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The purpose of this paper is to study the partitioned solution procedure for thermomechanical coupling, where each sub‐problem is solved by a separate time integration scheme.

In particular, the solution which guarantees that the coupling condition will preserve the stability of computations for the coupled problem is studied. The consideration is further generalized for the case where each sub‐problem will possess its particular time scale which requires different time step to be selected for each sub‐problem.

Several numerical simulations are presented to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed‐up of computations which follow from the adequate choice of the time step for each sub‐problem.

The paper confirms that one can make the most appropriate selection of the time step and carry out the separate computations for each sub‐problem, and then enforce the coupling which will preserve the stability of computations with such an operator split procedure.

The polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.

First, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.

Several examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.

The number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.

A pandemic causes abrupt and unanticipated disruptions in many facets of society. A lot of authorities have quickly turned to online teaching methods. The best methods for online teaching have become a hot topic of discussion due to this urgent fast transmission. It was difficult to teach physiology to medical and paramedical students online because of concerns about how to give the students an effective interactive online teaching practice and how to guarantee successful outcomes. Therefore, three approaches have been individually applied to medical and nursing students for the first time in the physiology department of the Faculty of Medicine in Rabigh, King Abdulaziz University. Through online lectures and assignments, the strategies attempted to capture the students’ interest and interaction. The second-year nursing students were given a mind map project to complete after the lecture. The third-year medical students used a crossword puzzle game to test the students’ understanding. The third-year medical students were presented with short stories to better comprehend the physiological processes covered in the lectures. Overall, the three instructional strategies received positive feedback from the students. Incorporating such cutting-edge and imaginative educational approaches, in conclusion, could significantly aid in managing the pressures that arise during pandemics.

Physical phenomena interact with each other in ways that one cannot be analyzed without considering the other. To account for such interactions between multiple phenomena, partitioning has become a widely implemented computational approach. Partitioned analysis involves the exchange of inputs and outputs from constituent models (partitions) via iterative coupling operations, through which the individually developed constituent models are allowed to affect each other’s inputs and outputs. Partitioning, whether multi-scale or multi-physics in nature, is a powerful technique that can yield coupled models that can predict the behavior of a system more complex than the individual constituents themselves. The paper aims to discuss these issues.

Although partitioned analysis has been a key mechanism in developing more realistic predictive models over the last decade, its iterative coupling operations may lead to the propagation and accumulation of uncertainties and errors that, if unaccounted for, can severely degrade the coupled model predictions. This problem can be alleviated by reducing uncertainties and errors in individual constituent models through further code development. However, finite resources may limit code development efforts to just a portion of possible constituents, making it necessary to prioritize constituent model development for efficient use of resources. Thus, the authors propose here an approach along with its associated metric to rank constituents by tracing uncertainties and errors in coupled model predictions back to uncertainties and errors in constituent model predictions.

The proposed approach evaluates the deficiency (relative degree of imprecision and inaccuracy), importance (relative sensitivity) and cost of further code development for each constituent model, and combines these three factors in a quantitative prioritization metric. The benefits of the proposed metric are demonstrated on a structural portal frame using an optimization-based uncertainty inference and coupling approach.

This study proposes an approach and its corresponding metric to prioritize the improvement of constituents by quantifying the uncertainties, bias contributions, sensitivity analysis, and cost of the constituent models.

As an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.

This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.

First, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.

The scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

The free vibration analysis of cyclic symmetric structures is considered as a Hermitian eigenvalue problem in semi‐complex domain using subspace iteration method is presented. The trial vectors are selected using a modified Ritz vector scheme. A modified convergence criterion which gives true error estimates which is suited for clustered eigenvalue problems is presented. Also the effect of purification of trial vectors on convergence is considered.

The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.

In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).

The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.

This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection.

The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM.

A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases.

The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

First of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.

The properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.

All the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.

The problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.

All the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.

Aiming at the problems of poor accuracy and limitation in strength assessment of spot welding vehicle body caused by uncertain factors, such as key component size and nugget diameter, the numerical models of strength uncertainty analysis of spot-welded joints were constructed based on evidence theory and fuzzy theory.

Evidence theory and fuzzy theory are used to deal with the uncertainty of design parameter, and differential evolution algorithms are used to calculate the propagation process of uncertainty in this model. Furthermore, efficient relationship between the strength of welded joints and each design parameter is constructed by using response surface proxy model, which effectively avoids the problem of repeated complex finite element analysis in uncertainty analysis.

The results show that the constructed uncertainty numerical model is effective for the multiple uncertainties and give interval results under different probabilities and affiliations, which can more effectively evaluate the strength of the welded body structure to avoid overly conservative estimates for deterministic design.

The evidence theory is improved and combined with differential evolution algorithm and response surface method to effectively improve the computational efficiency. Based on the improved evidence theory and fuzzy algorithm, the numerical models for the uncertainty analysis of solder joint strength of welded structures are constructed and their feasibility is verified.