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The purpose of this paper is to apply data envelopment analysis (DEA) techniques to the collective decision-making environment to appraise two-stage production process under different decision preferences.

The authors propose a novel multi-criteria group decision-making approach that uses consensus-strategic data envelopment analysis (CSDEA) to appraise two-stage production process under two different decision strategies, which are efficiency- and fairness-based group decision preferences.

The authors find that the proposed CSDEA model evaluates the performance of the decision-making units (DMUs) not by diminishing other competitors but rather based on group interests of the entire decision set.

The authors extend Li’s two-stage model to cases that consider both intermediate inputs and outputs. The authors address the issue of incorporating collective managerial strategy into multi-criteria group decision-making and propose a novel CSDEA model that considers not only the individual-level performance of a DMU but also the group-level or collective decision strategies.

The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.

Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.

The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.

These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

In the reliability assessment of composite laminate structures with multiple components, the uncertainty space defined around design solutions easily becomes over-dimensioned, and not all of the random variables are relevant. The purpose of this study is to implement the importance analysis theory of Sobol’ to reduce the dimension of the uncertainty space, improving the efficiency toward global convergence of evolutionary-based reliability assessment.

Sobol’ indices are formulated analytically for implicit structural response functions, following the theory of propagation of moments and without violating the fundamental principles presented by Sobol’. An evolutionary algorithm capable of global convergence in reliability assessment is instrumented with the Sobol’ indices. A threshold parameter is introduced to identify the important variables. A set of optimal designs of a multi-laminate composite structure is evaluated.

Importance analysis shows that uncertainty is concentrated in the laminate where the critical stress state is found. Still, it may also be reasonable in other points of the structure. An accurate and controlled reduction of the uncertainty space significantly improves the convergence rate, while maintaining the quality of the reliability assessment.

The theoretical developments assume independent random variables.

Applying Sobol’ indices as an analytical dimension reduction technique is a novelty. The proposed formulation only requires one adjoint system of equilibrium equations to be solved once. Although a local estimate of a global measure, this analytical formulation still holds because, in structural design, uncertainty is concentrated around the mean-values.