely relatedproblem of maximizing the gap between two adjacent eigenfrequencies ω n and ω n-1 of any given consecutive orders n (n>1) and n-1, is considered. This is justified by the fact that external time-harmonic dynamic loads cannot excite resonance with high vibration levels of standing waves, if the eigenfrequencies of the structure are moved outside the range of the external excitation frequencies by the optimization.Finally, the present study shows that if an infinite beam structure is constructed by repeated translation of an inner beam segment obtained by the aforementioned frequency gap optimization, then a band-gap of traveling waves in this infinite beam is found to correlate almost perfectly with the maximized frequency gap in the finite structure.

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Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency

Cited by 196 publications

References 43 publications

Simultaneous material and structural optimization by multiscale topology optimization

Simultaneous material and structural optimization by multiscale topology optimization

Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

On Optimum Design and Periodicity of Band-Gap Structures

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