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In the analysis of some near‐regular structures one can solve the regular part independently and then superimpose the effect of the additional part. For such models, the matrices corresponding to regular part have canonical forms and their eigensolution or inversion can easily be performed. The effect of member changing the regular to a near‐regular structure can then be added. The purpose of this paper is to analyze near‐regular structures using the force method.

The paper uses the force method, and instead of selecting a statically determinate basic structure (standard method), the paper employs the regular part of the structure as the basic structure.

A new algebraic method is introduced for the force method of analysis for efficient analysis of large near‐regular structures.

In this paper, the force method is used, however, instead of selecting a statically determinate basic structure, the regular part of the structure is employed as the basic structure. Those additional elements are considered as redundant elements. This method is applied to truss and frame structures. In the present approach it is possible to have missing elements instead of additional elements.

There are many structures that have a repetitive pattern. If a relationship can be established between a repetitive structure and a circulant structure, then the repetitive structure can be analyzed by using the properties of the corresponding circulant structure. The purpose of this paper is to develop such a transformation.

A circulant matrix has certain properties that can be used to reduce the complexity of the analysis. In this paper, repetitive and near-repetitive structures are transformed to circulant structures by adding and/or eliminating some elements of the structure. Numerical examples are provided to show the efficiency of the present method.

A transformation is established between a repetitive structure and a circulant structure, and the analysis of the repetitive structure is performed by using the properties of the corresponding circulant structure.

Repetitive and near-repetitive structures are transformed to circulant structures, and the complexity of the analysis of the former structures is reduced by analyzing the latter structures.

The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions.

The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis.

Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations.

No limitation.

Swift analysis has become possible.

Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

The purpose of this paper is to introduce a general equation for eigensolution. Eigenvalues and eigenvectors of graphs have many applications in combinatorial optimization and structural mechanics. Some important applications of graph products consist of nodal ordering and graph partitioning for structuring the structural matrices and finite element subdomaining, respectively.

In the existing methods for the eigensolution of Laplacian matrices, members have been added to the model of a graph product such that for its Laplacian matrix an algebraic relation between blocks become possible. These methods are categorized as topological approaches. Here, using concepts of linear algebra a general algebraic method is developed.

A new algebraic method is introduced for calculating the eigenvalues of Laplacian matrices in graph products.

The present method provides a simple tool for calculating the eigenvalues of the Laplacian matrices without using the configurational model and merely by using the Laplacian matrices. The developed formula for calculating the eigenvalues contains approximate terms which can be managed by the analyst.

Graph products are extensively used in the analysis and design of regular structures. It is often thought that these products are only applicable to regular graphs. The main aim of this paper is develop new products which are applicable to regular as well and non‐regular structural models.

New graph products are defined with specified domains. In these products the logical operations of the graph products are only performable in specified domains, and therefore these products can produce configurations which do not need to be regular.

New graph products are defined and a general theorem is proved for the formation of their adjacency matrices.

The presented graph products overcome the difficulty of employing graph products in structural mechanics, and in particular in space structures. The general theorem of this paper can efficiently be used in the formation of adjacency matrices of the structural models.

The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme.

The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities.

The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients.

The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

The use of AI for operations management, with its ability to evolve solutions, handle uncertainty and perform optimisation continues to be a major field of research. The growing body of publications over the last two decades means that it can be difficult to keep track of what has been done previously, what has worked, and what really needs to be addressed. Hence, the purpose of this paper is to present a survey of the use of AI in operations management aimed at presenting the key research themes, trends and directions of research.

The paper builds upon our previous survey of this field which was carried out for the ten‐year period 1995‐2004. Like the previous survey, it uses Elsevier's Science Direct database as a source. The framework and methodology adopted for the survey is kept as similar as possible to enable continuity and comparison of trends. Thus, the application categories adopted are: design; scheduling; process planning and control; and quality, maintenance and fault diagnosis. Research on utilising neural networks, case‐based reasoning (CBR), fuzzy logic (FL), knowledge‐Based systems (KBS), data mining, and hybrid AI in the four application areas are identified.

The survey categorises over 1,400 papers, identifying the uses of AI in the four categories of operations management and concludes with an analysis of the trends, gaps and directions for future research. The findings include: the trends for design and scheduling show a dramatic increase in the use of genetic algorithms since 2003 that reflect recognition of their success in these areas; there is a significant decline in research on use of KBS, reflecting their transition into practice; there is an increasing trend in the use of FL in quality, maintenance and fault diagnosis; and there are surprising gaps in the use of CBR and hybrid methods in operations management that offer opportunities for future research.

This is the largest and most comprehensive study to classify research on the use of AI in operations management to date. The survey and trends identified provide a useful reference point and directions for future research.

The purpose of this paper is to describe how the method recently developed for mass‐spring systems and frame structures is modified to include the free vibration of trusses.

Here, two methods are presented for calculating the eigenfrequencies of structures. The first approach is graph theoretical and uses graph symmetry. The graph models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels contain the eigenvalues of the entire model. The second method has an algebraic nature and uses special canonical forms. The present method is illustrated through three simple examples with odd and even number of bays.

The inter‐relation for the mechanical properties of elements is established using new weighted graphs, enabling easy calculation of the eigenvalues involved. Two methods are presented for calculating the eigenfrequencies of the truss structures.

Symmetry is used for easy calculation of the eigenfrequencies of structures.

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.

This study seeks to understand the connection of methodology by finding relevant papers and their full review using the “Preferred Reporting Items for Systematic Reviews and Meta-Analyses” (PRISMA).

Concrete-filled steel tubular (CFST) columns have gained popularity in construction in recent decades as they offer the benefit of constituent materials and cost-effectiveness. Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), Gene Expression Programming (GEP) and Decision Trees (DTs) are some of the approaches that have been widely used in recent decades in structural engineering to construct predictive models, resulting in effective and accurate decision making. Despite the fact that there are numerous research studies on the various parameters that influence the axial compression capacity (ACC) of CFST columns, there is no systematic review of these Machine Learning methods.

The implications of a variety of structural characteristics on machine learning performance parameters are addressed and reviewed. The comparison analysis of current design codes and machine learning tools to predict the performance of CFST columns is summarized. The discussion results indicate that machine learning tools better understand complex datasets and intricate testing designs.

This study examines machine learning techniques for forecasting the axial bearing capacity of concrete-filled steel tubular (CFST) columns. This paper also highlights the drawbacks of utilizing existing techniques to build CFST columns, and the benefits of Machine Learning approaches over them. This article attempts to introduce beginners and experienced professionals to various research trajectories.