Structural dynamic shape optimization and sensitivity analysis based on RKPM

Zhang, Jianping; Gong, Shengrong; Huang, Yunqing; Qiu, Aihong; Chen, Renke

doi:10.1007/s00158-007-0166-7

Cited by 15 publications

(7 citation statements)

References 20 publications

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“…The kernel function plays an important role in the reproducing kernel approximation. In this paper, the cubic spline function [10] that has a 2 C continuity is chosen as the kernel function. More details about RKPM can be found in the references [9,10].…”

Section: Review Of Rkpmmentioning

confidence: 99%

“…In this paper, the cubic spline function [10] that has a 2 C continuity is chosen as the kernel function. More details about RKPM can be found in the references [9,10].…”

Section: Review Of Rkpmmentioning

confidence: 99%

“…The emerging meshless methods that are based on node approximation can resolve above difficulties successfully. During many meshless methods, the Reproducing Kernel Particle Method (RKPM) [9] has its unique advantages of variable time-frequency property and multi-resolution characteristics, and it has been widely applied in structural dynamics and shape optimization [10].…”

Section: Introductionmentioning

confidence: 99%

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Structural Dynamic Topology Optimization and Sensitivity Analysis Based on RKPM

Zhang

Gong

Jiang

2010

AMR

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A numerical method for structural dynamic topology optimization and sensitivity analysis is presented by using RKPM. In this paper, the relative density of node and maximum fundamental eigenfrequency is respectively chosen as design variable and the objective function, and then the mathematical model for dynamic topology optimization based on RKPM is built. During the process of modeling, some effective measures are taken to dispose the multi-eigenvalues and localized modes. Subsequently, the sensitivity analysis equation is proposed by using Direct Differentiation Method. Finally, by integrating the above sensitivity analysis with Optimality Criteria method, the dynamic topology optimization of an example is performed successfully. Numerical example shows that both checkboards and localized eigenmodes do not occur during topology optimization, and it indicates the proposed method is valid.

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Section: Review Of Rkpmmentioning

confidence: 99%

“…In this paper, the cubic spline function [10] that has a 2 C continuity is chosen as the kernel function. More details about RKPM can be found in the references [9,10].…”

Section: Review Of Rkpmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Structural Dynamic Topology Optimization and Sensitivity Analysis Based on RKPM

Zhang

Gong

Jiang

2010

AMR

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“…Compared with other meshfree methods, RKPM has advantages as follows 19,20 : (1) RKPM retains the advantages of free Lagrangian or SPH methods; (2) RKPM is more accurate than SPH due to the addition of the correction function; (3) RKPM is more efficient in computer implementation than diffuse element method and EFG. Therefore, RKPM has attracted many researchers to use it to solve many problems in different fields, such as material analysis, 30–32 fluid mechanics, 33,34 and structural engineering 35–37 . Chen et al 38 and Memar Ardestani et al 39 successfully used the RKPM to effectively analyze the bending problems of flat and ribbed plates.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, RKPM has attracted many researchers to use it to solve many problems in different fields, such as material analysis, [30][31][32] fluid mechanics, 33,34 and structural engineering. [35][36][37] Chen et al 38 and Memar Ardestani et al 39 successfully used the RKPM to effectively analyze the bending problems of flat and ribbed plates. In view of this, this paper further used RKPM to conduct a meshfree analysis of the behavior of the ribbed folded plate roof under the vertical uniform loads.…”

Section: Introductionmentioning

confidence: 99%

Static behavior of ribbed folded plate roof under vertical uniform load—Experimental study and meshfree method analysis

Sun,

Ma,

Zhang

et al. 2023

Structural Design Tall Build

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SummaryFolded plate roofs are widely used in building roofs due to their light weight and high stiffness. However, traditional folded plate roofs are often limited in application due to insufficient stiffness under the current trend of pursuing larger‐span roofs. Ribbed folded plate roofs can effectively solve this problem because ribs not only increase the stiffness of the roof and reduce stress concentration, but they are also easy to be formed into various shapes to meet different needs for buildings. Therefore, the detailed analysis was carried out on a reinforced concrete ribbed folded plate roof (RCRFR) under the vertical uniform load to investigate its static behavior. The bearing capacity, failure mode, load–displacement relationship, and strain variation were obtained through the test. Additionally, based on the finite element (FE) method, not only a comparison was conducted between RCRFR and reinforced concrete ribless folded plate roof (RCLFR), but the influence of material nonlinearity and geometric nonlinearity on the structure was also investigated. Moreover, the bending characteristics of RCRFR under design load were analyzed based on the reproducing kernel particle method. The experimental results showed that this structure had good mechanical properties within the design load. In the overload stage, the concrete on the underside of the structure was severely damaged. Furthermore, the yielding of the ribbed plate's reinforcing bars caused the increased vertical deformation difference between the ribbed plate and the top chord, and the ribbed plate and the central ridge beam. Eventually, the failure of the anchorage of the ribbed plate's reinforcing bars anchored in the central ridge beam and the top chord led to the loss of structural load‐bearing capacity. The FE analysis results demonstrated that ribs enhance the stiffness of the structure, with material nonlinearity having the primary impact and geometric nonlinearity exerting a secondary effect. The meshfree method analysis was in concordance with the experimental results as well as those of the FE analysis.

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Parametric shape optimization techniques based on Meshless methods: A review

Daxini

Prajapati

2017

Struct Multidisc Optim

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Structural dynamic shape optimization and sensitivity analysis based on RKPM

Cited by 15 publications

References 20 publications

Structural Dynamic Topology Optimization and Sensitivity Analysis Based on RKPM

Structural Dynamic Topology Optimization and Sensitivity Analysis Based on RKPM

Static behavior of ribbed folded plate roof under vertical uniform load—Experimental study and meshfree method analysis

Parametric shape optimization techniques based on Meshless methods: A review

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