Authors: Wen Ying Chen, Fu Lei Chu, Shao Ze Yan, Ke Yun Wang

Abstract: The upper and lower bound estimation of natural frequencies for intelligent truss structure
with uncertain-but-bounded parameters is studied in this paper. Firstly, following the finite element
method, the expressions of the interval stiffness and interval mass matrix of piezoelectric intelligent
truss structures are derived directly from the interval parameters. Then, based on the matrix
perturbation and interval extension theory, an interval parameter perturbation method is proposed
for solving the upper and lower bound of natural frequencies. Finally, a 16-bar planar intelligent
truss structure is used as an example to illustrate the applicability and validity of the presented
method, and some useful conclusions are obtained.

569

Authors: Wei Zhao, J.K. Liu, Qiu Wei Yang

Abstract: The structural reliability analysis with uncertainty-but-bounded parameters is considered in this paper. Each uncertain-but-bounded parameter is represented as an interval number or vector, an interval reliability index is defined and discussed. Due to the wide application of the Meshless method, it is used in structural stress and strain analysis. The target variable of requiring reliability analysis is estimated via Taylor expansion. Based on optimization theory and vertex solution theorem, the upper and lower bounds of the target variables are obtained, and also the interval reliability index. A typical elastostatics example is presented to illustrate the computational aspects of interval reliability analysis in comparison with the traditional probability method, it can be seen that the result calculated by the vertex solution theorem is consistent with that calculated by probability method.

3034

Authors: Chang Hong Liu, X.C. Qing, F.Z. Xuan, S.T. Tu

Abstract: According to the non-probabilistic finite element algorithms, the random finite element equations are translated into the interval finite element equations. Firstly, with the concept of confidence interval in the probability, a interval number can be taken as the random variable with the uniform distribution. Secondly, the uniform random Monte Carlo (MC) finite element method and optimization finite element method are presented. Finally, the example shown, when the numbers of random parameters are small, the two algorithms are all effective. But when numbers of random parameters are large, only the uniform random finite element method has the stabilized solving ability.

272

Authors: Ai Rong Zhang, Xiao Liu

Abstract: Due to the dependence of the sample data for a probabilistic reliability model and the fuzzy model, the interval model was used to describe the uncertain parameters through which a new measure of non-probabilistic reliability was established. Studying the model with the non-probabilistic theory, a new measure of non-probabilistic reliability was established which was the minimum distance between the failure region and the total region constructed by all uncertain variables. This kind of measure not only is consistent with the criterion of the non-probabilistic robust reliability, but also has a clearer meaning. The validity and the feasibility were proved through a computational example.

1908

Authors: Yong Wen, Shu Fan Wang, Zhao Jie Yan, Na Liu

Abstract: The interval element-free Galerkin method (IEFGM) is proposed to analyze a bi-material cantilever beam, which is an interfacial mechanics problem including uncertain parameters. Interval method could be applied to study the influences of the uncertain parameters on structural responses. The IEFGM could be used to approximate the displacement fields without depending on meshes. Combining these two methods, the interval equilibrium equations are derived, and a method of dealing with the discontinuities on the interface is introduced.

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