Reliability mesh convergence analysis by introducing expanded control variates

doi:10.1007/s11709-020-0631-6

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (4) : 1012-1023 https://doi.org/10.1007/s11709-020-0631-6

RESEARCH ARTICLE

Reliability mesh convergence analysis by introducing expanded control variates

Alireza GHAVIDEL¹(

), Mohsen RASHKI², Hamed GHOHANI ARAB¹, Mehdi AZHDARY MOGHADDAM¹

¹. Civil Engineering Department, University of Sistan and Baluchestan, Zahedan 9816745563, Iran
². Department of Architecture, University of Sistan and Baluchestan, Zahedan 9816745563, Iran

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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 FEM-based 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 finite element reliability mesh convergence analysis expanded control variates

Corresponding Author(s): Mohsen RASHKI

Online First Date: 13 July 2020 Issue Date: 27 August 2020

Cite this article:

Alireza GHAVIDEL,Mohsen RASHKI,Hamed GHOHANI ARAB, et al. Reliability mesh convergence analysis by introducing expanded control variates[J]. Front. Struct. Civ. Eng., 2020, 14(4): 1012-1023.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0631-6
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I4/1012

Fig.1 The proposed algorithm.

Fig.2 The clamped beam with uniform load.

Tab.1 Description of basic random variables for the single edge notch

Fig.3 The convergence of maximum deflection of the beam at the mean point in FEA

Fig.4 Reliability mesh convergence of the clamped non-prismatic beam by the proposed approach.

Fig.5 Convergence of correction factor until to be constant.

Fig.6 CDF Vs. G value for the generated sample for FE models with different mesh density.

Fig.7 The clamped non-prismatic column.

Tab.2 Description of basic random variables for the prismatic column

Fig.8 Convergence of stress intensity at different mesh densities at the mean point and their relevant scaled computational time for the non-prismatic column.

Fig.9 Reliability index for different mesh densities of non-prismatic column.

Fig.10 Convergence history of the proposed correction factors for non-prismatic column.

Fig.11 The single edge notch specimen.

Tab.3 Description of basic random variables for the single edge notch

Fig.12 Convergence of stress intensity at different mesh densities at the mean point and their relevant scaled computational time.

Fig.13 Reliability index for different mesh densities of single edge notch specimen.

Fig.14 Convergence history of the proposed correction factor for single edge notch specimen.

Fig.15 A simply supported beam: (A) structure, (B) stress-strain curve of the hypoelastic material.

variable	mean	distribution	coefficient of variation
L (m)	3	normal	0.02
W (m)	0.5	normal	0.02
q (kN/m)	100	normal	0.20
$σ 0 (M P a)$	250	normal	0.05
$? 0$	0.03	normal	0.05
$n$	5	normal	0.05

Tab.4 Description of basic random variables for the nonlinear beam

Fig.16 Convergence of maximum deflection at different mesh densities at the mean point and their relevant scaled computational time for nonlinear simply supported beam.

Fig.17 Reliability index for different mesh densities of the nonlinear simply supported beam.

Fig.18 Convergence history of the proposed correction factor for the nonlinear simply supported beam.

1	A S Nowak, K R Collins. Reliability of Structures. New York: McGraw-Hill, 2000
2	L Gallimard. Error bounds for the reliability index in finite element reliability analysis. International Journal for Numerical Methods in Engineering, 2011, 87(8): 781–794 https://doi.org/10.1002/nme.3136
3	A Ghavidel, M Rashki, S R Mousavi. The effect of FEM mesh density on the failure probability analysis of structures. KSCE Journal of Civil Engineering, 2018, 22(7): 2371–2383
4	M Rashki, A Ghavidel, H Ghohani Arab, S R Mousavi. Low-cost finite element method-based reliability analysis using adjusted control variate technique. Structural Safety, 2018, 75: 133–142 https://doi.org/10.1016/j.strusafe.2017.11.005
5	A Javed, K Djijdeli, J T Xing. A coupled meshfree-mesh-based solution scheme on hybrid grid for flow-induced vibrations. Acta Mechanica, 2016, 227(8): 2245–2274 https://doi.org/10.1007/s00707-016-1614-5
6	Z Li, R Wood. Accuracy verification of a 2D adaptive mesh refinement method for incompressible or steady flow. Journal of Computational and Applied Mathematics, 2017, 318: 259–265 https://doi.org/10.1016/j.cam.2016.09.022
7	N R Morgan, J I Waltz. 3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement. Journal of Computational Physics, 2017, 336: 492–512 https://doi.org/10.1016/j.jcp.2017.02.030
8	C Anitescu, M N Hossain, T Rabczuk. Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes. Computer Methods in Applied Mechanics and Engineering, 2018, 328: 638–662 https://doi.org/10.1016/j.cma.2017.08.032
9	P Hennig, M Kästner, P Morgenstern, D Peterseim. Adaptive mesh refinement strategies in isogeometric analysis—A computational comparison. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 424–448 https://doi.org/10.1016/j.cma.2016.07.029
10	N Ray, I Grindeanu, X Zhao, V Mahadevan, X Jiao. Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes. Computer Aided Design, 2017, 85: 68–82 https://doi.org/10.1016/j.cad.2016.07.011
11	A Bespalov, A Haberl, D Praetorius. Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems. Computer Methods in Applied Mechanics and Engineering, 2017, 317: 318–340 https://doi.org/10.1016/j.cma.2016.12.014
12	T Rabczuk, H Ren, X Zhuang. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Computers, Materials & Continua, 2019, 59(1): 31–55 https://doi.org/10.32604/cmc.2019.04567
13	C Anitescu, E Atroshchenko, N Alajlan, T Rabczuk. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359 https://doi.org/10.32604/cmc.2019.06641
14	H Guo, X Zhuang, T Rabczuk. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456 https://doi.org/10.32604/cmc.2019.06660
15	S Weiber. Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM. Computers & Mathematics with Applications (Oxford, England), 2017, 73(2): 187–202 https://doi.org/10.1016/j.camwa.2016.11.013
16	J Wu, H Zheng. Uniform convergence of multigrid methods for adaptive meshes. Applied Numerical Mathematics, 2017, 113: 109–123 https://doi.org/10.1016/j.apnum.2016.11.005
17	G R Liu. The smoothed finite element method (S-FEM): A framework for the design of numerical models for desired solutions. Frontiers of Structural and Civil Engineering, 2019, 13(2): 456–477 https://doi.org/10.1007/s11709-019-0519-5
18	P Brambilla, P Brivio, A Guardone, G Romanelli. Grid convergence assessment for adaptive grid simulations of normal drop impacts onto liquid films in axi-symmetric and three-dimensional geometries. Applied Mathematics and Computation, 2015, 267: 487–497 https://doi.org/10.1016/j.amc.2015.01.097
19	D P Lockard. In search of grid converged solutions. Procedia Engineering, 2010, 6: 224–233 https://doi.org/10.1016/j.proeng.2010.09.024
20	P Płaszewski, K Banaś. Performance analysis of iterative solvers of linear equations for Hp-adaptive finite element method. Procedia Computer Science, 2013, 18: 1584–1593 https://doi.org/10.1016/j.procs.2013.05.326
21	A C Jones, R K Wilcox. Finite element analysis of the spine: Towards a framework of verification, validation and sensitivity analysis. Medical Engineering & Physics, 2008, 30(10): 1287–1304 https://doi.org/10.1016/j.medengphy.2008.09.006
22	K M Hamdia, H Ghasemi, X Zhuang, N Alajlan, T Rabczuk. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 337: 95–109 https://doi.org/10.1016/j.cma.2018.03.016
23	P L Liu, K G Liu. Selection of random field mesh in finite element reliability analysis. Journal of Engineering Mechanics, 1993, 119(4): 667–680 https://doi.org/10.1061/(ASCE)0733-9399(1993)119:4(667)
24	M Manjuprasad, C S Manohar. Adaptive random field mesh refinements in stochastic finite element reliability analysis of structures. Computer Modeling in Engineering & Sciences, 2007, 19(1): 23–54
25	B Tracey, D Wolper. Reducing the error of Monte Carlo algorithms by learning control variates. In: The 29th Conference on Neural Information Processing Systems (NIPS). Barcelona, 2016
26	M Rashki, M Miri, M Azhdary Moghaddam. A new efficient simulation method to approximate the probability of failure and most probable point. Structural Safety, 2012, 39: 22–29 https://doi.org/10.1016/j.strusafe.2012.06.003
27	H G Arab, M Rashki, M Rostamian, A Ghavidel, H Shahraki. Refined first-order reliability method using cross-entropy optimization method. Engineering with Computers, 2018, 35: 1–13 https://doi.org/10.1007/s00366-018-0680-9
28	D K E Green. Efficient Markov Chain Monte Carlo for combined subset simulation and nonlinear finite element analysis. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 337–361 https://doi.org/10.1016/j.cma.2016.10.012
29	T H G Megson. Structural and Stress Analysis. 2nd ed. Amsterdam/London: Elsevier Butterworth-Heinemann, 2005
30	R W Clough, J Penzien. Dynamics of Structures. 2nd ed. New York: McGraw-Hill, 1993
31	H Tada, P C Paris, G R Irwin. The Stress Analysis of Cracks Handbook. New York: ASME press, 2000
32	A F Bower. Applied Mechanics of Solids. Boca Raton: CRC Press, Taylor & Francis, 2009

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