Abstract

This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.

Highlights

  • The term free-form shells refers to shells whose geometric shapes cannot be represented by certain mathematical formulas or their combination [1]

  • The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process

  • The distribution of initial geometric imperfection throughout the shell is determined by the consistent mode imperfection method [24], while the shell thickness deviation and elastic modulus deviation are assumed to be uniformly distributed over the shell

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Summary

Introduction

The term free-form shells refers to shells whose geometric shapes cannot be represented by certain mathematical formulas or their combination [1]. Yan [4] developed a height adjusting method to obtain optimal shape of free-form shells, with respect to minimum strain energy. It can be seen that, in the past decades, numerical optimization methods have been developed for free-form shells, many of which made efforts to obtain a geometrical shape with minimum strain energy, i.e., largest structural stiffness. The construction process of free-form shells is more complex when compared with traditional shells, which tends to lead more uncertainty factors This further motivates this study to consider the effects of uncertainty factors on mechanical properties of free-form shells, on the dynamic characteristics. The stochastic natural vibration analyses of free-form shells is carried out while considering three uncertainty factors, including geometric imperfection, shell thickness deviation, and elastic modulus deviation. The results are reported along with discussions; Section 5 provides closing remarks

Shape Parametrization
Optimization
Stochastic and Sensitivity Analysis Method
Results and Discussion
Model Generation
Stochastic and Sensitivity Analysis
Evolution the first three natural frequencies of Model
Stochastic
Conclusions
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