Accurate Solution Procedure Research Articles

Determining the optimal parcel delivery method using one drone and one truck

Delivering parcels using a combination of drones and trucks represents a promising new package delivery method. In previous studies, several truck/drone delivery planning problems and their solutions have been proposed. However, little research has been done to determine which delivery method is most appropriate. The reason for this is that it is difficult to obtain an exact solution for such problems, and thus the accuracy of the solutions is an issue. In this study, we propose an accurate solution procedure for the flying sidekick travelling salesman problem (FSTSP) and the parallel drone scheduling travelling salesman problem (PDSTSP), and establish which delivery method is most suitable based on the solutions obtained.

The EOQ Model for Deteriorating Items with a Conditional Trade Credit Linked to Order Quantity in a Supply Chain System

For generality, we observed that some of the optimization methods lack the mathematical rigor and some of them are based on intuitive arguments which result in the solution procedures being questionable from logical viewpoints of a mathematical analysis such as those in the work by Ouyang et al. (2009). They consider an economic order quantity model for deteriorating items with partially permissible delays in payments linked to order quantity. Basically, their inventory models are interesting, however, they ignore explorations of interrelations of functional behaviors (continuity, monotonicity properties, differentiability, et cetera) of the total cost function to locate the optimal solution, so those shortcomings will naturally influence the implementation of their considered inventory model. Consequently, the main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures for different scenarios that overcome the shortcomings of Ouyang et al.

Elastodynamic wave propagation modelling in geological structures considering fully-adaptive explicit time-marching procedures

In this paper, two fully-adaptive explicit time-marching procedures are discussed for the time-domain solution of wave propagation in elastic media. In these procedures, the time integration parameters of the methods are adaptively locally evaluated, following the properties of the discretized model and the values of the calculated responses, engendering more accurate solution procedures. In addition, automated domain decomposition and sub-cycling procedures are also performed, providing more efficient analyses. In this case, a domain decomposition procedure divides the domain of the model into different time-marching subdomains according to the properties of the discretized problem and the stability limit of the adopted time-marching technique, so that a different time-step value is applied to each subdomain, leading to more efficient (and yet stable) explicit time-domain computations. As it is indicated in this work, the adoption of multi-time-steps/sub-cycling splitting procedures further improves the accuracy of the discussed adaptive time-marching formulations. At the end of the paper, benchmark analyses are performed to illustrate the effectiveness of the proposed techniques, followed by synthetic case analyses, with degrees of complexity equivalent to that of real geophysical applications in the OIL & GAS industry, demonstrating the robustness of the proposed explicit approaches. • Fully-adaptive time-marching procedures are proposed for elastodynamic analyses. • Two explicit formulations are discussed: the α-adaptive and the β-adaptive methods. • These procedures consider self-adjustable time integrators and time-step values. • They provide robust solution techniques, enabling enhanced accuracy and efficiency. • Complex geological models are applied to illustrate the effectiveness of the methods.

An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits

Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007) investigated the retailer’s optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article.

Efficient simulation of inclusions and reinforcement bars with the isogeometric Boundary Element method

The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the computed domain. This topic has been addressed in previous papers but the approach presented here is a considerable improvement in terms of efficiency and accuracy. One innovation is that initial stresses instead of body forces are used, resulting in discretised equations that can be written using matrix–vector multiplications. This allowed a one step solution to be implemented for elastic inclusions. In addition, a novel approach is used for the computation of strains, that avoids the use of highly singular fundamental solutions. Finally, a new type of inclusion is presented that can be used to model reinforcement bars or rock bolts and where analytical integration can be used. Test examples, where results are compared with Finite Element simulations, show that the proposed approach is sound.

Efficient exact solution procedure for quasi-one-dimensional nozzle flows with stiffened-gas equation of state

Abstract We propose an efficient and accurate exact solution procedure for the converging–diverging nozzle flows of compressible liquids governed by a stiffened-gas equation of state (SG-EOS). First, we elaborate on how to formulate a complete SG-EOS and suggest a new method to determine the parameters of SG-EOS. Next, we derive the relations for the quasi-one-dimensional nozzle flow of the SG-EOS liquids and propose an efficient solution procedure to obtain the exact solution at various boundary conditions. The proposed solution procedure can accurately calculate the position of the shock wave regardless of the number of computational grid points. We then verify the solution procedure against the previous results for the air and water nozzle flows. We also investigate the influence of the SG-EOS parameters on the nozzle flow of liquid water containing a shock wave. The proposed solution procedure can be used for the basic design of a compressible liquid nozzle and the validation of compressible two-phase flow model.

Advanced simulation of coupled physics in thrust bearings

In hydro power units with very large reversible pump turbines, tilting pad thrust bearings may operate at the edge of the field of experience regarding sliding speed, contact pressure, size, and shape. Here, advanced numerical simulation methodologies offer the possibility to precisely predict the bearing performance and to safely reach guaranteed properties while minimizing the need for experimental investigations. Hence, objective of this work is to develop and validate an advanced method which fully resolves coupled physics in large thrust bearings of reversible pump turbine units. By applying this method, layout tools can be validated and calibrated for an extended design space. Moreover, a better understanding of physical phenomena and how they interact allows for the improvement of design standards. The present contribution introduces an accurate and robust coupling and solution procedure including finite element analyses of thermal and mechanical deformations of pad and thrust runner, mesh motion analyses, and conjugate heat transfer (CHT) analyses. CHT analyses account for flow and heat generation in oil film and groove as well as heat transfer in pad and runner. By applying the procedure to a large bearing investigated at a prototype-sized test rig, all analysis steps are verified and validated using accurate and extended measuring data.

On the inertio-elastic instability of variable-thickness functionally-graded disks

Abstract Instability is observed at certain speeds for rotating disks when the radial displacement in the centrifugal force is taken into consideration. The critical angular velocity values which cause unbounded displacement and stresses will be determined. Analysis of functionally-graded variable-thickness disks requires solving variable-coefficient governing differential equations. Analytical solutions of such equations can be obtained only for certain material grading functions and uniform thickness profiles. In the present study, disks with non-uniform thickness profiles and heterogeneous material properties graded in the radial direction are considered. Solution of the resulting variable-coefficient governing equation of displacement requires the implementation of numerical methods. To this end, a novel approach, Complementary Functions Method is employed as the solution scheme. Complementary Functions Method provides an accurate and efficient solution procedure by reducing the two-point boundary value problem to a system of initial value problems. It is applicable for any continuous material grading functions and thickness profiles. The presented method is validated using a benchmark disk problem with uniform-thickness and material properties graded by a simple power function. Also, the efficiency of the solution scheme is demonstrated by comparing the results with those of finite element method (ANSYS).

Vibration Characteristics Analysis of Cylindrical Shell‐Plate Coupled Structure Using an Improved Fourier Series Method

A simple yet accurate solution procedure based on the improved Fourier series method (IFSM) is applied to the vibration characteristics analysis of a cylindrical shell‐circular plate (S‐P) coupled structure subjected to various boundary conditions. By applying four types of coupling springs with arbitrary stiffness at the junction of the coupled structure, the mechanical coupling effects are completely considered. Each of the plate and shell displacement functions is expressed as the superposition of a two‐dimensional Fourier series and several supplementary functions. The unknown series‐expansion coefficients are treated as the generalized coordinates and determined using the familiar Rayleigh‐Ritz procedure. Using the IFSM, a unified solution for the S‐P coupled structure with symmetrical and asymmetrical boundary conditions can be derived directly without the need to change either the equations of motion or the expressions of the displacements. This solution can be verified by comparing the current results with those calculated by the finite‐element method (FEM). The effects of several significant factors, including the restraint stiffness, the coupling stiffness, and the situation of coupling, are presented. The forced vibration behaviors of the S‐P coupled structure are also illustrated.

Reply to Comments on “A simple and accurate numeric solution procedure for nonlinear buckling model of drill string with frictional effect”

Abstract This paper is concerned with the comments on “A simple and accurate numeric solution procedure for nonlinear buckling model of drill string with frictional effect”. The authors discussed each of those comments in detail. In summary, the authors do not agree with those comments made by Li (2016).

Comment on “A simple and accurate numeric solution procedure for nonlinear buckling model of drill string with frictional effect” by Sun Youhong, Yu Yongping, Liu Baochang [J. Petrol. Sci. Eng. 128(2015)44–52

Abstract Fig. 1 in this paper by Sun Youhong, Yu Yongping, Liu Baochang [J. Petrol. Sci. Eng. 128(2015)44–52] is not correct. This paper's title refers to nonlinear buckling while its content is linear, and it ignores numerous relevant references.

A new mixed finite-element approach for the elastoplastic analysis of Mindlin plates

The objective of this paper is to develop an accurate and efficient solution procedure for elastoplastic problems in structural mechanics in the framework of a two-field mixed variational principle. A novel solution algorithm is proposed and applied to the elastoplastic analysis of Mindlin plates. The Hellinger–Reissner principle is adopted to obtain the global finite-element equations of the problem. Instead of a static condensation, the stress-type field variables are preserved during the solution. According to the proposed approach, the strain increments within a nonlinear solution step are obtained directly at the nodal points from matrix operations instead of gradients of a displacement field. In the present implementation, the von Mises yield criterion with linear hardening is adopted. For the integration of the elastoplastic constitutive rate equations at the nodal points, a 3D fully implicit algorithm is employed. A layered approach is followed to enable the resolution of the plastic strains through the plate thickness. The mixed formulation of the Mindlin plate theory is shear-locking free by construction. The proposed solution strategy is verified by solving several benchmark problems that demonstrate the high accuracy and convergence rate of the presented layered mixed formulation for elastoplastic analyses.

On the plastic zone size of solids containing doubly periodic rectangular-shaped arrays of cracks under longitudinal shear

Multiple cracks interaction plays an important role in fracture behavior of materials. A number of studies have been devoted to analytical and numerical analyses of the doubly periodic arrays of cracks. A very natural and highly accurate solution procedure is proposed to describe the interaction effect among the doubly periodic rectangular-shaped arrays of cracks. The proposed solution is implemented in the framework of continuously distributed dislocation model and singular integral equation approach. The accuracy of this solution is proved through a comparison of results from the present simulation and known closed form solutions. Further, the interaction effects among the periodic cracks on the plastic zone size and crack tip opening displacement are studied. It is found that the interaction distance among the vertical and horizontal periodic cracks is quite different.

A simple and accurate numeric solution procedure for nonlinear buckling model of drill string with frictional effect

Abstract The nonlinear buckling analysis of drill string in a rigid well is presented in this paper. Considering effects of friction and boundary constraints, this problem could be taken as a model of a rod laterally constrained in a rigid cylinder (horizontal, oblique and vertical rigid cylinder could be included). After introducing a new variable, the resulting coupled nonlinear integral–differential equations are successfully solved by employing the extended system shooting method. Examples with various friction coefficients and combinations of boundary conditions are proposed. It is found that the axial frictional force plays a more significant part on buckling load for horizontal well than vertical one. Compared to experimental data or results obtained by using the discrete singular convolution algorithm (DSC) and the finite element method (FEM), the accuracy of the formulations and solution procedures, is verified. What’s more, the nonlinear buckling behaviors of two instances of vertical scientific wells are analyzed. The present results are useful for practical design applications related to calculation of buckling loads and selection of bottom hole assembly (BHA) elements.

Numerical Modeling of Fluid Flow and Thermal Behavior of Different Nanofluids on a Rotating Disk

The thermal and velocity profiles of various nanofluid systems on a rotating disk are simulated. Finite difference method, the orthogonal collocation method, and the differential quadrature method (DQM) of numerical approaches are used to solve the governing equations and are compared to determine the faster and more accurate solution procedure. Five nanoparticles Al, Al2O3, Cu, CuO, and TiO2 solved in three base fluids water, ethylene glycol, and engine oil are considered to be used on the disk at different volume fractions. A new general algorithm is presented for solving equations of a rotating‐disk problem quickly and accurately and it is found that the DQM method is the best approach for this numerical simulation. Heat transfer performance of a rotating disk would be much better enhanced with water based Al nanofluid. A wide range of results for different base–fluid combinations with nanoparticles is presented with untransformed 3D results and effects of the variation of different parameters provides comprehensive insight and prevents inaccurate deductions.

A Three-Dimensional Layerwise-Differential Quadrature Free Vibration of Thick Skew Laminated Composite Plates

Using the layerwise theory in conjunction with the differential quadrature method (DQM), an accurate and efficient solution procedure for the free vibration analysis of thick skew laminated composite plates is introduced. By employing Hamilton's principle and the layerwise theory, the discretized form of the equations of motion in the thickness direction is obtained. Then, the DQM is used to solve the resulting system of differential equations. The fast rate of convergence and high accuracy of the method is established. Then, some new results for skew laminated plates are presented, which can be used as a benchmark solution for future works.

Robust DC and efficient time-domain fast fault simulation

Purpose – Imperfections in manufacturing processes may cause unwanted connections (faults) that are added to the nominal, “golden”, design of an electronic circuit. By fault simulation one simulates all situations. Normally this leads to a large list of simulations in which for each defect a steady-state (direct current (DC)) solution is determined followed by a transient simulation. The purpose of this paper is to improve the robustness and the efficiency of these simulations. Design/methodology/approach – Determining the DC solution can be very hard. For this the authors present an adaptive time-domain source stepping procedure that can deal with controlled sources. The method can easily be combined with existing pseudo-transient procedures. The method is robust and efficient. In the subsequent transient simulation the solution of a fault is compared to a golden, fault-free, solution. A strategy is developed to efficiently simulate the faulty solutions until their moment of detection. Findings – The paper fully exploits the hierarchical structure of the circuit in the simulation process to bypass parts of the circuit that appear to be unaffected by the fault. Accurate prediction and efficient solution procedures lead to fast fault simulation. Originality/value – The fast fault simulation helps to store a database with detectable deviations for each fault. If such a detectable output “matches” a result of a product that has been returned because of malfunctioning it helps to identify the subcircuit that may contain the real fault. One aims to detect as much as possible candidate faults. Because of the many options the simulations must be very efficient.

An Accurate Solution Procedure for Calculation of Voltage Flicker Components

Voltage flicker is one of many serious power quality disturbances, which would deteriorate the stability and operation efficiency of a power system. Effective evaluation of flicker severity plays an important role in the monitoring and control of developing advanced metering infrastructure. Since the evaluation process for voltage flicker is complicated, some inaccurate intermediate results may give rise to the propagation of estimation errors. Therefore, an accurate solution procedure for the calculation of voltage flicker components is proposed in this paper. With the extraction technique for envelope signal and high-frequency resolution mechanism for flicker spectral analysis, the superior performance to achieve the instantaneous flicker severity evaluation can be obtained.

A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints

Abstract A unified accurate solution procedure for free vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints is presented. The material properties of the spherical shells are assumed to change continuously in the thickness direction and two different four-parameter power-law distributions are considered. The proposed method is formulated by the Ritz procedure on the basis of the first-order shear deformation shell theory. Each of admissible functions, regardless of boundary conditions, is composed of a standard Fourier cosine series and several auxiliary functions introduced to ensure and accelerate the convergence of series representations. The accuracy and reliability of the current solution are validated by comparing the results with existing results and those generated from the finite element analyses, and numerous new results for functionally graded spherical shells subjected to elastic restraints are presented, which can serve as the benchmark solutions for other computational techniques in the future research. The effects of the boundary conditions, power-law exponents, and shell segments on the free vibrations of the spherical shells are also investigated, and some interesting insights into the parameter effects on frequency behaviors are illustrated.

Free vibration analysis of composite laminated cylindrical shells using the Haar wavelet method

Abstract In this paper, a simple yet accurate solution procedure based on the Haar wavelet discretization method (HWDM) is applied to the free vibration analysis of composite laminated cylindrical shells subjected to various boundary conditions. The Reissner–Naghdi’s shell theory is adopted to formulate the theoretical model. The initial partial differential equations (PDE) are first converted into system of ordinal differential equations by the separation of variables. Then the discretizations of governing equations and corresponding boundary conditions are implemented by means of the HWDM, which leads to a standard linear eigenvalue problem. Accuracy and reliability of the current solutions are validated by comparing the results with those available in the literature. The effects of several significant aspects including boundary conditions, length to radius ratios, lamination schemes and elastic modulus ratios on natural frequencies are discussed. The advantages of the current solutions consist in its simplicity, fast convergence, low computational cost and high accuracy.