Xuwen An^1,2, Jianguo Hou³, P.D. Gosling⁴, Dong Dai⁵, Long Xiao⁶, Xiaoyi Zhou⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.1, pp. 1-25, 2015, DOI:10.3970/cmes.2015.107.001

Abstract Studies on the theory of structural system reliability includes identification of main the failure modes and calculation of inclusive failure probabilities for the structural system. The efficient and accurate identification of failure modes in structural systems is difficult and represents a key focus for research in system reliability. The fundamental theory of the branch and bound algorithm for stage critical strength is reviewed in this paper. Some deficiencies in this method are highlighted. Corresponding approaches to overcome these deficiencies are proposed. Calculated system reliability solutions to the classical model, a truss with 10 elements, indicate that the improvement measures proposed… More >

Damian Sokolowski¹, Marcin Kamiński², Michal Strakowski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 209-231, 2014, DOI:10.3970/cmes.2014.099.209

Abstract The main issue in this paper is to present stochastic analysis of the steel plate girder with the corrugated web subjected to Gaussian random fluctuations in its web thickness. Such an analysis is carried out using the Stochastic Finite Element Method based on the generalized stochastic perturbation technique and discretization of structure with the quadrilateral 4-noded shell finite elements. It is numerically implemented using the FEM system ABAQUS and the symbolic algebra system MAPLE, where all the probabilistic procedures are programmed. We compare the perturbation-based results with these obtained from traditional Monte-Carlo simulation and, separately, analytical solution calculated by a… More >

Zichun Yang^1,2, Maolin Peng^1,3,4, Yueyun Cao¹, Lei Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.4, pp. 409-442, 2014, DOI:10.3970/cmes.2014.098.409

Abstract A new multi-objective reliability-based robust design optimization (M ORBRDO) model is proposed which integrats the multi-objective robustness, the reliability sensitivity robustness and the six sigma robustness design idea. The pure-quadratic polynomial functions are adopted to fit the performance objective functions (POF) and the ultimate limited state functions (ULSF) of the structure. Based on the ULSF and the checking point method, the equations of the first order reliability index are calculated. The mapping transformation method is employed when the non-normal distribution variables are included. According to the POF and the Taylor series expansion method, the equations of mean value and standard… More >

Xiyong Huang¹, M. H. Aliabadi², Z. Sharif Khodaei³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 291-330, 2014, DOI:10.3970/cmes.2014.102.291

Abstract In this paper, a stochastic dual boundary element formulation is presented for probabilistic analysis of fatigue crack growth. The method involves a direct differentiation approach for calculating boundary and fracture response derivatives with respect to random parameters. Total derivatives method is used to obtain the derivatives of fatigue parameters with respect to random parameters. First- Order Reliability Method (FORM) is applied to evaluate the most probable point (MPP). Opening mode fatigue crack growth problems are used as benchmarks to demonstrate the performance of the proposed method. More >

Zichun Yang^1,2,3, Kunfeng Li^1,4, Qi Cai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 143-171, 2013, DOI:10.3970/cmes.2013.095.143

Abstract The conventional probabilistic reliability model for structures is based on the “probability assumption” and “binary-state assumption”. These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the “mixed probability and possibility assumption” and “fuzzy state… More >

W. Zhao^1,2, J.K. Liu³, X.Y. Li², Q.W. Yang⁴, Y.Y. Chen⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 469-488, 2013, DOI:10.3970/cmes.2013.093.469

Abstract In order to obtain reliable structural design, it is of extreme importance to evaluate the failure probability, safety levels of structure (reliability analysis) and the effect of a change in a variable parameter on structural safety (sensitivity analysis) when uncertainties are considered. With a computationally cheaper approximation of the limit state function, various response surface methods (RSMs) have emerged as a convenient tool to solve this especially for complex problems. However, the traditional RSMs may produce large errors in some conditions especially for those highly non-linear limit state functions. Instead of the traditional least squares approximation, in the present paper,… More >

Mohsen Sadeghbeigi Olyaie¹, Mohammad Reza Razfar², Edward J. Kansa³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.1, pp. 43-88, 2011, DOI:10.3970/cmes.2011.075.043

Abstract This paper presents integration of reliability analysis with topology optimization design for a linear mircroactuator, including multitude cantilever piezoelectric bimorphs. Each microbimoph in the mechanism can be actuated in both axial and flexural modes simultaneously. We consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Since microfabrication methods are used for manufacturing this type of actuator, uncertainty variables become very important. Hence, these variables are considered as constraints during our topology optimization design process and reliability based topology optimization (RBTO) is conducted. To avoid the overly-stiff behavior in FEM… More >

M.M. Kamiński¹, J. Szafran¹

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 143-168, 2012, DOI:10.32604/cmes.2012.083.143

Abstract The main issue in this article is computational probabilistic analysis and reliability assessment of the steel telecommunication towers subjected to material and environmental uncertainty. Such a discussion is important since very wide, frequent and relatively modern application of these structures, which are subjected to various sources of uncertainty and having at this moment no rich and time-dependent failure evidence. Numerical analysis is based on the generalized stochastic perturbation technique implemented as the Stochastic Finite Elements using the Response Function Method applied with the use of computer algebra system. A simultaneous usage of the engineering FEM system and mathematical package enables… More >

S.R. Santos¹, L.C. Matioli², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 23-56, 2012, DOI:10.3970/cmes.2012.083.023

Abstract Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on… More >

Fangyi Li^1,2, Zhen Luo³, Guangyong Sun⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.1, pp. 39-64, 2011, DOI:10.3970/cmes.2011.074.039

Abstract This paper studies the reliability-based multiobjective optimization by using a new interval strategy to model uncertain parameters. A new satisfaction degree of interval, which is significantly extended from [0, 1] to [–∞, +∞], is introduced into the non-probabilistic reliability-based optimization. Based on a predefined satisfaction degree level, the uncertain constraints can be effectively transformed into deterministic ones. The interval number programming method is applied to change each uncertain objective function to a deterministic two-objective optimization. So in this way the uncertain multiobjective optimization problem is transformed into a deterministic optimization problem and a reliability-based multiobjective optimization is then established. For… More >