FORTRAN Research Articles

Dynamic Response of Offshore Wind Turbine on 3×3 Barge Array Floating Platform under Extreme Sea Conditions

Offshore wind farm construction is nowadays state of the art in the wind power generation technology. However, deep water areas with huge amount of wind energy require innovative floating platforms to arrange and install wind turbines in order to harness wind energy and generate electricity. The conventional floating offshore wind turbine system is typically in the state of force imbalance due to the unique sway characteristics caused by the unfixed foundation and the high center of gravity of the platform. Therefore, a floating wind farm for 3×3 barge array platforms with shared mooring system is presented here to increase stability for floating platform. The NREL 5 MW wind turbine and ITI Energy barge reference model is taken as a basis for this work. Furthermore, the unsteady aerodynamic load solution model of the floating wind turbine is established considering the tip loss, hub loss and dynamic stall correction based on the blade element momentum (BEM) theory. The second development of AQWA is realized by FORTRAN programming language, and aerodynamic — hydrodynamic — Mooring coupled dynamics model is established to realize the algorithm solution of the model. Finally, the 6 degrees of freedom (DOF) dynamic response of single barge platform and barge array under extreme sea condition considering the coupling effect of wind and wave were observed and investigated in detail. The research results validate the feasibility of establishing barge array floating wind farm, and provide theoretical basis for further research on new floating wind farm.

Probabilistic fatigue life prediction of metallic components based on continuum damage mechanics

Based on continuum damage mechanics, a probabilistic method of predicting high-cycle fatigue life for metallic components is proposed. First, macro-meso two-scale stress-strain equations are established by combining Eshelby-Kroner localization law and classic elastic-plastic constitutive equation. Second, some parameters in Lemaitre's fatigue damage evolution model are randomized. Probabilistic properties of which are obtained by inverse-analysis and optimization. Then, the probabilistic method of predicting high-cycle fatigue life is established by coupling the model with macro-meso two-scale equations. And the proposed algorithm is coded with Fortran language, which is non-intrusive post-program of FEM analysis. Next, constant amplitude fatigue test of Al 2024-T3 coupon is performed to determine probabilistic properties of model parameters. Finally, as the object of study, wallboard is analyzed by FEM. Taking skin-strip component as research object, the fatigue life of hot spot is predicted by proposed method. The corresponding fatigue test of the component is performed, which verifies the effectiveness of proposed method to predict probabilistic life of metallic components.

Modified spectral format based on probability level using site-specific uniform hazard spectrum

Deficiencies of the four spectral formats i.e., 2%/50-yr, 5%/50-yr, 10%/50-yr and AASHTO (American Association of State Highway Officials) 2009 demand modification of the spectral formats for bridge design application in Canada. Among them the 10%/50-yr spectrum is dropped from current investigation as its difference with Canadian Highway Bridge Design Code (CHBDC) 2006 is too large to modify. This study introduces an approach calibrating on the values of elastic seismic response coefficient to provide a new shape of the Canadian bridge design spectrum based on modified 2%/50-yr, modified 5%/50-yr and modified AASHTO spectral formats. A Digital Visual Fortran program was prepared to determine the optimum values of the modification factors incorporated into the three spectral formats calibrated on the data of 389 cities of Canada. Thus, here it is developed the strategies of modifying the three spectral formats based on the best probability level for CHBDC using site-specific Uniform Hazard Spectrum (UHS). Finally, select the most suitable spectral format to apply for the design base shear calculations for the bridges of Canada.

Study on sealing performance of bolted flange structure after creep based on ABAQUS

In this paper, a finite element analysis model is established based on ABAQUS software and DN600 bolted flange connection structure is the research object. The elastic-plastic constitutive relation is adopted for the flange and bolt materials, and the user subroutine of Creep is written in Fortran language according to the creep constitutive equations. Each component can meet the requirements of strength and seal evaluation, and it is found that after creep, the seal stress of gasket decreases significantly, and the stress increases almost linearly from the inside to the outside of the gasket. After cooling and heating, the stress is redistributed. The residual pre-tightening force of bolt is increased, and the flange deflection angle is slowed down, which improves the sealing performance. The study of gasket sealing performance in this paper has a positive guiding significance for preventing leakage accidents.

Numerical simulation of periodic MHD casson nanofluid flow through porous stretching sheet

The perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, Pr ≥ 0.447 indicates the value of Prandtl number and Le ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.

The impact of drilling and slitting construction on damage field: evolution characteristics in low-permeability coal seam

ABSTRACT The fracture field of coal and rock mass is the main channel for gas migration and accumulation. Exploring the evolution law of fracture field of coal and rock mass under the condition of drilling and slitting construction has important theoretical significance for guiding efficient gas drainage. The generation and evolution process of coal and rock fissures is also the development and accumulation process of its damage. Therefore, based on damage mechanics and finite element theory, the mathematical model is established. The damage variable of coal mass is defined by effective strain, the elastoplastic damage constitutive equation is established and the secondary development of finite element program is completed by FORTRAN language. Using this program, the numerical simulation of drilling and slitting construction of the 15-14120 mining face of Pingdingshan No. 8 Mine is carried out, and the effects of different single borehole diameters, different kerf widths and different kerf heights on the distribution area of surrounding coal fracture field and the degree of damage are studied quantitatively. These provide a theoretical basis for the reasonable determination of the slitting and drilling arrangement parameters at the engineering site.

Characterisation of B type hydraulic jump by experimental simulation and numerical modeling using MacCormack technique

A hydraulic jump occurs when the supercritical flow transforms into subcritical nature along with the dissipation of energy. It occurs on a variety of horizontal and inclined channels. In this study, two types of jumps were classified, namely the B types that occur partially in the sloping and partially in the horizontal level of plane sections and the plane types that are typical hydraulic jumps occurring on beds with continuous slopes or horizontal beds. Froude numbers at inlet ranged from 2 to 6 for the study and tests were performed at four different angles for B-type jumps. The profiles of the jumps and streamwise flow velocities at different sections of the jumps were determined. From these data, the nature of the rate of decay of stream wise velocity across the jumps was established for both B and plane jumps. To validate the experimental results, numerical simulation was done for both B and plane jumps using the de-Saint Venant hyperbolic equations as governing equations and an explicit scheme MacCormack technique for the second-order accuracy of time and space. A source code was written in Fortran language using the G-Fortran compiler to numerically determine post-jump profiles. Using the appropriate initial boundary conditions, accurate simulated profiles of the jumps were obtained by it. The numerically simulated jump profiles were compared with experimentally obtained jump profiles in current and previous research studies and were found to be consistent. Based on the accuracy achieved, a combined empirical relation was proposed to determine jump profiles that operate both plane and B jumps.

Application of Direct Integration Methods in the solution of a nonlinear beam problem

This work applies different numerical methods involved in the solution of a nonlinear clamped beam problem. The methodology used in the discretization of the dynamic problem is based on the Finite Element Method (FEM), followed by mode superposition, where a localized nonlinearity is applied at the free end of the beam. The solution of the nonlinear problem is performed by five different integration methods. The solution code is implemented in FORTRAN language, validated with ANSYS and the dynamic response and the graphs are obtained with the help of MATLAB software. The work shows the convergence of the implemented methods with various validation problems.

Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method

The finite element method (FEM) is a widely used technique in research, including but not restricted to the growth of cracks in engineering applications. However, failure to use fine meshes poses problems in modeling the singular stress field around the crack tip in the singular element region. This work aims at using the original source code program by Visual FORTRAN language to predict the crack propagation and fatigue lifetime using the adaptive dens mesh finite element method. This developed program involves the adaptive mesh generator according to the advancing front method as well as both the pre-processing and post-processing for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip is characterized by the stress intensity factor associated with the rate of crack growth. The quarter-point singular elements are constructed around the crack tip to accurately represent the singularity of this region. Under linear elastic fracture mechanics (LEFM) with an assumption in various configurations, the Paris law model was employed to evaluate mixed-mode fatigue life for two specimens under constant amplitude loading. The framework includes a progressive analysis of the stress intensity factors (SIFs), the direction of crack growth, and the estimation of fatigue life. The results of the analysis are consistent with other experimental and numerical studies in the literature for the prediction of the fatigue crack growth trajectories as well as the calculation of stress intensity factors.

Numerical analysis of fretting wear in lateral contact of sphere/sphere

The fretting wear characteristics of spherical/spherical lateral contacts under different load conditions, contact angles, and the number of fretting cycles are studied. A spherical/spherical lateral fretting wear model is established in ABAQUS software. A UMESHMOTION subroutine for spherical/spherical contact models is written to simulate the fretting wear based on the energy model and the Fortran language. The results show that as the load increases, the contact width increases significantly and the wear depth decreases. It is also found that the rate of change of the wear depth gradually increases in the central portion of the contact area, and is relatively smooth in the contact edge portion. An increase in the magnitude of the moving load causes a small increase in the contact width and a significant increase in the wear depth. The rate of increase of the wear depth at the edge of the contact area gradually increases and the rate of increase of the wear depth at the center of the contact area changes linearly. As the contact angle increases, the contact form gradually changes to a positive contact. Meanwhile, the wear depth variation shifted from a “U” shape to a “W” shape, which caused the wear depth to decrease significantly at the contact center and eventually approach zero as the adhesive area appeared. In addition, with an increase in the number of fretting cycles, the wear depth was almost unchanged at the contact center portion but significantly increased at the edge portion.

Experimental and simulation study of solidification of commercial pure aluminium by sand casting

This paper presents an experimental and numerical study of the solidification process of commercial pure Aluminum to estimate the shrinkage defects. The numerical solution has been carried out using a program written in a FORTRAN language by adopting the explicit finite difference method using [3-D] transient heat conduction differential equation. Several factors were taken into consideration in this system, such as solidification parameters. The model was built up to calculate the solidification parameters: gradient temperature and solidus time. After the simulation of a specified sample, solidification parameters were calculated. This is done to show the variations in solidification parameters along the mid surface for each casting were drawn using MATLAB. The shrinkage cavities have been predicted from the results of calculating the solidus time. The form of a closed-loop within the solidus time contours was taken because of the criterion for this kind of shrinkage. By comparison, between the sliced samples and simulated diagram, the simulation program showed a good ability of cavity prediction of location and extension. Also, the program developed to give a good response to the cooling direction and variation which was confirmed by adding a copper chill in the casting mold of one sample.

STUDY ON DAMAGE CONSTITUTIVE MODEL OF RECYCLED AGGREGATE CONCRETE IN CODE FOR DESIGN OF CONCRETE STRUCTURES AND DEVELOPMENT IN ABAQUS

Based on the damage constitutive of ordinary concrete in code for Design of Concrete Structures and considering the similarity of mechanical properties between recycled aggregate concrete and ordinary concrete, a uniaxial damage constitutive of recycled concrete was proposed. At the same time, the above model was programmed as a subroutine by FORTRAN language, and the subroutine was embedded into finite element analysis software ABAQUS to simulate and analyze the uniaxial compression mechanical properties of recycled concrete. The results of finite element simulation and test are compared from the aspects of stress-strain curve and damage evolution curve. The results show that the proposed elastic-plastic damage constitutive model can effectively represent the mechanical properties of recycled aggregate concrete under uniaxial compression at different substitution rates.

Research and application of numerical simulation of ship maneuvering under non-uniform wind

Taking Fortran language as the platform, a depth-integrated two-dimensional non-uniform flow mathematical model and a ship maneuvering mathematical model were developed from the bottom layer. By further coupling the influence of wind, the mathematical model of ship maneuvering motion based on wind and current effects was constructed. Taking a typical river section in the Three Gorges Reservoir area as an example, the numerical simulation of ship maneuvering motion under still wind and non-uniform wind effect was carried out. Results show that the ships are obviously affected by wind in this river section. With the increasing change frequency of wind speed and direction, the difficulty of ship control increases correspondingly. In order to avoid the average accident, the ship must change its steer in time accordingly. This model can simulate the ship maneuvering motion and navigation status under wind effect quite well, which can provide some references for the ship’s navigation and maneuvering in inland rivers.

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

In this article, we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes. The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high. We can obtain sparse matrices by applying compact schemes. In this article, we compare compact and exponential finite difference schemes of fourth order. The numerical solutions are calculated in quadruple precision (Real * 16 or extended precision) in FORTRAN language, and iteratively obtained until reaching the round-off error magnitude around 1.0E −32. This procedure is performed to ensure that there is no iteration error. The Repeated Richardson Extrapolation (RRE) method combines numerical solutions in different grids, determining higher orders of accuracy. The main contribution of this work is based on a process that initializes with fourth order solutions combining with RRE in order to find solutions of sixth, eighth, and tenth order of precision. The multigrid Full Approximation Scheme (FAS) is also applied to accelerate the convergence and obtain the numerical solutions on the fine grids.

A fast spectral conjugate gradient method for solving nonlinear optimization problems

<span>This paper proposes a new spectral conjugate gradient (SCG) approach for solving unregulated nonlinear optimization problems. Our approach proposes Using Wolfe's rapid line scan to adjust the standard conjugate descent (CD) algorithm. A new spectral parameter is a mixture of new gradient and old search path. The path provided by the modified method provides a path of descent for the solution of objective functions. The updated method fits the traditional CD method if the line check is correct. The stability and global convergence properties of the current new SCG are technically obtained from applying certain well-known and recent mild assumptions. We test our approach with eight recently published CD and SCG methods on 55 optimization research issues from the CUTE library. The suggested and all other algorithms included in our experimental research were implemented in FORTRAN language with double precision arithmetic and all experiments were conducted on a PC with 8 GB ram Processor Intel Core i7. The results indicate that our proposed solution outperforms recently reported algorithms by processing and performing fewer iterations in a shorter time.</span>

Hamiltonian Monte Carlo method for estimating variance components.

A Hamiltonian Monte Carlo algorithm is a Markov chain Monte Carlo method, and the method has a potential to improve estimating parameters effectively. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamilton's equations, which are expressed as two differential equations. In the sampling process of Hamiltonian Monte Carlo, a numerical integration method called leapfrog integration is used to approximately solve Hamilton's equations, and the integration is required to set the number of discrete time steps and the integration stepsize. These two parameters require some amount of tuning and calibration for effective sampling. In this study, we applied the Hamiltonian Monte Carlo method to animal breeding data and identified the optimal tunings of leapfrog integration for normal and inverse chi-square distributions. Then, using real pig data, we revealed the properties of the Hamiltonian Monte Carlo method with the optimal tuning by applying models including variance explained by pedigree information or genomic information. Compared with the Gibbs sampling method, the Hamiltonian Monte Carlo method had superior performance in both models. We have provided the source codes of this method written in the Fortran language at https://github.com/A-ARAKAWA/HMC.

A Designed System for Providing Solutions to BasicEngineering Problems

Engineering and the manner in which engineers think is largely visual and functional, and yet engineers are typically provided with a lot of other basic engineering problems to be solved and applied to complex ones. This paper present a designed software for providing solutions to some basic engineering problems. C++ programming language was used in writing the codes. The paper explains the activities involved in C++program development and touched areas such as the general concept of programming, programming languages, compilation and interpretation, storage and execution, functional lines to which computer programs maybe categorized. Several engineering problems and their various real-world applications were considered to accomplish the aim of the work. The problem requirements were properly understood, and the program adequately developed using the Dev-C++ software. The program was coded in a modular fashion, and constructed in a manner that can be fairly understood. Algorithms and flow charts for the basic engineering problems considered were obtained and using formula translation, solutions to such issues were dynamically programmed using the Dev C++ software. The results from the developed software when compared with other methods such as numerical and approximate analytical solutions were observed to be the same. The developed software is however, more user friendly and can be implemented at A Level Higher Institutions, as well as have many other real-world applications.

Development of the smoothed particle hydrodynamics (SPH) method for modeling movement of fluid layer interaction between impermeable soil layers with boundary conditions sloping surface

Liquefaction usually occurs on a saturated sand deposit when the pore water pressure increases during the earthquake, and the water level will rise that could even burst out above the liquefied layer. If there is a relatively impermeable soil layer above the liquefied one, then the water could be trapped between the liquefied soil and other layers on the top. This research tries to develop a numerical model to simulate the phenomenon using the Smoothed Particle Hydrodynamics (SPH) method. SPH is a numerical method based on particle interactions that initially developed to solve the problems in astrophysics. Two sets of particles are assigned to behave like water and impermeable soil, where the thin layer of water is placed between two layers of soil. The model is built using the Fortran programming language developed in the previous research to simulate the impermeable layer’s behavior by controlling the stiffness coefficient and coefficient of damping. The soil and water layers are aligned at specific angles to simulate the field’s sloping surface condition. The simulation results are presented in graphical animation using Gnuplot and visually checked that the particle’s movement could represent the field’s actual movements.

Influence of Trapezoidal Shapes and Cutout Sizes on the Buckling Behaviour of Composite Laminates Under Thermally Induced Loads

Trapezoidal laminated plates with cutouts are commonly found in many engineering field, especially in aerospace structures. In many cases these plates are subjected to various harsh environmental conditions during its service life. Thermally induced load is the one which seriously affect the buckling characteristics of the structural components. The study presents the effect of rise in temperature on the thermal buckling characteristics of trapezoidal laminated composite plates with and without cutouts by using finite element technique. In order to model the plate, a 9-noded heterosis plate element has been used by incorporating the effect of shear deformation. By correlating present findings with the available literature, the effectiveness of the present formulation is verified. The computer program FORTRAN language has been developed to investigate the effect of different parameters such as trapezoidal shapes, cutout offsets, plate aspect ratio, ply-orientations, different thickness and plate edge conditions. The influence of each parameter on the thermal buckling behavior is well investigated through this work.

Non-isothermal Bingham fluid flow between two horizontal parallel plates with Ion-slip and Hall currents

This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.