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The purpose of this paper is to study the deterministic elastic buckling behavior of cylindrical fiber–metal laminate panels subjected to uniaxial compressive loading and the investigation of GLAss fiber-REinforced aluminum laminate (GLARE) panels using probabilistic finite element method (FEM) analysis.

The FEM in combination with the eigenvalue buckling analysis is used for the construction of buckling coefficient–curvature parameter diagrams of seven fiber–metal laminate grades, three glass-fiber composites and monolithic 2024-T3 aluminum. The influences of uncertainties concerning material properties and laminate dimensions on the buckling load are studied with sensitivity analyses.

It is found that aluminum has a stronger impact on the buckling behavior of the fiber–metal laminate panels than their constituent uni-directional or woven composites. For the classical simply supported boundary conditions, it is found that there is an approximately linear relation between the buckling coefficient and the curvature parameter when the diagrams are plotted in double logarithmic scale. The probabilistic calculations demonstrate that there is a considerable probability to overestimate the buckling load of GLARE panels with deterministic calculations.

In this study, the deterministic and probabilistic buckling response of fiber metal laminate panels is investigated. It is shown that realistic structural uncertainties could substantially affect the buckling strength of aerospace components.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This paper aims to reasonably quantify the radial deformation of turbine blade from a probabilistic design perspective. A probabilistic design for turbine blade radial deformation considering non-linear dynamic influences can quantify risk and thus control blade tip clearance to further develop the high performance and high reliability of aeroengine. Moreover, the need for a cost-effective design has resulted in the development of probabilistic design method with high computational efficiency and accuracy to quantify the effects of these uncertainties.

An extremum response surface method-based support vector machine (SVM-ERSM) was proposed based on SVM of regression to improve the computational efficiency and precision of blade radial deformation dynamic probabilistic design regarding non-linear material properties and dynamically thermal and mechanical loads.

Through the example calculation and comparison of methods, the results show that the blade radial deformation reaches at the maximum at t = 180 s; the probabilistic distribution and inverse probabilistic features of output parameters and the major factors (rotor speed and gas temperature) are gained; besides, the SVM-ERSM holds high computational efficiency and precision in the non-linear dynamic probabilistic design of aeroengine typical components.

The present efforts provide a method to design turbine besides other aeroengine components considering dynamic and non-linear factors base on probabilistic design for further research.

Moreover, the present study provides a way to design dynamic (motion) structures from a probabilistic perspective.

It is proved that the dynamic probabilistic design-based SVM-ERSM could produce a more reasonable blade radial deformation while maintaining low failure probability, as well as offer a useful reference for blade-tip clearance control and a promising insight to the optimal design of aeroengine typical components.

The performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability index approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, the purpose of this paper is to propose an efficient PMA-based reliability analysis technique using radial basis function (RBF).

The RBF is adopted to approximate the implicit limit state functions in combination with latin hypercube sampling (LHS) strategy. The advanced mean value method is applied to obtain the most probable point (MPP) with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained MPP and reconstruct RBF until a criteria is satisfied.

The method is shown to be better in the computation time to the PMA based on the actual model. The analysis results of probabilistic performance measure are accurately close to the reference solution. Five numerical examples are presented to demonstrate the effectiveness of the proposed method.

The main contribution of this paper is to propose a new reliability analysis technique using reconstructed RBF approximate model. The originalities of this paper may lie in: investigating the PMA using metamodel techniques, using RBF instead of the other types of metamodels to deal with the low efficiency problem.

This paper aims to reliability analysis of axially loaded steel columns at elevated temperatures considering the probabilistic features of fire.

The response function used in the reliability analysis is based on the non-linear FEM calculations. The stochastic variability of temperature is integrated with the procedure similar to the parameters of loading and material properties. Direct Monte Carlo simulations (MCSs) are implemented for probabilistic analysis. Computational costs are reduced by polynomial approximation of the response function of the column.

A design method for practical applications in the common Eurocode format is proposed. The proposed method can be used to estimate the failure probability of a steel column in fire conditions. If standard reliability criteria are applied, the results of the steel column buckling capacity in the fire according to the proposed procedure deviate from the Eurocode results in certain parameter ranges.

The proposed method for design calculations makes use of the advantages of MCS results, while the need for the tedious amount of calculations for the end user are avoided as the predefined factors are implemented in the procedure of Eurocode format. The proposed method allows better differentiation of the fire probability in the capacity assessment compared to the existing design methods.

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

Describes a probabilistic methodology for fracture assessments of flawed structures constructed of ferritic steels using the research code WSTRESS. The probabilistic formulation for cleavage fracture implements a multiaxial form of the weakest link model which couples the macroscopic fracture behavior with a micromechanics model based on the statistics of microcracks. The Weibull stress, σ_w, emerges as a suitable near‐tip parameter to provide a connection between the microregime of failure and remote loading (J). WSTRESS builds on an iterative procedure to incorporate a 3‐D finite element description of the crack‐tip stress field and measured values of fracture toughness to calibrate the Weibull modulus, m, and the scale parameter, σ_u. Specific features of the code include statistical inference of Weibull parameters based on uncensored and censored models (with maximum likelihood method), construction of confidence intervals, several definitions for the near‐tip fracture process zone and other general facilities such as spatial integration of the stress field (to incorporate the random orientation of microcracks) and stochastic simulation of fracture data using the Monte Carlo method. The code also includes a convenient free‐form command language and a seamless interface with finite element results files stored in Patran binary or ASCII format.

This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.

Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.

CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.

The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.

For gravity dams built on foundations with directional joint sets, the seepage in the foundation possesses anisotropic characteristics and may have adverse effects on the foundation stability. A methodology for system reliability analysis of gravity dam foundations considering anisotropic seepage and multiple sliding surfaces is proposed in this paper.

Anisotropic seepages in dam foundations are simulated using finite element method (FEM) with the equivalent continuum model (ECM), and their effect on dam foundation stability is involved by uplift pressures acting on the potential sliding surfaces. The system failure probability of the dam foundation is efficiently estimated using Monte Carlo method (MCM) combined with response surface method (RSM).

The case study shows that it is necessary to consider the possibly adverse effect of anisotropic seepage on foundation stability of gravity dams and the deterministic analysis of the foundation stability may be misleading. The system reliability analysis of the dam foundation is justified, as the uncertainties in shear strength parameters of the foundation rocks and joint sets as well as aperture, connectivity and spacing of the joint sets are quantified and the system effect of the multiple potential sliding surfaces on the foundation reliability is reasonably considered.

(1) A methodology is proposed for efficient system reliability analysis of foundation stability of gravity dams considering anisotropic seepage and multiple sliding surfaces (2) The influence of anisotropic seepage on the stability of gravity dam foundation  is revealed (3) The influence of estimation errors of RSMs on the system reliability assessment of dam foundation is investigated.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.