FORTRAN Research Articles

Numerical simulation of fracture behaviour of the shot-earth 772

Earth building techniques have been around for thousands of years. Among them, it is worth mentioning: cut blocks, poured earth, superadobe, adobe, cob, rammed earth, compressed stabilised earth blocks, wattle and daub, shaped earth, and straw-clay. An innovative technique among the earth building ones, and named shot-earth technique, is the topic of the present paper. The technology employs a specific mixture of the shot-earth (named shot-earth 772) consisting of 7 parts of excavated soil, 7 parts of aggregates and 2 parts of cement (by volume): the mixture stream is projected at high velocity onto a surface, adding about 3% of water (by volume) at the spraying nozzle. The present research work deals with the numerical simulation of the fracture behaviour of the shot-earth 772. More precisely, an experimental campaign performed to compute the fracture toughness of the material is here numerically simulated. To such an aim, a homemade Finite Element numerical model, developed in standard Fortran language, is used to simulate both flexural and fracture tests on the shot-earth considered. In fact, such a model is able to properly consider. The material fracture process is described by means of a cohesive law, which is introduced within the cracked zone, whereas an elastic law is adopted for the un-cracked region of the material. Subsequently, the Modified Two-Parameter Model is used in order to compute the fracture toughness, from both the experimental fracture tests and the corresponding numerical simulations. Finally, the numerical results are compared with the experimental ones.

Numerical simulation of two-dimensional crack propagation using stretching finite element method by Abaqus

Fatigue is a phenomenon that appears in items subjected to cyclic loads. Thus, rupture and partial oxidation are initiated from the beginning of the process. For this, the study of such a problem of material in fracture mechanics is based on the numerical analysis of the characteristics of a crack. In this article, we propose a modelling of crack propagation by a new method of stretching the mesh by 2D finite element in mixed mode, based on the creation of the elements through a program in the computer language Fortran. The parametric mesh with 4 nodes (CPE4) was created to make the simulation and to characterise the stress intensity factors, by the Abaqus computer code. For this, the validation of stretching finite element method (SFEM) results is done by other methods: extended finite element method (XFEM) and analytical method to simulate the crack propagation. The stress intensity factor (SIF) is an essential parameter of this study. Two possibilities for determining the SIF have been retained: one by the numerical method of our choice and the other by the analytical method. Parameters to characterise the stress state at the crack front KI and KII were evaluated in two stages one by the crack length and the other by the a/c ratio.

Study on dynamic mechanical properties and constitutive model description of Inconel718

In this study, the effects of strain rate and temperature on the flow stress of Inconel718 were analyzed by Split Hopkinson Pressure Bar (SHPB) experiment and quasi-static compression experiment. The classical JC constitutive model was established by combining the quasi-static compression experiment with the SHPB experiment. According to the effects of different grain sizes and [Formula: see text] phase on dislocation pile-up, the dislocation pile-up theory was introduced to modify the JC constitutive model. The modified constitutive model was compiled in FORTRAN language, and VUMAT user material subroutine was called and secondary development was carried out to establish the polycrystalline simulation model with different grain sizes. The uniaxial tensile and compression simulation process of polycrystal with different grain sizes was performed. Through comparing the simulation results with the experimental data. The correlation coefficient R, between the simulation and experimental values, is 0.97,981, and the average relative error is only 3.72%. The accuracy of the modified constitutive model was verified.

Incompatible Deformation Model of Rocks with Defects around a Thick-Walled Cylinder

Before the excavation of underground engineering, joints, fissures, and voids already exist in the rock—that is, there are defects in the rock. Due to the existence of these defects, the rock produces plastic deformation, which can lead to incompatible deformation. Therefore, the classic continuum theory cannot accurately describe the deformation of the rock. In this paper, a relationship between the strain tensor and metric tensor was studied by analyzing the three states of elastic plastic deformation, and the elasto-plastic incompatible model was built. Additionally, the stress and deformation of a thick-walled cylinder under hydrostatic pressure was investigated by using a finite element program written in the FORTRAN language. The results show that the plastic strain is associated with not only deviator stress but also the distribution of defects (represented by the incompatible parameter R). With the value of R increasing, the defects in the rock increased, but the elastic plastic stiffness matrix decreased. Thus, as more rock enters the plastic state, the deformation of the surrounding rock is enlarged.

Numerical Simulation of Laminar Boundary Layer Flow Over a Horizontal Flat Plate in External Incompressible Viscous Fluid

In this paper, steady laminar boundary layer flow of a Newtonian fluid over a flat plate in a uniform free stream was investigated numerically when the surface plate is heated by forced convection from the hot fluid. This flow is a good model of many situations involving flow over fins that are relatively widely spaced. All the solutions given here were with constant fluid properties and negligible viscous dissipation for two-dimensional, steady, incompressible laminar flow with zero pressure gradient. The similarity solution has shown its efficiency here to transform the governing equations of the thermal boundary layer into a nonlinear, third-order ordinary differential equation and solved numerically by using 4th-order Runge-Kutta method which in turn was programmed in FORTRAN language. The dimensionless temperature, velocity, and all boundary layer functions profiles were obtained and plotted in figures for different parameters entering into the problem. Several results of best approximations and expressions of important correlations relating to heat transfer rates were drawn in this study of which Prandtl’s number to the plate for physical interest was also discussed across the tables. The same case of solution procedure was made for a plane plate subjected to other thermal boundary conditions in a laminar flow. Finally, for the validation of the treated numerical model, the results obtained are in good agreement with those of the specialized literature, and comparison with available results in certain cases is excellent.

Study of Some Nuclear Properties of 170-178W Isotopes by Using Interacting Bosons Model-1

We looked into the structure of energy levels for some Tungsten isotopes W the (even-even) and electromagnetically probability transmission for it with the Model of Interacting Bosons type one (IBM-1) to evaluate the nuclear structure for Tungsten isotopes are investigated in this study (170-178W). The data was gathered using an IBM software written in the Fortran programming language The values of the parameters in this computation show that the characteristics of tungsten isotopes fall between the γ_ unstable limit O(6) and the rotational limit SU(3). The energy and branching ratios demonstrate this. The computed results are in very excellent agreement with experimental data for the isotopes under investigation.

A non-local method in peridynamic theory for simulating elastic wave propagation in solids

In order to simulate the elastic wave propagation in unbounded solids, this paper introduces a non-local method to construct absorbing boundary conditions in the bond-based peridynamic theory. To construct non-local absorbing boundary conditions in the form of absorbing layers with increasing damping, we first re-derived the particle motion equilibrium equation of the bond-based peridynamic theory, based on the principle of virtual work and Lagrange's equation on the premise of considering material damping. We also give the expression for the inter-particle damping force density which satisfies the balance laws of linear momentum and angular momentum. This paper also provides a process and algorithm for realizing the non-local absorbing boundary conditions in the bond-based peridynamic theory, and adopts the Fortran language for computer program compilation. Finally, we simulate the elastic wave propagation in semi-unbounded and unbounded solids as numerical examples. The results show that such non-local absorbing boundary conditions can stably absorb and attenuate incident elastic waves. Since it is derived in the time domain, this method does not require frequency-domain operations, such as Fourier and Laplace transformations, nor does it require wave field splitting.

A Current Amplifier Circuit and Control Strategy Based on FPGA

With the extensive application of electric vehicles, energy storage systems and other power electronic equipment, the research on large capacity controllable current source will be an important direction in the future. This paper proposes controllable current source controlled by a full digitally hysteresis current based on field programmable gate array(FPGA), in which the single phase full bridge topology is adopted as the main circuit of current source. The two levels and three levels hysteresis current control strategies are analyzed and compared with the platform of PSCAD/EMTDC. The user defined component was adopted to realize the two difference control strategies with fortran language program. The simulation results verified that the two levels hysteresis current control strategy is much more fit for the controllable current source. Finally, a prototype is designed and fulfilled and it is controlled by the digitally controller with FPGA. The hysteresis current control is realized by FPGA controller with VHDL programming. The experimental results show that the researched hysteresis current control technology is effective for the current amplifier

Computing the heat flux required for warming up of frozen wooden prisms for veneer production in the beginning of their autoclave steaming

An approach for computing the heat flux required for warming up of frozen wooden prisms in the regimes for their autoclave steaming at limited heat power of the steam generator, depending on the dimensions of the prisms cross section, wood moisture content, and loading level of the autoclave has been suggested. The approach is based on the use of two personal mathematical models: 2D non-linear model of the temperature distribution in subjected to steaming frozen wooden prisms and model of the non-stationary heat balance of autoclaves for steaming wood materials. For numerical solving of the models and practical application of the suggested approach, a software program was prepared in the calculation environment of Visual FORTRAN Professional developed by Microsoft. Using this program computation and research of the non-stationary change of the processing medium temperature and heat fluxes in an autoclave with a diameter of 2.4 m, length of 9.0 m and loading level of 50% at a limited heat power of the steam generator, equal to 500 kW during the initial part of the steaming in it of frozen beech prisms with different moisture content have been carried out. The suggested approach can be used for computing and model based automatic realization of energy efficient optimized regimes for autoclave steaming of different wood materials.

An Efficient Mixed Finite Element Perfectly Matched Layer with Optimal Parameters Selection for Two-Dimensional Time Domain Soil-Structure Interaction Analysis

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

An evaluation of force term in the lattice Boltzmann method for mixed convection with large Richardson numbers

PurposeThe purpose of this study is the identification of the best method to apply the body force in the lattice Boltzmann method (LBM). In the simulation of mixed convection, especially for large Richardson number flows in a square cavity.Design/methodology/approachFirst, three methods for applying the body force were compared to each other in the LBM. Then, an LBM-based code was written in the FORTRAN language using these three methods. Next, that code was used to simulate natural/mixed convection in a two-dimensional cavity to evaluate the methods for applying the body force. Finally, the optimum way for applying the body force was used for the simulation of free convection heat transfer in a concentric annulus with Rayleigh number in a range of 1,000 to 50,000, and mixed convection heat transfer in a concentric annulus with Rayleigh number in a range of 10,000 to 50,000 and Reynolds number in a range of 100 to 400.FindingsMixed convection heat transfer was simulated in a two-dimensional cavity with Richardson number in a range of 0.0001 to 100. The results which were obtained in low Richardson number flows have shown good adaptation to the available data. However, the results of large Richardson number flows, for example, Ri = 100, have shown a significant difference to the available data. Investigations revealed that this difference was due to the method of applying the body force. Therefore, the choice of the best way to apply the body force was investigated. Finally, for the large Richardson number flows, the best method to apply the body force has been identified among the several techniques.Originality/valueTo the authors’ knowledge, the effects of methods for applying the body force were not investigated in the cavities mixed convection, even though there are numerous investigations conducted on mixed convection with the LBM. In this study, the effects of techniques to apply the body force were investigated in large Richardson number flows. Finally, the best method to apply the body force is distinguished between several techniques for the large Richardson number mixed convection flows.

Gyrotron Development at High Order Modes

The present work has been characterized by higher order modes in the cavities of the Gyrotron; they are capable of producing RF plasma by developments of it. It uses for fusion systems. We choose the TE31,8 mode in our study. The main problem of gyrotron is the device of the thermal cavity loading. The problem of the thermal loading is solved when any parasitic modes suppress, absence of desired modes; the thermal loading is increased when the high power tube of gyrotron operation is unstable. The mathematical interaction model contains equations that describe the electron motion and the field profiles of the transferred electric modes of the resonator, these are interacting with electrons based on the finite difference method that has been designed to study the starting current, the frequency, quality factor and calculates the roots of the Bessel function by the program we designed in Fortran language. They are used to calculate the operation frequency. Good agreement is between our results and the previous published results both confirm the accuracy of the performance of the designed program.

Experimental and Numerical Analysis on TIG Arc Welding of Stainless Steel Using RSM Approach

This study involves the validating of thermal analysis during TIG Arc welding of 1.4418 steel using finite element analyses (FEA) with experimental approaches. 3D heat transfer simulation of 1.4418 stainless steel TIG arc welding is implemented using ABAQUS software (6.14, ABAQUS Inc., Johnston, RI, USA), based on non-uniform Goldak’s Gaussian heat flux distribution, using additional DFLUX subroutine written in the FORTRAN (Formula Translation). The influences of the arc current and welding speed on the heat flux density, weld bead geometry, and temperature distribution at the transverse direction are analyzed by response surface methodology (RSM). Validating numerical simulation with experimental dimensions of weld bead geometry consists of width and depth of penetration with an average of 10% deviation has been performed. Results reveal that the suggested numerical model would be appropriate for the TIG arc welding process. According to the results, as the welding speed increases, the residence time of arc shortens correspondingly, bead width and depth of penetration decrease subsequently, whilst simultaneously, the current has the reverse effect. Finally, multi-objective optimization of the process is applied by Derringer’s desirability technique to achieve the proper weld. The optimum condition is obtained with 2.7 mm/s scanning speed and 120 A current to achieve full penetration weld with minimum fusion zone (FZ) and heat-affected zone (HAZ) width.

A Coupled Elastoplastic Damage Dynamic Model for Rock

Rock dynamic constitutive model plays an important role in understanding dynamic response and addressing rock dynamic problems. Based on elastoplastic mechanics and damage mechanics, a dynamic constitutive model of rock coupled with elastoplastic damage is established. In this model, unified strength theory is taken as the yield criterion; to reflect the different damage evolution law of rocks under tension and pressure conditions, the effective plastic strain and volumetric plastic strain are used to represent the compressive damage variable and the equivalent plastic strain is used to represent the tensile damage variable; the plastic hardening behavior and strain rate effect of rocks are characterized by piecewise function and dynamic increase factor function, respectively; Fortran language and LS-DYNA User-Defined Interface (Umat) are used to numerically implement the constitutive model; the constitutive model is verified by three classical examples of rock uniaxial and triaxial compression tests, rock uniaxial tensile test, and rock ballistic test. The results show that the constitutive model can describe the dynamic and static mechanical behavior of rock comprehensively.

Numerical implementation of the mathematical model of combined effect on the formation using FORTRAN programming language

The main method of high-viscosity oil production is heating, but there are difficulties in delivering heat to the formation and distributing this heat there quite evenly. The existing methods of delivering heat to the formation are often ineffective – small heat coverage area, excessively high temperatures in some places, loss of a large amount of heat from the wellhead to the bottomhole, need for large areas around the well for thermal action. Combined electromagnetic-acoustic action with the injection of solvent onto the formation could significantly increase the effectiveness of formation heating. The study solves the problem of finding a temperature field with a two-stage effect on the formation: electromagnetic-acoustic heating and then pumping solvent into the formation in order to increase the radius of coverage with thermal impact. With this setting of the problem, the resulting mathematical model does not have an analytical solution. A numerical solution using the finite difference method with an implicit scheme gives fairly accurate results.

COMPUTER SIMULATION IN THE PROBLEMS OF STABILITY OF THIN-WALLED RODS OF AN OPEN PROFILE WITH SHAPE IMPERFECTIONS

The presented numerical methodology is based on the finite element method (FEM) and computational procedures of the NASTRAN software package. It allows to investigate the influence of geometric imperfections in the shape of thin-walled rods of open profile on the critical values of the load, the shape of the stability loss and the stress-strain state. It has been developed an algorithm for computer modeling of initial imperfections in the shape of thin-walled rods, which is implemented in the NASTRAN software package using a neutral NASTRAN PC file and a specially developed program written in FORTRAN language and adapted to this software package. Geometric imperfections of the rods can be represented as their form of loss of stability or the form of deformation from the action of the load with the possibility of varying the maximum value of the imperfections amplitude. Computational procedures for solving the Lanczos stability problem and the geometrically nonlinear static problem by the Newton-Rafson method can be used to model imperfections. The program developed by the authors allows to form new nodal coordinates of a finite-element model of rods and to visualize geometric imperfections in a given scale. The article provides a step-by-step description of finite-element construction models of thin-walled rod of open profile with an ideal surface and taking into account the imperfection of the form, which is presented as the first form of loss of rod stability from longitudinal load applied with eccentricity. With the help of the FEMAP NASTRAN preprocessor is forming the geometry of the middle surface of an ideal rod, and setting the mechanical characteristics of the material, boundary conditions and load. The middle surface of the rod is fed as a set of flat quadrangular finite elements with six degrees of freedom in the node. In the article, a linear calculation of the stability by the Lanzosch method is performed to obtain the form of rod geometric imperfection. Setting the maximum amplitude of imperfections was performed using the program developed by the authors. Using the Newton-Rafson method, the geometrically nonlinear problem of rod statics with a given shape imperfection is solved, the critical value of the longitudinal load is determined, and the corresponding form of the rod stability loss is obtained. The presented numerical technique and the developed algorithm of computer modeling of shape imperfections allow to investigate in nonlinear formulation the stability of open profile thin-walled rods taking into account geometric imperfections of different amplitude as different forms of rod deformation, including the form of stability loss, to assess the impact of imperfections on the critical value of the load, the form of stability loss and stress-strain state. The presented algorithm and numerical technique can be used to study the stability of such thin-walled structural elements as shells, plates and others.

Multiphase-field modeling of disproportionation performance of ZrCo alloy during hydrogen absorption

This work attempts to develop a multiphase field model to study ZrCoHy, ZrH2, and ZrCo2 phase formation paths in the ZrCoH0.5 matrix. Interestingly, one conserved phase-field variable (c) and four non-conserved phase-field variables (ϕi) are utilized to construct free energy function, where c represents the hydrogen concentration and ϕi stands for the ZrCoHx, ZrCoHy, ZrH2, and ZrCo2 phase. Some valuable material parameters, such as the Gibbs formation enthalpy, are also taken into account. Importantly, the system energy fluctuation is taken as the driving force of phase evolution, and then, governing equations are solved by self-programming complied with the Fortran language. The results demonstrate that disproportionation products are most likely to be derived from the initial ZrCoHy. The presence of ZrH2 and ZrCo2 promotes the nucleation incubation of disproportionation products. Besides, ZrCoHy is more prone to generate ZrH2 and ZrCo2 in comparison with ZrCoHx, which is attributed to the fact that the crystal structure of ZrCoHy is closer to that of ZrCo2. Because ZrCoHy could be regarded as the transition state when ZrCoHx is transformed into ZrCo2, ZrCoHy is easy to be produced in advance during the ZrCoHx disproportionation process, instead of ZrH2 and ZrCo2 directly generated by the ZrCoHx disproportionation.

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes.

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance.

First-Order Logic in Finite Domains: Where Semantic Evaluation Competes with SMT Solving

In this paper, we compare two alternative mechanisms for deciding the validity of first-order formulas over finite domains supported by the mathematical model checker RISCAL: first, the original approach of semantic evaluation (based on an implementation of the denotational semantics of the RISCAL language) and, second, the later approach of SMT solving (based on satisfiability preserving translations of RISCAL formulas to SMT-LIB formulas as inputs for SMT solvers). After a short presentation of the two approaches and a discussion of their fundamental pros and cons, we quantitatively evaluate them, both by a set of artificial benchmarks and by a set of benchmarks taken from real-life applications of RISCAL; for this, we apply the state-of-the-art SMT solvers Boolector, CVC4, Yices, and Z3. Our benchmarks demonstrate that (while SMT solving generally vastly outperforms semantic evaluation), the various SMT solvers exhibit great performance differences. More important, we identify classes of formulas where semantic evaluation is able to compete with (or even outperform) satisfiability solving, outlining some room for improvements in the translation of RISCAL formulas to SMT-LIB formulas as well as in the current SMT technology.

ADAPTATION OF THE TSAI-HILL CRITERION FOR THE STUDY OF THE BEHAVIOR OF MASONRY ARCHES ADAPTATION OF THE THAI-HILL CRITERION FOR THE STUDY OF THE BEHAVIOR OF MASONRY ARCHES: COMPARISON BETWEEN MASOMODEL, EXPANDED MICROMODEL AND DETAILED MICROMODEL

Since the beginning of the structural analysis of masonry structures, it has been sought to know their behavior taking into account the influence of the different elements that make it up, evolving the structural analysis of masonry arches to analyze the fracto-mechanical behavior of the masonry. This article presents the adaptation of the Tsai-Hill failure criterion for orthotropic materials, for the study of masonry arches. Implementing the adaptation in a VUSFLD subroutine of ABAQUS in Fortran programming language. This subroutine has been validated in view of the failure of the mortar, and the effect of considering mortar in the analysis of a masonry arch. The subroutine implemented in a masomodel allows observing its contribution to the bearing capacity of an arch. Key Words: Masonry Arch; ABAQUS subroutine; failure Criterion; Mortar; structural analysis; Tsai-Hill failure criterion