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The Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.

First, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.

An example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.

The proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.

The proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

This paper aims to study and modify the notch equivalent stress method, as well as to establish the notch equivalent stress range S–N curve and apply it to the fatigue assessment of engineering examples.

This paper studies the notch equivalent stress method and puts forward the concept of “singular equivalent crack”. Combined with the fatigue test results, by proposing to consider the singular coefficient of the transition angle of the welded structure and the introduction of material correction factors, this paper derives the notch equivalent stress equation for commonly used welded joints applicable to steel, and finally establishes the notch equivalent stress range of the S–N curve.

The obtained results show that the dispersion of fatigue data is 65.6 and 75.4% for T-joints and transverse cross-joints, respectively, under S–N curves using notched equivalent stress compared to the nominal stress range. The fatigue evaluation error of the modified notch equivalent stress equation for transverse cross welded joints improved by 50.65%, 53.1 and 39.6% on average, respectively, compared to the original other methods. The fatigue evaluation error for T-joints improved by 13.4 and 13.9%, respectively, compared to the original other methods.

There are relatively few studies on the fatigue assessment of notch equivalent stress method. In this paper, the notch equivalent stress method is studied and modified to improve the accuracy of fatigue assessment of welded structures with singular stresses.

The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve.

Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution.

By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method.

The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

Various time integration methods and time finite element methods have been developed to obtain the responses of structural dynamic problems, but the accuracy and computational efficiency of them are sometimes not satisfactory. The purpose of this paper is to present a more accurate and efficient formulation on the basis of the weak form quadrature element method to solve linear structural dynamic problems.

A variational principle for linear structural dynamics, which is inspired by Noble's work, is proposed to develop the weak form temporal quadrature element formulation. With Lobatto quadrature rule and the differential quadrature analog, a system of linear equations is obtained to solve the responses at sampling time points simultaneously. Computation for multi-elements can be carried out by a time-marching technique, using the end point results of the last element as the initial conditions for the next.

The weak form temporal quadrature element formulation is conditionally stable. The relation between the normalized length of element and the suggested number of integration points in one element is given by a simple formula. Results show that the present formulation is much more accurate than other time integration methods and its dissipative property is also illustrated.

The weak form temporal quadrature element formulation provides a choice with high accuracy and efficiency for solution of linear structural dynamic problems.

This paper aims to propose an efficient and accurate method to analyse the transient heat conduction in a periodic structure with moving heat sources.

The moving heat source is modelled as a localised Gaussian distribution in space. Based on the spatial distribution, the physical feature of transient heat conduction and the periodic property of structure, a special feature of temperature responses caused by the moving heat source is illustrated. Then, combined with the superposition principle of linear system, within a small time-step, computation of results corresponding to the whole structure excited by the Gaussian heat source is transformed into that of some small-scale structures. Lastly, the precise integration method (PIM) is used to solve the temperature responses of each small-scale structure efficiently and accurately.

Within a reasonable time-step, the heat source applied on a unit cell can only cause the temperature responses of a limited number of adjacent unit cells. According to the above feature and the periodic property of a structure, the contributions caused by the moving heat source for the most of time-steps are repeatable, and the temperature responses of the entire periodic structure can be obtained by some small-scale structures.

A novel numerical method is proposed for analysing moving heat source problems, and the numerical examples demonstrate that the proposed method is much more efficient than the traditional methods, even for larger-scale problems and multiple moving heat source problems.

To improve the accuracy of parameter prediction for small-sample data, considering the existence of error in samples, the error circle is introduced to analyze original samples.

The influence of surface roughness on fatigue life is discussed. The error circle can treat the original samples and extend the single sample, which reduces the influence of the sample error.

The S-N curve obtained by the error circle method is more reliable; the S-N curve of the Bootstrap method is more reliable than that of the Maximum Likelihood Estimation (MLE) method.

The parameter distribution and characteristics are statistically obtained based on the surface roughness, surface roughness factor and intercept constant. The original sample is studied by an error circle and discussed using the Bootstrap and MLE methods to obtain corresponding S-N curves. It provides a more trustworthy basis for predicting the useful life of products.

Fatigue and creep are the key factors for the failure of polymethyl methacrylate (PMMA) in the engineering structure, so a great of quantity attention is focused on the life prediction under the creep and fatigue conditions. This paper aims to mainly summarize the traditional life assessment method (S–N curve), life assessment method based on crazing density and life assessment method based on transmittance. S–N curve and classical creep curve are introduced on the traditional life assessment method; the variation of the craze density with the logarithm of cyclic numbers is given in different fatigue load. A linear relationship is obtained, and a higher stress leads to a higher slope, suggesting a faster growth of craze. Furthermore, a craze density model is purposed to describe this relationship; the variation of craze density with the time at different creep load is given. The craze density has two obvious stages. At the first stage, craze density ranged from approximately 0.02 to 0.17, and a linear relationship is obtained. In the following stage, a nonlinear relationship appears till specimen rupture, a new creep life model is proposed to depict two stages. The relationship between transmission and time under creep load is shown. With increasing of time, the transmittance shows a nonlinear decrease. Through polynomial nonlinear fitting, a relationship between the transmittance and residual life can be obtained. To provide reference for the life assessment of transparent materials, the paper compares three life assessment methods of PMMA.

This paper uses the traditional life assessment method (S–N curve), life assessment method based on crazing density, life assessment method based on transmittance.

The variation of the craze density with the logarithm of cyclic numbers is given in different fatigue loads. A linear relationship is obtained, and a higher stress leads to a higher slope, suggesting a faster growth of craze. Furthermore, a craze density model is proposed to describe this relationship, and the variation of craze density with the time at different creep loads is given. The craze density has two obvious stages. The relationship between transmission and time under creep load is shown. With increasing of time, the transmittance shows a nonlinear decrease. Through polynomial nonlinear fitting, a relationship between the transmittance and residual life can be obtained.

Fatigue and creep are the key factors for the failure of PMMA in the engineering structure, so a great of quantity attention is focused on the life prediction under the conditions of creep and fatigue. This paper mainly summarizes traditional life assessment method (S–N curve), life assessment method based on crazing density and life assessment method based on transmittance.

Due to the limitation of experimental conditions and budget, fatigue data of mechanical components are often scarce in practical engineering, which leads to low reliability of fatigue data and reduces the accuracy of fatigue life prediction. Therefore, this study aims to expand the available fatigue data and verify its reliability, enabling the achievement of life prediction analysis at different stress levels.

First, the principle of fatigue life probability percentiles consistency and the perturbation optimization technique is used to realize the equivalent conversion of small samples fatigue life test data at different stress levels. Meanwhile, checking failure model by fitting the goodness of fit test and proposing a Monte Carlo method based on the data distribution characteristics and a numerical simulation strategy of directional sampling is used to extend equivalent data. Furthermore, the relationship between effective stress and characteristic life is analyzed using a combination of the Weibull distribution and the Stromeyer equation. An iterative sequence is established to obtain predicted life.

The TC4–DT titanium alloy is selected to assess the accuracy and reliability of the proposed method and the results show that predicted life obtained with the proposed method is within the double dispersion band, indicating high accuracy.

The purpose of this study is to provide a reference for the expansion of small sample fatigue test data, verification of data reliability and prediction of fatigue life data. In addition, the proposed method provides a theoretical basis for engineering applications.

The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.