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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.

In structural, earthquake and aeronautical engineering and mechanical vibration, the solution of dynamic equations for a structure subjected to dynamic loading leads to a high order system of differential equations. The numerical methods are usually used for integration when either there is dealing with discrete data or there is no analytical solution for the equations. Since the numerical methods with more accuracy and stability give more accurate results in structural responses, there is a need to improve the existing methods or develop new ones. The paper aims to discuss these issues.

In this paper, a new time integration method is proposed mathematically and numerically, which is accordingly applied to single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. Finally, the results are compared to the existing methods such as Newmark's method and closed form solution.

It is concluded that, in the proposed method, the data variance of each set of structural responses such as displacement, velocity, or acceleration in different time steps is less than those in Newmark's method, and the proposed method is more accurate and stable than Newmark's method and is capable of analyzing the structure at fewer numbers of iteration or computation cycles, hence less time-consuming.

A new mathematical and numerical time integration method is proposed for the computation of structural responses with higher accuracy and stability, lower data variance, and fewer numbers of iterations for computational cycles.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.

The analysis of certain structures must be performed with due consideration to non‐linear behavior, such as material and geometric non‐linearities. The existing methods for treating non‐linear structural behavior generally make use of repeated linearization, such as load increment methods. This paper demonstrates that there is an alternative type of linearization that appears to have significant advantages when applied to the analysis of non‐linear structural systems. Briefly stated, this alternative linearization can be thought of as a “monomialization”. This monomial (single‐termed power function) approximation more faithfully models the power function behavior inherent in typical structural systems. Conveniently, it becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Preliminary results indicate that the monomial approximation provides a higher quality approximation to non‐linear phenomena exhibited in structural applications. Consequently, incremental and iterative methods become more effective because larger steps can be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. Two examples are presented to demonstrate the method.

The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.

Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.

This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.

Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.

This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.

The aim of this paper is to present a novel multifactor structural optimisation method incorporating reliability performance.

This research addresses structural optimisation problems in which the design is required to satisfy multiple performance criteria, such as strength, stiffness, mass and reliability under multiple loading cases simultaneously. A MOST technique is extended to accommodate the reliability‐related optimisation. Structural responses and geometrical sensitivities are analysed by a FE method, and reliability performance is calculated by a reliability loading‐case index (RLI). The evaluation indices of performances and loading cases are formulated, and an overall performance index is presented to quantitatively evaluate a design.

The proposed method is applicable to multi‐objective, multi‐loading‐case, multi‐disciplinary and reliability‐related optimisation problems. The applications to a star‐like truss structure and a raised‐access floor panel structure confirmed that the method is highly effective and efficient in terms of structural optimisation.

A systematic method is proposed. The optimisation method combines the MOST technique with a RLI (a new alternative route to calculate the reliability index at multiple loading cases) using a parametric FE model.

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.

The purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.

Two-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.

This paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.

Optimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

This paper aims to introduce a multiscale computational method for structural failure analysis with inheriting simulation of moving trans-scale boundary (MTB). This method is motivated from the error in domain bridging caused by cross-scale damage evolution, which is common in structural failure induced by damage accumulation.

Within the method, vulnerable regions with high stress level are described by continuum damage mechanics, while elastic structural theory is sufficient for the rest, dividing the structural model into two scale domains. The two domains are bridged to generate mixed dimensional finite element equation of the whole system. Inheriting simulation is developed to make the computation of MTB sustainable.

Numerical tests of a notched three-point bending beam and a steel frame show that this MTB method can improve efficiency and ensure accuracy while capturing the effect of material damage on deterioration of components and structure.

The proposed MTB method with inheriting simulation is an extension of multiscale simulation to structural failure analysis. Most importantly, it can deal with cross-scale damage evolution and improve computation efficiency significantly.