Reliability mesh convergence analysis by introducing expanded control variates
- PDF / 1,521,256 Bytes
- 12 Pages / 595.276 x 785.197 pts Page_size
- 58 Downloads / 180 Views
RESEARCH ARTICLE
Reliability mesh convergence analysis by introducing expanded control variates Alireza GHAVIDELa, Mohsen RASHKIb* , Hamed GHOHANI ARABa, Mehdi AZHDARY MOGHADDAMa a b *
Civil Engineering Department, University of Sistan and Baluchestan, Zahedan 9816745563, Iran Department of Architecture, University of Sistan and Baluchestan, Zahedan 9816745563, Iran
Corresponding author. E-mail: [email protected]
© Higher Education Press 2020
ABSTRACT The safety evaluation of engineering systems whose performance evaluation requires finite element analysis is a challenge in reliability theory. Recently, Adjusted Control Variates Technique (ACVAT) has proposed by the authors to solve this issue. ACVAT uses the results of a finite element method (FEM) model with coarse mesh density as the control variates of the model with fine mesh and efficiently solves FEM-based reliability problems. ACVAT however does not provide any results about the reliability-based mesh convergence of the problem, which is an important tool in FEM. Mesh-refinement analysis allows checking whether the numerical solution is sufficiently accurate, even though the exact solution is unknown. In this study, by introducing expanded control variates (ECV) formulation, ACVAT is improved and the capabilities of the method are also extended for efficient reliability mesh convergence analysis of FEMbased reliability problems. In the present study, the FEM-based reliability analyses of four practical engineering problems are investigated by this method and the corresponding results are compared with accurate results obtained by analytical solutions for two problems. The results confirm that the proposed approach not only handles the mesh refinement progress with the required accuracy, but it also reduces considerably the computational cost of FEM-based reliability problems. KEYWORDS
1
finite element, reliability mesh convergence analysis, expanded control variates
Introduction
Structural reliability estimates the safety level of an engineering system by expressing the following probability integral [1]: Pf ¼ Prob½GðxÞ£0 ¼
!GðxÞ£0f ðxÞdx,
(1)
where Pf is the failure probability, x is a vector of random variables. G(x) represents the limit state function and f(x) denotes the joint probability density function (PDF) of x. When the performance evaluation of the system (value of G(x)) is not computable by an analytical method, finite element (FE) as the most popular and powerful numerical method is applied. Herein, a FE model with very fine mesh density is required to achieve a proper solution in reliability process [2–4]. Therefore, Eq. (1) reads: Article history: Received Apr 8, 2019; Accepted Jul 26, 2019
Pf ¼
!GðxÞ£0 f ðxÞdx ¼ !GðxÞ£0IðGFEA f ine mesh Þf ðxÞdx,
(2)
in which GFEA f ine mesh is the performance of structure obtained by the finite element analysis (FEA) using a model with very fine mesh density and pðGFEA f ine mesh Þ is the index function of the probability integral as follows: ( 1, GFEA f ine mesh £0, IðGFEA (3) f ine mesh Þ ¼ 0, GFEA
Data Loading...
