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This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary K0${{K}_0}$ values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with K0=1${K}_{0}=1$. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between 5π3$\frac{{5\pi }}{3}$ and 11π6$\frac{{11\pi }}{6}$ or on the specific line of θ=11π6$\theta = \frac{{11\pi }}{6}$. The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils. [ABSTRACT FROM AUTHOR]

Stress and deformation analysis of a cavity in an infinite/finite medium is a fundamental applied mechanics problem of interest in multiple physics and engineering disciplines. This paper develops a complete semianalytical solution for the cylindrical cavity expansion in nonassociated Mohr–Coulomb materials, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single material point at the cavity wall). The novelty of the new solution framework lies not only in the relaxation of the stringent intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but also in the comprehensive consideration of nonhydrostatic initial stress conditions via arbitrary values of K0 (the coefficient of earth pressure at rest defined as the ratio between the horizontal and vertical initial stresses). The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during cavity expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K0 being covered. Some selected results are presented for the calculated cavity pressure-expansion curve and limit cavity pressure through an example analysis. The definitive semianalytical solution proposed will be not only substantially advancing the current state of knowledge on the fundamental cavity expansion theory, but also able to serve as a unique benchmark for truly verifying the correctness and capability of the classical cornered Mohr–Coulomb constitutive model built in commercial finite element programs. [ABSTRACT FROM AUTHOR]

The powerful image analysis and statistical capabilities of computers can effectively solve problems such as insufficient precision in clastic rock particle size measurements and the heavy workload during the process. The MATLAB programming language was employed to process the samples of the Zhoutian Formation in the Upper Cretaceous of the Huichang Basin through techniques such as grayscale transformation, binarization, adaptive median filtering, and color annotation, accurately measuring their grain size parameters. The results indicate the following. The average grain size obtained using MATLAB,s direct calculation method and the graphical method are 4. 008φ and 3. 103φ, respectively. The standard deviations are 0. 8φ and 0. 803φ, the skewness values are - 0. 195φ and - 0. 041φ, and the kurtosis values are 0. 911φ and 0. 916φ. The standard deviation and kurtosis errors are small, allowing for mutual substitution between the two calculation methods, while the standard deviation and skewness errors are relatively large, making them unsuitable for mutual substitution. Both MATLAB,s direct calculation method and microscopic rock mineral identification indicate a relatively poor roundness of the Zhoutian Formation as a whole, with angular to sub-angular clastic particles. The sedimentary environment discrimination formula reflects the formation of the Zhoutian Formation in a fluvial depositional environment, consistent with the geological background and microscopic observation results. Through the MATLAB programming language, it is possible to accurately identify particle outlines and calculate various parameters in clastic rocks, providing great convenience for sediment grain size research, eliminating subjective interference, and improving work efficiency [ABSTRACT FROM AUTHOR]

This paper introduces a more streamlined and convenient graphical approach to investigate the stability of fractional-order dynamical systems comprehensively. In particular, we focus on the utilization of Kharitonov theorem, renowned for robust stability analysis of incommensurate fractional-order systems in the presence of uncertainty. A novel graphical framework is illustrated, promising to streamline the stability analysis of such systems, which leads to reducing the computational burden. Using the proposed method, we can achieve the least possible Kharitonov polynomials among the existing methods to analyze the robust stability of the incommensurate fractional-order systems. To validate our approach, we perform numerical simulations on four illustrative examples, demonstrating its effectiveness. Simulation results underscore the real-world utility of our methodology, emphasizing its potential significance in fractional-order system analysis. [ABSTRACT FROM AUTHOR]

A four-bar mechanism is a basic kinematic chain in most of planar mechanisms. Four-bar chains are synthesized for a specific task. The output deviates from the desired one due to many reasons broadly from the group of systematic and random input sources. The work presented herewith deals with the error estimation in the four-bar path generation mechanism under link tolerance. The primary estimation of error is carried out using a Taylor series approximation with a modified error equation. The inaccuracy is estimated using sample independent variables. A geometrical method for the estimation of specific errors is developed. The results are verified using the CAD model. The appropriateness of the Taylor series approximation with modified error equation estimations is compared with exact solutions from the geometrical method. The methodology is demonstrated through a sample case of the four-bar mechanism presented to compare the capability of the two methods. The deviations due to single systematic inaccuracy are exposed, and one of the methods- i.e. the geometrical method is found to be the robust method of error evaluation. [ABSTRACT FROM AUTHOR]

Single-point incremental forming (SPIF) has emerged as a cost-effective and rapid manufacturing method, especially suitable for small-batch production due to its minimal reliance on molds, swift production, and affordability. Nonetheless, SPIF's effectiveness is closely tied to the specific characteristics of the employed sheet materials and the intricacies of the desired shapes. Immediate experimentation with SPIF often leads to numerous product defects. Therefore, the pre-emptive use of numerical simulations to predict these defects is of paramount importance. In this study, we focus on the critical role of the forming limit curve (FLC) in SPIF simulations, specifically in anticipating product fractures. To facilitate this, we first construct the forming limit curve for Al1050 sheet material, leveraging the modified maximum force criterion (MMFC). This criterion, well-established in the field, derives FLCs based on the theory of hardening laws in sheet metal yield curves. In conjunction with the MMFC, we introduce a graphical approach that simplifies the prediction of forming limit curves at fracture (FLCF). Within the context of the SPIF method, FLCF is established through both uniaxial tensile deformation (U.T) and simultaneous uniform tensile deformation in bi-axial tensile (B.T). Subsequently, the FLCF predictions are applied in simulations and experiments focused on forming truncated cone parts. Notably, a substantial deviation in fracture height, amounting to 15.97%, is observed between simulated and experimental samples. To enhance FLCF prediction accuracy in SPIF, we propose a novel method based on simulations of truncated cone parts with variable tool radii. A FLCF is then constructed by determining major/minor strains in simulated samples. To ascertain the validity of this enhanced FLCF model, our study includes simulations and tests of truncated cone samples with varying wall angles, revealing a substantial alignment in fracture height between corresponding samples. This research contributes to the advancement of SPIF by enhancing our ability to predict and mitigate product defects, ultimately expanding the applicability of SPIF in diverse industrial contexts. [ABSTRACT FROM AUTHOR]

This paper attempts to expand the graphical analysis concept proposed by Chen and Abousleiman (Géotechnique, 2022. https://doi.org/10.1680/jgeot.21.00172) to deduce the undrained expansion solution of a cylindrical cavity in shear strain-hardening Drucker–Prager frictional soil. Based on the geometrical representation of the stress state/path and strain increments in the deviatoric planes, it is shown that the deviatoric stress-Lode angle stress path can be desirably determined by solving a first-order differential equation for the stress ratio (deviatoric stress over mean effective stress) in term of the Lode angle. The essential cavity expansion curve may also be readily constructed by calculating the internal cavity pressure and the corresponding expanded cavity radius, respectively, through simple numerical integrations with respect to the same variable of stress ratio. In particular, the ultimate cavity pressure can be easily evaluated by directly integrating the expression for cavity pressure with the stress ratio up to its limiting value. Some numerical results obtained from the proposed graphical method are presented to illustrate the impacts on the cavity responses of the earth pressure coefficient at rest, K 0 , and the key plasticity hardening parameters, which have also been compared with alternative solutions that require dealing with a system of coupled differential equations involving three principal effective stress components. [ABSTRACT FROM AUTHOR]

In this study, we propose two estimators called the 3-step modified maximum likelihood (MML) and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators. [ABSTRACT FROM AUTHOR]

The armature reaction of the hybrid excitation starter generator (HESG) under load conditions will affect the distribution of the main magnetic field and the output performance. However, using the conventional field-circuit combination method to study the armature reaction has the problem of low accuracy and inaccurate influencing factors. Therefore, this paper proposed a graphical method to analyze the armature reaction and a new type of HESG with a combined-pole permanent magnet (PM) rotor and claw-pole electromagnetic rotor. The analytical formula of the voltage regulation rate under the armature reaction was derived using the graphical method. The main influencing parameters of the armature reaction magnetic field (ARMF) were analyzed, and the overall output performance was analyzed using finite element software. On this basis, comparison analyses before and after optimization and the prototype test were carried out. The results show that the direct-axis armature reaction reactance, quadrature-axis armature reaction reactance, and voltage regulation rate of the optimized HESG were significantly reduced, the output voltage range of the whole machine was wide, and the voltage regulation performance was good. [ABSTRACT FROM AUTHOR]

Through data mining, this paper completes collecting and mining information in the database using artificial intelligence. Secondly, the graphical method is analyzed, image normalization calculation is carried out to complete the technical support for green concept packaging design, and a green concept product packaging design system based on artificial intelligence technology is constructed. Finally, the ease of use experiment and user satisfaction test confirmed it. The user satisfaction test showed a satisfaction rate of 95% for response time and 97% for material recycling. The fact that other test options are above 90% indicates that the green concept product packaging design based on artificial intelligence technology is feasible.

The objective is to solve the college physics problem of a block sliding down a movable smooth wedge without friction anywhere using a spatial-numeric perspective. The drawing method used the sum of the normal force and weight of the block to find the wedge acceleration. The drawing method results are equivalent to the algebra method results within drawing accuracy. The result of a geometric construction with regular drawing uncertainly was shown for the case without any horizontal applied force. For the case of a given horizontal applied force, an additional numeric graphing method was shown with additional drawing uncertainty in the result. The geometric construction without graphing resuted in solving the horizontal applied force case via scaling in the concept of modified gravity experienced by the block on the wedge’s slant edge, assuming a pre-requisite knowledge of algebra and trigonometry. The presented spatial numeric method and results imply a Physics First pedagogy of using the spatial numeric abilities, with the inclusion of the pre-projectile problem, pre-traffic-light problem, and post-collision problem in a one-semester syllabus.

Precipitation is the most critical element of the hydrological cycle that might influence the frequency of floods or drought. Therefore, for drought and flood forecasting, knowing the precipitation pattern and its trend is mandatory. The research aims to estimate the monthly, seasonal, and annual precipitation trend using statistical (Mann Kendall test & Sen's Slope estimator) and graphical (Innovative Trend Analysis method) for the Hanumangarh district of N-E Rajasthan. The mean monthly precipitation data were gathered from the India-WRIS from 1901 to 2022 (122 years). Seasonal and annual precipitation trend variations were examined by statistical methods and compared with the graphical method. The study results conclude that precipitation trends showed variability for the SW monsoon season from the graphical to the statistical method. For the SW monsoon season, the decreasing trend was seen using statistical methods. In contrast, the graphical method revealed an increasing trend. During the annual precipitation, increasing trends were seen using statistical and graphical methods. It is found that the ITA method is more efficient in finding trends because it does not assume any assumptions like that of the MK test. This study will help water resources engineers and local people with sustainable management, planning, and development of water resources in the Hanumangarh district. HIGHLIGHTS Trends in seasonal and annual precipitation time series are assessed using both statistical and graphical methods and then results are compared.; The results of the statistical method are well-matched with the graphical method.; The ITA method is easier to apply for finding trends.; The ITA method is more accurate because it does not consider any assumptions.;

The fanning compression stress pattern in RC deep beams under uniform load presents a challenge to formulating the configuration of strut‐and‐tie model (STM). To this end, this paper proposes an alternative method for creating a graphical discontinuous stress field model (DSFM) to fill up the whole beam continuum. It comprises a certain number of trapezoidal stress‐bands with varying bandwidths, and their stress values can be calculated based on force equilibrium conditions. Several stress subfields are defined through a certain stress combination from several directions. The DSFM is implementable for both service limit state (SLS) and ultimate limit state (ULS) in that its configuration is primarily oriented by elastic stress field and only a limited plastic redistribution is allowed for plastic failure. The graphical procedure of DSFM is demonstrated and examined by a test deep beam example, which shows that the predictions are fairly in good agreement with the test results. [ABSTRACT FROM AUTHOR]

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Ellipsometrically obtained spectral dependences of ordinary αxy and extra-ordinary αz extinction/attenuation coefficients within the spectral range λ = 300…980 nm of uniaxially anisotropic polytetrafluoroethylene (PTFE) films were analyzed. We considered the capabilities and specific features of the graphical representation technique for determining the contribution of Rayleigh scattering and Urbach absorption to light attenuation in the spectral range beyond fundamental absorption. It has been shown that the graphical approach enables to estimate these contributions qualitatively, semi-quantitatively or quantitatively, depending on the situation. The conclusions made using the analysis of graphical representation are confirmed by numerical solution of the inverse problem via simulation of the αxy (λ), αz (λ) experimental dependences within the framework of a best-fit procedure. Being based on both of these approaches, we have ascertained that, in the as-prepared PTFE films, the so-called anomalous light scattering (ALS) with the spectral dependence of scattering coefficient αs ≈ as λ–p (p > 4) takes place. Transformation of scattering from ALS to the Rayleigh one with p ≅ 4 due to annealing is accompanied by an increase of Urbach (subband) absorption. Both of these factors cause narrowing the dynamic range of extinction coefficient values. Both scattering and absorption coefficients are higher for the component of light polarized along the normal to the substrate as compared to the component polarized in parallel to it. The relationship between observed behavior of the scattering and absorption coefficients and the film structure has been discussed. [ABSTRACT FROM AUTHOR]

The Bayesian approach is applied to estimation of the Weibull-power law process (WPLP) parameters as an alternative to the maximum likelihood (ML) method in the case when the number of events is small. For the process model considered we propose to apply the independent Jeffreys prior distribution and we argue that this is a useful choice. Comparisons were also made between the accuracy of the estimators obtained and those obtained by using other priors—informative and weakly informative. The investigations show that the Bayesian approach in many cases of a fairly broad collection of WPLP models can lead to the Bayes estimators that are more accurate than the corresponding ML ones, when the number of events is small. The problem of fitting the WPLP models, based on ML and Bayes estimators, to some real data is also considered. It is shown that the TTT-concept, used in the reliability theory, is not fully useful for the WPLP models, and it may be so for some other trend-renewal processes. In order to assess the accuracy of the fitting to the real data considered, two other graphical methods are introduced. [ABSTRACT FROM AUTHOR]

One of the main reasons for the decline of urban historic areas in China is the co-existence of multiple property rights. It also deeply affects conservation and regeneration practice. This paper aims to propose a graphical method that illustrates the association between property rights, space, and resident behavior. Based on typological maps and justified graphs, a three-step method was proposed to visualize the relationships between these three elements. The final graph and quantitative data were used to observe the evolution of the courtyard building from a diachronic perspective, as well as to compare the residential behavior in different types from a synchronic perspective. The results show that following the subdivision of property rights, the building layout become more diverse due to various illegal additions, while the residential behavior within different building types tends to be consistent. Moreover, the study observed the traditional Chinese courtyard buildings’ adaptability. The findings contribute to understand the evolution of Chinese urban historic areas and internal motivation, and provide guidance for the conservation and regeneration practice.

The newsvendor model is widely used in production systems to determine the optimal quantity of products to be produced in the presence of random demand. In addition, in industrial production, many modern processes and services are significantly affected by random yield. This paper begins by describing the general background of the random demand and random yield newsvendor model. Next, we summarize the mathematical formulation. Then, we present our approach and the proposed graphical solution technique. [ABSTRACT FROM AUTHOR]

P. W. Bridgman developed a method to measure the force acting on a moving piston of known area and conducted experiments on gases, liquids and solids at high pressures. He reported that there is no critical point on the freezing curve in his experiments on various materials. Researchers working in universities and laboratories in the USA, France, England, Germany, Russia, the Netherlands and other universities and laboratories have reported that there is no critical point on the melting curve at high pressures in their experiments on gases, liquids and solids with this method developed by P. W. Bridgman. The main method of research in physical chemistry is experience. The new physical chemistry is an experimental science. A real physicochemical experiment is of great importance in the study of physical laws and processes. The method and methodology applied in determining the hypothesis put forward is the most important factor. Experiments are key to propose a hypothesis and solve a problem. Although the existence of a critical point on the melting curve seems theoretically and graphically possible, P. W. Bridgman and other researchers have reported that there is no critical point. In our opinion, it is not possible to determine the existence of a critical point on the freezing curve by the method applied by P. W. Bridgman and other researchers in their experiments. With this method it was possible to determine the pressure and temperature dependent melting curve. For nearly a century, the presence or absence of a critical point on the freezing curve has been a matter of debate. In the experiments conducted by P. W. Bridgman and other researchers, it was found that there was no critical point, but it is possible to determine the existence of a critical point by the experimental results of the intermittent metastable state on the freezing curve at high pressures or by applying the geometric method depending on the thermodynamic parameters of the substance. [ABSTRACT FROM AUTHOR]

Rainfall is an important part of the hydrological cycle, as well as its variability, and is relevant to drought and floods. Long-term changes in hydrological processes are referred to as climate change for an area. Urbanization, population growth, and economic growth are all having negative effects on the environment. The study of trends in the long term is essential from climatic change and socioeconomic perspectives. Examining the temporal variations in rainfall is crucial because changes in rainfall patterns and distribution can have a significant impact on the amount of water available in a watershed. The objective of the study is to assess the long-term (1902–2021) temporal trends in seasonal (winter, pre-monsoon, monsoon, and post-monsoon) and annual rainfall for the Rajsamand district of Rajasthan state using the innovative trend analysis (ITA) technique. Due to its ability to provide results in graphical form, the ITA approach is a very useful tool for detecting patterns in rainfall time series data. This technique is also used to detect trends as ‘low,’ ‘medium,’ and ‘high,’ which should be considered in future studies on floods ‘high’ and drought ‘low’, respectively. Based on the above study, it is observed that no trend is detected for the annual season, a positive trend is detected in the winter season and a negative trend is detected for pre-monsoon and post-monsoon seasons in some regimes respectively. The ITA of the S-W monsoon also specifies that in the low regime the nature of the trend is increasing and in the high regime nature of the trend is decreasing. This research will serve as a scientific foundation for assessing and mitigating the effect of climate change on the environment to reduce the risk of weather patterns. HIGHLIGHTS The innovative trend analysis (ITA) method is used in the study.; To apply the ITA approach to examine the annual and seasonal patterns of various precipitation intensities in Rajsamand.; To discuss the patterns of seasonal and annual rainfall variability across the region.; ITA method is a very useful tool for detecting patterns in rainfall time series.; ITA method is both simple and effective.;

Single-point incremental forming (SPIF) has emerged as a cost-effective and rapid manufacturing method, especially suitable for small-batch production due to its minimal reliance on molds, swift production, and affordability. Nonetheless, SPIF’s effectiveness is closely tied to the specific characteristics of the employed sheet materials and the intricacies of the desired shapes. Immediate experimentation with SPIF often leads to numerous product defects. Therefore, the pre-emptive use of numerical simulations to predict these defects is of paramount importance. In this study, we focus on the critical role of the forming limit curve (FLC) in SPIF simulations, specifically in anticipating product fractures. To facilitate this, we first construct the forming limit curve for Al1050 sheet material, leveraging the modified maximum force criterion (MMFC). This criterion, well-established in the field, derives FLCs based on the theory of hardening laws in sheet metal yield curves. In conjunction with the MMFC, we introduce a graphical approach that simplifies the prediction of forming limit curves at fracture (FLCF). Within the context of the SPIF method, FLCF is established through both uniaxial tensile deformation (U.T) and simultaneous uniform tensile deformation in bi-axial tensile (B.T). Subsequently, the FLCF predictions are applied in simulations and experiments focused on forming truncated cone parts. Notably, a substantial deviation in fracture height, amounting to 15.97%, is observed between simulated and experimental samples. To enhance FLCF prediction accuracy in SPIF, we propose a novel method based on simulations of truncated cone parts with variable tool radii. A FLCF is then constructed by determining major/minor strains in simulated samples. To ascertain the validity of this enhanced FLCF model, our study includes simulations and tests of truncated cone samples with varying wall angles, revealing a substantial alignment in fracture height between corresponding samples. This research contributes to the advancement of SPIF by enhancing our ability to predict and mitigate product defects, ultimately expanding the applicability of SPIF in diverse industrial contexts.

The armature reaction of the hybrid excitation starter generator (HESG) under load conditions will affect the distribution of the main magnetic field and the output performance. However, using the conventional field-circuit combination method to study the armature reaction has the problem of low accuracy and inaccurate influencing factors. Therefore, this paper proposed a graphical method to analyze the armature reaction and a new type of HESG with a combined-pole permanent magnet (PM) rotor and claw-pole electromagnetic rotor. The analytical formula of the voltage regulation rate under the armature reaction was derived using the graphical method. The main influencing parameters of the armature reaction magnetic field (ARMF) were analyzed, and the overall output performance was analyzed using finite element software. On this basis, comparison analyses before and after optimization and the prototype test were carried out. The results show that the direct-axis armature reaction reactance, quadrature-axis armature reaction reactance, and voltage regulation rate of the optimized HESG were significantly reduced, the output voltage range of the whole machine was wide, and the voltage regulation performance was good.

One of the main reasons for the decline of urban historic areas in China is the co-existence of multiple property rights. It also deeply affects conservation and regeneration practice. This paper aims to propose a graphical method that illustrates the association between property rights, space, and resident behavior. Based on typological maps and justified graphs, a three-step method was proposed to visualize the relationships between these three elements. The final graph and quantitative data were used to observe the evolution of the courtyard building from a diachronic perspective, as well as to compare the residential behavior in different types from a synchronic perspective. The results show that following the subdivision of property rights, the building layout become more diverse due to various illegal additions, while the residential behavior within different building types tends to be consistent. Moreover, the study observed the traditional Chinese courtyard buildings' adaptability. The findings contribute to understand the evolution of Chinese urban historic areas and internal motivation, and provide guidance for the conservation and regeneration practice. [ABSTRACT FROM AUTHOR]

This study presents a method for finite element (FE) simulation of a deep drawing process of a cold-rolled carbon steel (SPCC) sheet material based on the graphical method. First, uniaxial tensile specimens were prepared and experimental tests were conducted to determine the flow stress curves. The calculation of the fracture points at special strain modes (plane strain, uniaxial tensile strain, and biaxial tensile strain) was presented using the modified maximum force criterion (MMFC). After that, the graphical method was adopted for the estimation of the forming limit curve (FLC) based on several hardening laws. FE models for a deep drawing process of the SPCC sheet were then built using the calculated FLCs. Using FE simulations, the fracture heights of cylinder cups formed by the deep drawing process were finally determined and compared with those from experiments. The results showed a good agreement between simulated and measured fracture height with a maximum of 3.6 % deviation. Additionally, simulations and corresponding experiments were performed to investigate the effects of the blank holder force, punch corner radius, and drawing ratio on the fracture height of cylinder cups.

This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.

This paper presents timber lamella structures applied to the circular cylinder surface when all lamellae axes intersect at the nodes. To achieve the uniformity of all elements in this structure, the geometry of the structure must be carefully designed. The main methods for the research are graphical and numerical methods for geometric design and a prototype construction for a specific geometric pattern. The methods are discussed for their ease of replication, as well as the possibility of reinterpretation on other surfaces, while the prototype design and construction give insight into the process from design to execution. The combination of these methods allows for a thorough analysis of the geometry for lamella structures. The analysis shows that geometrical design must begin from the whole to the lamella, and that the number of element types in the structure depends on the disposition of the elements and the angle of the pattern. The discussion shows the advantages and limitations of the proposed methods, while the conclusions give the guidelines for the implementation of lamella structures into new design projects. [ABSTRACT FROM AUTHOR]

This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths in the deviatoric plane for the spherical and cylindrical cavity expansions turn out to be two straight lines, which correspond to Lode angles equal to 11π6$\frac{{11\pi }}{6}$ and 5π3$\frac{{5\pi }}{3}$, respectively. The desired limiting cavity pressure therefore can be directly and accurately evaluated through simple numerical integration with respect to the mean effective stress, while the relationship between the internal cavity pressure and the cavity radius, the cavity expansion curve, may be equally conveniently determined. Numerical results obtained from the current graphical method, for a range of the values of over consolidation ratio considered, compare extremely well with those from the conventional semianalytical formulations of the undrained cavity problem that involve solving a system of coupled governing differential equations. It is interesting to note that the representative and approximate solution developed by Collins & Yu in 1996 indeed is a correct one for the spherical cavity expansion problem, and, with minor modifications, will be applicable for the accurate calculation of the responses of the cylindrical cavity as well. [ABSTRACT FROM AUTHOR]

In this study, the graphical method, which is widely used to find the coefficients of the Weibull distribution function (WDF), has been improved by using the moving least squares approximation (MLSA) replace least squares method (LSM). The accuracy of the results obtained by the moving least squares method is shown by two different error analysis tests. In order to implement this method, Osmaniye region, which is rich in wind potential maintenance, has been selected. The root mean square error (RMSE) and mean percentage error (MPE) are used to compare the efficiency of proposed method. In this study, the results of the graphical method developed by the MLSA were compared monthly and yearly with the results obtained according to the least squares method. It was observed that the results of the proposed method in the two error analysis tests were much better. Also, the mean wind speed and average wind power values of the selected region were calculated with the coefficients found by MLSA. These calculated values were compared with actual values. [ABSTRACT FROM AUTHOR]

Energy integration in petrochemical and refining industries is an effective concept to minimize dependence on heating and cooling utilities through networks of exchanger equipment. Pinch Analysis is very popular and successful technique to optimize heat recovery between heat sources and sinks. Yet, design of networks of exchangers is challenging and requires careful attention to energy consumption and exchanger areas. This work presents a graphical methodology to design exchanger networks taking into account both heat loads and transfer areas of exchanger units in one single information. A new parameter is introduced for design that is the ratio between the heat load and the exchanger area, and is determined in kW/m2. It is defined as an energy-area parameter expressing how much heat the exchanger would transfer per every meter square of area. Such parameter will be valuable key in design to screen matches of exchangers providing that both the heat and area are considered. The higher the value of the parameter, the better the performance of the exchanger, i.e. maximum heat transfer rate for minimum exchanger area. The design methodology embedding the energy-area parameter guarantees HEN designs with energy targets and minimum areas. A case is studied for the production of 100,000 t/y of dimethyl ether. An optimum network is generated by applying the new parameter with less exchanger areas and hot utility of 25% and 30%, respectively compared with an automated design by Aspen Energy Analyzer®. Also, substantial savings of about 47% in the total cost of the network are earned.

In the present work, a new method for the determination of the outrigger loads in mobile cranes is proposed. The approach adopted assumes the mobile crane as a rigid body and the ground having a linear elastic behavior. The outrigger reactions are determined, using the concept of complete support pattern, through the calculation of the area of triangles constructed within it. The main feature of the method is that the determination of the outrigger reactions can be done by means of graphical considerations with the advantage to perform the task quickly and without the use of complicated calculations. The knowledge of the outrigger pattern, the resultant of all the forces applied and the center of mass of the system crane-payload are only needed as input data. Although the method is suitable for cranes with an outrigger system of any number and shape, the simplification deriving from the use of the graphical approach is fully available only for an outrigger system with four outriggers having a specific shape. These configurations, however, represent the most common configuration found in real applications. The validity of the method proposed has been proven comparing the results with data available in the cranes' manuals and with actual reactions of the outriggers of a mobile cranes operating on site. [ABSTRACT FROM AUTHOR]

The study of phase transitions and critical parameters has a history of nearly one century. The interest shown in this field of science has provided an accumulation of knowledge about phase transitions and critical states of matter through significant researches. On the other hand, theoretical and experimental studies still show that the pressure and temperature diagram of the material is not completed. In particular, the absence of plasma in the (p-T) phase diagram, the uncertainty of the pressure-dependent boundary range of the liquid phase and the state of the equilibrium curves are the focus of the studies. In the phase diagram of pure substance (p-T), the representation of only three phases and the boundary curves separating these phases with two basic points limits the phase diagram. However, as long as the plasma, which constitutes 98% of the universe and is accepted as the fourth phase of matter, does not take place in the phase diagram (p-T) and the liquid phase remains uncertain, phase transitions and critical parameters cannot be fully resolved. [ABSTRACT FROM AUTHOR]

Reinforced concrete beams lose resistance at high temperatures and so as to guarantee their good performance, it is mandatory to consider this accidental action in design. As an alternative to the methods proposed by the European and Brazilian standards, above all the tabular method that, despite its simple application, limits calculations to a few pre-defined values, a new tool for fire design of these beams is proposed herein. A graphical method was developed with the Temperature Calculation and Design (TCD) software, which performs transient bi-dimensional thermo-structural analysis using the finite element method. The main variable of this method consists of the resistance to the bending moment of a heated cross-section. For its validation, the moment of four rectangular sections was determined according to four simplified methods. These results were compared among themselves and to those obtained by a more advanced method. They were all verified to lead to similar results. With regard to the TCD, whose results were used for the preparation of the graphical method, the maximum difference compared to a more advanced method was approximately 2.5%. After validation, graphs that associate the ratio between the applied moment in fire and the resistance to bending moment at ambient temperature to the fire resistance for different beams were created. These graphs present design solutions for more than 2300 beam models with T-shaped cross-sections in assorted lengths, heights, covers and reinforcement arrangements, both positive and negative. In the application examples, the results from the graphical method were generally more economic when compared to the tabular method of the fire design standards. [ABSTRACT FROM AUTHOR]

This study presents a method for finite element (FE) simulation of a deep drawing process of a cold-rolled carbon steel (SPCC) sheet material based on the graphical method. First, uniaxial tensile specimens were prepared and experimental tests were conducted to determine the flow stress curves. The calculation of the fracture points at special strain modes (plane strain, uniaxial tensile strain, and biaxial tensile strain) was presented using the modified maximum force criterion (MMFC). After that, the graphical method was adopted for the estimation of the forming limit curve (FLC) based on several hardening laws. FE models for a deep drawing process of the SPCC sheet were then built using the calculated FLCs. Using FE simulations, the fracture heights of cylinder cups formed by the deep drawing process were finally determined and compared with those from experiments. The results showed a good agreement between simulated and measured fracture height with a maximum of 3.6 % deviation. Additionally, simulations and corresponding experiments were performed to investigate the effects of the blank holder force, punch corner radius, and drawing ratio on the fracture height of cylinder cups. [ABSTRACT FROM AUTHOR]

Permutation methods are commonly used to test the significance of regressors of interest in general linear models (GLMs) for functional (image) data sets, in particular for neuroimaging applications as they rely on mild assumptions. Permutation inference for GLMs typically consists of three parts: choosing a relevant test statistic, computing pointwise permutation tests, and applying a multiple testing correction. We propose new multiple testing methods as an alternative to the commonly used maximum value of test statistics across the image. The new methods improve power and robustness against inhomogeneity of the test statistic across its domain. The methods rely on sorting the permuted functional test statistics based on pointwise rank measures; still, they can be implemented even for large data. The performance of the methods is demonstrated through a designed simulation experiment and an example of brain imaging data. We developed the R package GET, which can be used for the computation of the proposed procedures. [ABSTRACT FROM AUTHOR]

In this study, the coefficients of Weibull Distribution Function (WDF) were calculated at two different heights using by six different methods. One-year wind data were used to determine the coefficients of WDF at different heights, and the wind data were obtained from a metrology station with a height of 10 m and a real wind turbine with a height of 80 m in Turkey's Hatay region. The used methods in this study were Graphical Method (GM), Empirical Method, Energy Pattern Method (EPM), Energy Trend Method, Maximum Likelihood Method and Moment Method.\ Three different statistical error analysis tests were used to compare the performance of the used methods at two different heights. Estimated mean wind speed and power values are the most important indicators to evaluate the performance of the used methods. In this study, mean wind speeds and powers were estimated in all methods for both heights using the WDF. These obtained values were compared with the actual real data and the best performing method was determined at both different heights for selected region. When the results were evaluated in general at both different heights, it was seen that the best performance method was the EPM and the worst performance method was the GM. [ABSTRACT FROM AUTHOR]

Issues are examined in the calculation of the secondary currents of an arc in the implementation of single-phase auto-reclosing (SPAR) for elimination of unstable single-phase faults of 500 and 750-kV ultra-high-voltage lines. Dependences are shown for the backfeed arc extinguishment time, and the SPAR currentless pause recommended in the references, on the amplitude of the forced component of the secondary arc current. A graphical method is proposed for the calculation of secondary arc currents in ultra-high-voltage lines under the condition of SPAR currentless pause. The adequacy of the modeling of a backfeed arc was confirmed by a comparison of the calculated and experimental data from a 750-kV 525-km line. Examples are presented of the application of the graphical method proposed in this article for calculation of secondary backfeed arc currents in 500 kV lines of various length. The features of the implementation of SPAR in 300 and 1000 km lines are noted, and in particular, the effect of zero-power reactors connected to the neutral of the shunt reactors. An example of the implementation of SPAR using automatic phase shunting (APS) in a 500 km line is also examined. [ABSTRACT FROM AUTHOR]

This paper presents timber lamella structures applied to the circular cylinder surface when all lamellae axes intersect at the nodes. To achieve the uniformity of all elements in this structure, the geometry of the structure must be carefully designed. The main methods for the research are graphical and numerical methods for geometric design and a prototype construction for a specific geometric pattern. The methods are discussed for their ease of replication, as well as the possibility of reinterpretation on other surfaces, while the prototype design and construction give insight into the process from design to execution. The combination of these methods allows for a thorough analysis of the geometry for lamella structures. The analysis shows that geometrical design must begin from the whole to the lamella, and that the number of element types in the structure depends on the disposition of the elements and the angle of the pattern. The discussion shows the advantages and limitations of the proposed methods, while the conclusions give the guidelines for the implementation of lamella structures into new design projects.

A graphical method is extended to and applied for visual inspection of solution patterns (region of complex natural frequencies sn) in the complex s-plane for dispersive materials characterized by the Debye and Lorentz models. These patterns are in the form of exponential decay and C-shaped profiles for the Debye and Lorentz models, respectively. Their forms are observed to be affected (e.g., moving left/right) in different manners with a variation of dispersion parameters. This method, thanks to its visual inspection capability, can help in analyzing/synthesizing filters and frequency-selective surfaces. [ABSTRACT FROM AUTHOR]

• A comprehensive decision support system to characterize tails of probability distributions is proposed. • The robustness of proposed DSS is evaluated through a simulation experiment. • The utility of the DSS is demonstrated through its application to Indian precipitation data. • Precipitation analysis (4801 stations) shows around 98% of records have heavy tails over India. A conventional Decision Support System (DSS) can be used to characterize tails of probability distributions into distribution families using various graphical methods. Existing DSSs lack efficient segregation of the Lognormal distribution from the Regularly varying and Subexponential distribution families. Also, they lack the ability to identify the distributions from the hyper-exponential distributions. Recently developed graphical diagnostic tools, such as concentration profile, concentration adjusted expected shortfall, discriminant moment ratio plot, maximum-to-sum plot, and Zenga plot can classify the tails of distributions into various classes if used in an appropriate order in combination with tools of conventional DSS. The present study proposes a comprehensive DSS that alleviates the shortcomings associated with the conventional DSS and characterizes the tails of distributions into classes B\A (Pareto type), C\B (regularly varying), D\C (subexponential), E (Exponential type), hyper-exponential class (outside class E) and LN (Lognormal) distribution (the limiting case between class C and D). The robustness of the proposed DSS over the conventional DSS is established through a simulation experiment. Further, this study also evaluates the influence of the sample size on the effective implementation of the proposed DSS. Finally, the proposed DSS is applied to characterize the tails of daily gridded precipitation data over India. Results indicate that precipitation data from about 98% of grids over India exhibit distributions from heavy-tailed families. The study recommends the use of heavy-tailed distributions to model daily precipitation data over India. The study also suggests that one should rely on more than one graphical method for deducing rational conclusions regarding tail characterization. [ABSTRACT FROM AUTHOR]

At gauged watersheds, the time of concentration can be estimated using rainfall-runoff data; however, at ungauged watersheds, empirical methods are used instead. Large errors in the application of empirical methods may cause inaccurate modeling of floods and unreliable structure design. In this paper, methods for calculating the time of concentration (Tc) were compared to identify the best equation for estimating Tc in ungauged watersheds of an arid region. The graphical method, based on measured data, was compared to 15 empirical methods to determine which empirical method returned the best results. The graphical method was applied to 33 rainfall-runoff events in four rural sub-watersheds located in the central parts of Hormozgan province, Iran. A ranking-based procedure was used to select the best performing empirical methods. To minimize bias and improve accuracy, the best performing empirical methods were modified by adjusting their formulas. According to the study, three empirical methods: (1) Williams, (2) Pilgrim and Mac Dermott, and (3) Arizona DOT, performed the best in the study areas. The results also showed that the modified Williams and Arizona DOT’s formulas were able to estimate the time of concentration in ungauged watersheds with an error lower than 1%.

This paper proposes a simple and fast method to obtain the aeroelastic response of a square cylinder following different modelling approaches underpinned by a novel graphical technique that establishes abstract relationships between different key physical parameters involved in the mathematical models. The method is applied to the analysis of three important aeroelastic problems in the crosswind response of a square cylinder, including the transverse galloping defined with a quasi-steady model, the vortex-induced vibration (VIV) using a nonlinear oscillator model, and the VIV-galloping interaction following a combined effects model. The results demonstrate that the proposed analytical method simplifies the analysis and it is able to capture most of the complex aeroelastic crosswind behaviors of a square bluff body. • A graphical method to obtain the aeroelastic response of a square cylinder following different modelling approaches is proposed. • Compared with conventional analytical methods, the new analytical method has advantages of simplicity and effectiveness. • The graphical analytical method is successfully applied to the study of transverse galloping, VIV and their potential interaction. [ABSTRACT FROM AUTHOR]