Abstract
For a long time, spatial structures have been widely used. However, compared with the high strength of their material, their stability is weak, and especially sensitive to damage and defects. This feature has increased the engineering industry’s high requirements for their stability analysis. As we all know, this problem is more prominent for the reticulated shell structure, which is a classic representative of the spatial structure. However, in the current analysis methods for the stability of reticulated shells, the deterministic analysis method cannot consider the random characteristics of defects. Other random methods, such as the random defect modal method, and many improved methods, require more samples and calculation time. This unfavorable situation makes its engineering application greatly restricted. In addition, the random modal superposition method and derivation method based on Monte Carlo has not fundamentally changed this limitation. In order to fundamentally overcome this traditional shortcoming, this paper comprehensively studies the advantages of the high accuracy of the random defect modal method and the improved method, and at the same time, investigates the speed advantage of the response surface method, and then creates a new stochastic analysis method based on the response surface method. Finally, the analysis results of the calculation examples in this paper prove that it successfully balances and satisfies the dual requirements of accuracy and speed required for calculating the stability of the reticulated shell structure. Moreover, it has universal applicability to different forms of reticulated shells, such as classic 6-point flat domes, traditional reticulated shell structures, and bionic reticulated shell structures, and even other types of spatial structures.
Highlights
This method is limited to Monte Carlo sampling (MCS), which requires increasing number of sample capacity
The above figures prove that the optimal fitting function is the Quax polynomial when employing the central composite design (CCD) collocation method
Compared with the result of MCS method, the relative error of pcr under each random variable number of the new method meets the engineering accuracy requirement, not larger than 5%; The number of different random variables will cause the results of the new method to fluctuate to a certain extent
Summary
The current main popular analysis methods for the stability of reticulated shells are either theoretical methods [21] or deterministic analysis methods [22,23], such as optimization methods [24], critical imperfection methods [25], and the consistent mode imperfection methods [26,27], and their improvement methods cannot consider the imperfection randomness In response to this problem, some scholars have proposed a random analysis method based on numerical methods—the random defect modal method [28,29]. Some other scholars have proposed more improved methods [30] As a result, they can accurately solve the random distribution of geometric node defects but generally require more samples and time consumption [31]. A new method devoted overcoming the abovementioned shortcomings is described in the present work
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