Solution Method Research Articles

Application of the finite element method to the endochronic theory of thermoplasticity for isotropic materials in a plane stress state

Abstract To describe the nonlinear deformation of isotropic materials under non-isothermal loading, it is proposed to use the endochronic theory of thermoplasticity. In this study, the governing equations of this theory are obtained for the general case of loading and for the case of a plane stress state. The calculated dependences of the finite element method in relation to endochronic theory are given, and computational methods of solution are also presented. In the last part of the study, an example of calculating a thin plate under complex loading is considered.

Design and implementation of software modularization in T-type three-level inverter

Abstract This paper addresses the issues of logical allocation state constraints, invalid state switching, and program redundancy in the software design process of the signal processor in the T-type three-level inverter. It combines the importance and advantages of modular thinking in software design to propose a solution method for software modularization based on functional analysis and hierarchical module division. The article presents simulation tests and experimental results of the software modularization of the T-type three-level inverter implemented based on FPGA/CPLD chips, validating the feasibility and effectiveness of this design approach.

Growth, Characterizations of Oxalic Acid Di-Hydrate Crystals of Pure, Milled, Shocked Impact of 50 Scaling for Electronic, Photonic, Display and Sensor Usefulness by Theory and Practice

Oxalic acid dihydrate (OADH) crystal was grown by slow evaporation solution method, milled to micro-OADH, impacted with shocked 50 pulses and harvested in a 16-day period. The 2 MPa pressure with 2.2 Mach number of 864 K temperature specifies the product as shocked 50 scaled OADH. Single crystalline X-ray diffraction of OADH macro are as specified with P21/n as space group with monoclinic as the crystal system and shocked 50 scaled OADH are with lattice constants; the % of elements of OADH specimen are confirmed by theory and practice. The dielectric constant of OADH is higher at lower frequency values by space charge polarization. OADH of all scales are of the negative photo-conductivity type. The influx data of OADH of three types of scaling are identified as better electronic filter. The micro-OADH is confirmed by the scanning electron microscopy analysis as 10 micrometer scaling without any flaws. The Fluorescence (FL) study shows bluish FL emission for all samples of OADH; sensitivity is 8.88>6.6>2.2 for shocked 50-OADH, micro-OADH, macro-OADH. The Miller’s indices of (101) profile for RGB display is shown without as well with recursive colors of OADH.

Semi-analytical vibration modeling of complex axisymmetric shells using shifted Legendre series

This paper presents a semi-analytical approach based on the shifted Legendre series for vibration modeling of complex axisymmetric shells. This method divides the structure along its generator into complex axisymmetric shells comprised solely of conical and spherical shell segments. A global cylindrical coordinate system is established to unify the coordinate system of complex axisymmetric shells. Coupling between segments and the simulation of arbitrary boundary conditions are achieved using artificial spring technology. Based on the first-order shear deformation theory (FSDT), the energy functional of each segment is derived. The circumferential displacement is expanded using Fourier series, while the meridional displacement is expanded using the shifted Legendre series at shifted Gauss-Lobatto nodes. Utilizing the inner product matrix and differential matrix of the shifted Legendre series, the integration and differentiation processes in the vibration characteristic equation are simplified into a product form, significantly enhancing computational efficiency. Through convergence analysis and comparison of the computational results of the present method with numerical simulation results, experimental results and literature results demonstrate the advantages of high convergence, high accuracy and fast solution speed of this solution method. On this basis, the vibration characteristics of ring-stiffened double-layer hemispherical shells are investigated. The results demonstrate the great applicability of this method for vibration modeling of complex axisymmetric shells in engineering.

Structural and antibacterial assessment of two distinct dihydroxy biphenyls encapsulated with β-cyclodextrin supramolecular complex

β-Cyclodextrin plays a vital role in biological application because it can enhance the stability and solubility of the guest molecules in the supramolecular inclusion complexes. Moreover, the β-Cyclodextrin inclusion complex has control-releasing behavior and lower toxicity than bare guest molecules. To improve the solubility and stability properties of two structurally different fluorescent guest molecules, namely 2,2′-dihydroxy biphenyl and 3,3′-dihydroxy biphenyls, they involve the β-Cyclodextrin inclusion complex process. Optical measurements clearly described the efficient binding through the changes in the absorbance and emission intensities of guest molecules in the presence of β-Cyclodextrin. The Job's plot from absorbance measurements reveals the 1:1 stochiometric ratio of binding of guests and the β-Cyclodextrin host. The FT-IR spectra of the solid complex show the characteristic stretching and bending vibrations from both the guests and the host molecule. The 1HNMR spectra of the inclusion complex promote downfield shifting of guest molecule protons upon binding with the β-Cyclodextrin host. The solid complex prepared using the solution method exhibits superior antibacterial activity against both gram-positive and gram-negative bacteria compared to the kneading and physical mixing methods.

Extension of Analytical Solution Methods to the Stability of Exposed Stratified Cemented Backfills

Extension of Analytical Solution Methods to the Stability of Exposed Stratified Cemented Backfills

Preemptive and non-preemptive multi-skill multi-mode resource-constrained project scheduling problems considering sustainability and energy consumption: A comprehensive mathematical model

Modern project managers cope with significant challenges to schedule and control projects considering dynamic environments, frequent uncertainties, strict project deadlines, and stricter sustainable requirements above all. Sustainability taking into account resource utilization has been recently associated with project management. Hence, this paper presents a new mixed-integer linear programming (MILP) model with two objectives for a resource-constrained project scheduling problem (RCPSP) with multiple skills and multiple modes, assuming preemptive and non-preemptive activities in an uncertain environment. Given the importance of sustainable developments in projects, the considered objectives are to maximize job opportunities and minimize project duration, resource costs, and total energy consumption. To deal with the model, an AUGNMECON2VIKOR algorithm is utilized to create Pareto solutions. In this model, project activities can be crashed by allocating extra resources. Furthermore, multi-skill resources are used to perform project activities. This study also investigates the impact of these resources on project scheduling. To deal with uncertain circumstances, a fuzzy chance-constrained programming method is employed to develop a robust possibilistic programming model. With respect to the increasing significance of sustainability in project management, this study pioneers the examination of the impact of sustainable factors on project scheduling. Finally, the proposed formulation is validated using instances from the well-known PSPLIB and MMLIB test sets. Finally, a comparison is drawn between the presented solution method considering AUGMECON2VIKOR and AUGMECON2.

Sequential testing in batches with resource constraints

This paper studies a problem of determining the state of a system through costly tests of its components, where components can be tested simultaneously in batches to exploit economies of scale. This problem is a generalization of the classical sequential testing problem and it has applications in various settings, including machine maintenance, disease diagnosis, and new product development. We prove that the problem is strongly NP-hard, model it as a mixed-integer programming formulation, and we also propose a dynamic program for it. Additionally, we design a tabu search and a hybrid solution method that combines a tabu search metaheuristic and a proximity search matheuristic. Based on extensive computational experiments, we find that the dynamic program can solve instances with up to 25 components within a 15-minute time limit and 16 GB of RAM. With respect to larger instances, the proposed metaheuristic and hybrid method are better than a greedy heuristic.

Reviewing extensions and solution methods of the planar Weber single facility location problem

Reviewing extensions and solution methods of the planar Weber single facility location problem

Exact and Fractional Solution of MHD Generalized Couette Hybrid Nanofluid Flow with Mittag-Leffler and Power Law Kernel

This study investigates the complex behavior of Jeffrey nanofluid flow in a porous oscillating microchannel under the influence of magnetohydrodynamic (MHD) effects. The research explores how magnetic field distortions lead to diverse accumulation patterns of nanofluid particles, a phenomenon attributed to homogeneous magnetization in fluid dynamics. Nanoparticles ranging from 0.25% to 0.5% (low and inexpensive concentrations) are remarkably consistent for best results in most machining procedures. Different concentrations of various nanomaterial's is utilized (φ1 = φ2 = 0.01, 0.02, 0.03, 0.04) to make the simple nanfluid and hybrid nanofluid suspensions. By employing fractal-fractional derivatives governed by power law, a mathematical model developed to describe the time-varying, compressible MHD flow of Jeffrey nanofluid. The model incorporates the effects of heat transfer, pressure, and magnetic fields on the fluid dynamics. A novel fractional approach utilizing the Laplace transform is applied to solve the fractal MHD hybrid-fluid model integrated into a porous medium. The study reveals velocity flow decrease with increasing Reynolds numbers but increase with channel inclination. Additionally, both the Darcy number and magnetic field orientation enhance heat transfer rates. In addition, the velocity profile enhanced by the hybrid nanofluid suspension as compared to simple nanofluid flow. The research validates its findings by demonstrating the convergence of fractional and numerical solution methods. Furthermore, the study compares the performance of different hybrid nanofluids, concluding that water-based (H2O + GO + MoS2) hybrid fluids exhibit slightly superior characteristics compared to (CMC + GO + MoS2) hybrid nanofluids.

Optimizing Frequencies of Functionally Graded Material Plates via Multi-Objective Genetic Algorithm: Positioning Point Supporters for Maximum Performance

In the presented study, an approach is introduced for optimizing the vibrational characteristics of aerospace structures that are composed of Functionally Graded Materials (FGM). The focus is placed on the strategic positioning of point supporters to enhance the structural performance under various operational conditions. The effective elasticity properties of the FGMs are determined using the Mori-Tanaka method for homogenization. The deformation behavior of these structures is analyzed by employing the first-order shear deformation theory. Solutions are computed through the 2D Ritz method, which utilizes Chebyshev polynomials, forming the basis for the objective function of a multi-objective genetic algorithm. This algorithm is designed to optimize the positioning and the number of point supporters aimed at targeting specific vibration frequencies. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is utilized to efficiently generate Pareto optimal solutions, which illustrate the trade-offs between conflicting objectives. The validation of the solution method is achieved through comparisons with experimental data, confirming the accuracy and practical relevance of the approach. The application of the optimization framework is extended to various configurations of aerospace structures, including diverse compositions of FGM and different boundary conditions. This methodology is shown not only to enhance the operational performance of aerospace structures but also to contribute to the precise design and manufacturing of components in aircraft and satellites, aligning with the central interests of aerospace engineering.

A solution method for decomposing vector fields in Hamilton energy

A solution method for decomposing vector fields in Hamilton energy

Unsteady Lifting-Line Theory for Camber Morphing Wings State-Space Aeroelastic Modeling

A novel frequency-domain analytical-numerical model for the aerodynamic solution of camber morphing wings is developed. The model combines an unsteady lifting-line formulation with Küssner–Schwarz aerodynamic theory to provide the pressure distribution and thus the transcendental aerodynamic matrix that relates the generalized aerodynamic forces to the Lagrangian coordinates of a given wing structural dynamics model. The state-space form of the aerodynamic loads is obtained from the rational matrix approximation of the aerodynamic matrix. This, combined with the wing structural dynamics operator, can readily provide the state-space form of the aeroelastic problem. To assess the accuracy of the proposed aerodynamic solution method, numerical investigations are performed. These consist of its application to several conventional wing configurations and wings with camber morphing, followed by the comparisons of the corresponding solutions with the predictions given by a well-validated panel-method solver for potential flows. These results are shown to be in very good agreement, thus demonstrating that the proposed approach can capture the effects due to wing tapering, sweep angle, and camber morphing, while requiring a remarkably lower computational effort. The excellent accuracy of a few-pole finite-state approximation of the aerodynamic matrix is finally proven for a swept wing with camber morphing.

THE SIMPLEX - PREEMPTIVE GOAL PROGRAMMING WITH BRANCH AND BOUND METHOD FOR OPTIMIZING WASTE VEHICLE ROUTES AND TRANSPORTATION

This research discusses the optimization of the assignment of waste vehicle routes and transportation, which are responsible for transporting waste from temporary disposal sites to final disposal sites. The aim is to minimize the remaining waste at temporary disposal sites, thus creating a clean and comfortable environment. The focus of this research is determining the number of trips (rit) for each vehicle (dump trucks and arm roll trucks) on each route. Besides aiming to minimize the remaining waste at temporary disposal sites as the main priority, there are also other priorities, namely minimizing fuel usage and the working time within a day. Therefore, in accordance with the characteristics of the problem, where there are multiple objectives and an integer solution is required, The Simplex-Preemptive Goal Programming with the Branch and Bound method is proposed as the solution method. The optimal solution has been obtained. The result includes the optimal number of trips (rit) for each waste transport vehicles (dump trucks and arm roll trucks) on each routes.

A methodology to correlate river inflows in state sampling Monte Carlo simulation

This paper proposes a methodology to sample inflow states of run-of-the-river hydropower plants that are spatially correlated, preserving the statistical dependence among them, in Non-Sequential Monte Carlo Simulation (MCS). The technique used to correlate the inflows of hydro plants in the Brazilian synthetic series generation model, which is based on the correlation matrix and Cholesky Decomposition, is adapted to be used in the sampling stage. Nataf transformation is used for addressing non-normality of the inflow data. The solution method is such that no assumption about the data probability distribution is necessary. Although the methodology is applied to inflows in this paper, it can be applied to any other quantity, such as winds. A case study is proposed to evaluate the correlation of the sampled inflows and the impact on the reliability indices. Besides, it is investigated the effect when inflows states are clustered to reduce the number of states in the system for better computational efficiency. Case study shows that the reliability indices obtained with the proposed methodology are within the confidence interval of the indices calculated by the Sequential MCS with an execution time as fast as the Non-Sequential one, while the non-consideration of correlation causes very significant errors. Simulation with 50 clusters produces equally good results with a reduction of 75 % of the execution time. Sensitivity analysis showed that halving the number of clusters maintains the accuracy of the results, while 10 clusters results in overestimating system reliability. Different degrees of correlation have been simulated, showing that the higher the correlation among the hydro plants, the less reliable the system becomes.

A Portrayal of Integer Solutions to Transcendental Equation with Six Unknowns 𝟑√ 𝐗 + 𝐘 + √ 𝐱𝐲 = 𝑧𝟐 + 𝑤𝟐

Objectives: This research article focuses on finding non-zero integer solutions to the Transcendental equation with six unknowns represented by . Methods: There is no universal method for finding integer solutions to Diophantine equations involving surds. Various substitutions strategies are employed to obtain non-zero distinct integer solutions to the surd equation under consideration. Findings: Five different choices of substitutions are utilized to determine many non-zero distinct integer solutions to the transcendental equation with six unknowns in title. Novelty: In this analysis, the transcendental equation with six unknowns given by has been reduced to either Space Pythagorean equation or non-homogeneous ternary quadratic equation through suitable transformations and for which integer solutions can be found elegantly. Keywords: Transcendental Equation With Six Unknowns, Surd Equation, Integer Solutions, Space Pythagorean Equation, Ternary Quadratic Equation

Homogeneous Quadratic Equation with Four Unknowns 𝑥2 + 𝑥𝑦 + 𝑦2 = 𝑧2 + 𝑧𝑤 + 𝑤2

Objectives: Diophantine research focuses on various ways to tackle multi variable and multi-degree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions. The objective of this manuscript is to find the solutions to Polynomial Diophantine equation . Methods: Diophantine equations may have finite, infinite, or no solutions in integers. There is no universal method for finding solutions to Diophantine equations. Different choice of solutions in integers is obtained through using linear transformations and employing the factorization method. Findings: Many distinct patterns of integer solutions are obtained. Novelty: The main thrust is to illustrate different ways of obtaining various choices of solutions in integers to second-degree equations with four variables . Different choice of solutions in integers is obtained through using linear transformations and employing the factorization method. Utilization of substitution strategy reduces the given equation to a ternary quadratic equation for which solutions can be found easily. Mathematics Subject Classification:11D09 Keywords: Homogeneous second degree with four variables, Solutions in integers, Factorization method, Linear transformation, Polynomial diophantine equation

Analyzing energy transition for industry 4.0-driven hybrid energy system selection with advanced neural network-used multi-criteria decision-making technique

This study aims to select the appropriate renewable energy alternatives for the efficiency of hybrid energy systems to increase energy transition performance. For this purpose, a novel neural network (NN)-based fuzzy decision-making model is constructed that has three different stages. In the first stage, NN-based fuzzy decision matrix is created. Secondly, 6 different variables based on industry 4.0 are weighted with the sine trigonometric Pythagorean fuzzy entropy technique. Additionally, another calculation has been implemented with criteria importance through intercriteria correlation (CRITIC) to identify the consistency of the results. Furthermore, in the third stage, considering 5 different renewable energy alternatives, 10 different combinations are identified for hybrid energy systems. The most effective alternatives are defined by the sine trigonometric Pythagorean fuzzy ranking technique by geometric mean of similarity ratio to optimal solution (RATGOS) method. Moreover, to test the validity of these results, another analysis is conducted using the additive ratio assessment (ARAS) technique. The main contribution of the study is that the optimal renewable energy combination required for an efficient hybrid energy system is determined by performing a priority analysis between the variables. This situation has a significant guiding feature for investors. Similarly, the development of the RATGOS technique both increases the methodological originality of the study and enables more accurate alternative ranking. It is identified that the results of all methods are similar. Therefore, this situation gives information about the coherency and validity of the findings. It is concluded that the most important criterion is real-time capability. It is also denoted that the best combination for hybrid energy systems is Solar-Wind.

ANALYSIS OF PRIORITY AREAS FOR HANDLING STUNTING CASES IN SIGI REGENCY USING THE TOPSIS METHOD BASED ON WEB DASHBOARD

Stunting is a condition of growth failure in children, where a toddler has a length or height below the average. Stunting is a problem for children because it has the potential to slow down brain development with prolonged effects. Central Sulawesi Province is one of the provinces with the highest stunting prevalence rate and the area with the highest stunting rate is in Sigi Regency at 36.8%. Stunting cases are an important concern for the Sigi Regency government, especially the Health Office and Community Health Centers. To identify and determine areas that are prioritized for handling stunting cases, seven indicators are used, including the number of stunting cases, number of villages covered, number of health workers, number of integrated service posts, number of exclusive breastfeeding, percentage of clean drinking water, and percentage of proper sanitation. To support in reducing the percentage of stunting in Sigi Regency, research was conducted and a web dashboard system application was made to support priority area selection decisions using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, a best alternative method that has the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. The results obtained in this study are the areas that are prioritized for handling stunting cases in Sigi Regency is the Sigi Biromaru area with a total of 495 stunting cases, the number of coverage villages is 18, the number of integrated service posts is 53, the number of health workers is 96, the number of exclusive breastfeeding is 35, the percentage of proper drinking water is 44%, and the percentage of proper sanitation is 84.00% with the highest preference value through the TOPSIS method analysis of 0.660.

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

Suppressing spurious oscillations is crucial for designing reliable high-order numerical schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated over the past several decades. This paper proposes a novel, robust, and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method on general meshes, motivated by the damping technique (see J. Lu, Y. Liu, and C. W. Shu [SIAM J. Numer. Anal. 59 (2021), pp. 1299–1324]). The OEDG method incorporates an oscillation-eliminating (OE) procedure after each Runge–Kutta stage, and it is devised by alternately evolving the conventional semidiscrete discontinuous Galerkin (DG) scheme and a damping equation. A novel damping operator is carefully designed to possess both scale-invariant and evolution-invariant properties. We rigorously prove the optimal error estimates of the fully discrete OEDG method for smooth solutions of linear scalar conservation laws. This might be the first generic fully discrete error estimate for nonlinear DG schemes with an automatic oscillation control mechanism. The OEDG method exhibits many notable advantages. It effectively eliminates spurious oscillations for challenging problems spanning various scales and wave speeds, without necessitating problem-specific parameters for all the tested cases. It also obviates the need for characteristic decomposition in hyperbolic systems. Furthermore, it retains the key properties of the conventional DG method, such as local conservation, optimal convergence rates, and superconvergence. Moreover, the OEDG method maintains stability under the normal Courant–Friedrichs–Lewy (CFL) condition, even in the presence of strong shocks associated with highly stiff damping terms. The OE procedure is nonintrusive, facilitating seamless integration into existing DG codes as an independent module. Its implementation is straightforward and efficient, involving only simple multiplications of modal coefficients by scalars. The OEDG approach provides new insights into the damping mechanism for oscillation control. It reveals the role of the damping operator as a modal filter, establishing close relations between the damping technique and spectral viscosity techniques. Extensive numerical results validate the theoretical analysis and confirm the effectiveness and advantages of the OEDG method.