Статті в журналах: "Finite element method Computer programs"

1

Agapov, Vladimir P., and Alexey S. Markovich. "Dynamic method for determining critical loads in the PRINS computer program." Structural Mechanics of Engineering Constructions and Buildings 16, no. 5 (December 15, 2020): 380–89. http://dx.doi.org/10.22363/1815-5235-2020-16-5-380-389.

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Relevance. Buckling analysis is important in the design of buildings and structures. It is used in various fields of engineering - mechanical engineering, aircraft and shipbuilding, civil engineering, etc. Until the second half of the twentieth century, mainly analytical methods of buckling were applied in practice. With the appearance of computers, numerical methods, in particular, the finite element analysis, began to prevail. Buckling analysis was implemented in programs of finite element analysis, such as NASTRAN, ANSYS, ABAQUS, ADAMS, DIANA, and others. In view of great responsibility, buckling analysis of structure should be carried out using at least two different programs. However, due to the high cost of software products, not all project organizations are able to have a number of programs. An alternative is to develop programs that can complete buckling analysis using several methods. This would increase the reliability and quality of calculation results. The PRINS computer program has opportunity for buckling analysis using two methods - static and dynamic. The aims of the work - to show the theoretical aspects and practical implementation of the dynamic principle of buckling analysis in buildings and structures using finite element method, as well as to give the algorithm implemented in the PRINS program and the results of verification calculations confirming its reliability. Results. The algorithm presented in this article and implemented in the PRINS computer program allows to determine critical loads using a dynamic buckling criterion. On the basis of numerous verification calculations, it was established that the implemented algorithm was effective for determining critical loads in frame, thin-walled and ribbed plate structures. The use of the PRINS computer program enables to use an alternative method for determining critical loads for a wide class of engineering problems in addition to the classical (static) method.

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Mufti, A. A., G. Tadros, and A. C. Agarwal. "On the use of finite element programs in structural evaluation and development of design charts." Canadian Journal of Civil Engineering 21, no. 5 (October 1, 1994): 797–804. http://dx.doi.org/10.1139/l94-086.

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In many phases of structural design and analytical evaluation, the solution of stress and strain distribution in an elastic continuum is required. Special cases of such problems may range from two-dimensional plane stress or plain strain distribution, plate bending to analysis of fully three-dimensional solids. The finite element programs are often used to predict the critical regions for stress analysis and design. Stresses are generally of greater practical importance than displacements for structural design and evaluation. Most of the finite element computer programs calculate element stresses at the centroids, integration points, or nodes of elements. In this paper, examples of bridge deck analysis are used to illustrate the stress interpretation using the finite element programs. It is demonstrated that the stresses at nodes calculated by some finite element programs violate the equilibrium conditions and do not converge to the correct answers. These calculated stresses at nodes are usually too low and lead to unsafe designs and evaluations. Key words: finite element method, finite element programs, structural analysis, least square smoothing, stress interpolation.

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Maslennikov, A. M., E. A. Kobelev, and N. A. Maslennikov. "Solution of sustainability tasks by finite element method." Вестник гражданских инженеров 17, no. 2 (2020): 68–74. http://dx.doi.org/10.23968/1999-5571-2020-17-2-68-74.

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New functions are proposed to describe the deformed state of rods upon loss of stability for two types of rods with different boundary conditions. To solve stability problems with a kinematic uncertainty number of more than two, it is recommended to reduce solution to a characteristic equation with the further use of computer programs with matrix operations. For this purpose, a stiffness matrix and potential loading matrix were developed for the adopted functions. Following the example of classical displacement method for the mentioned rods, there was developed a table of reactions for single displacements. Several examples are given that illustrate fairly close results to the exact solutions.

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4

Tin, Trinh Van. "The motion equation of turbine blade by the finite element method." Vietnam Journal of Mechanics 15, no. 4 (December 31, 1997): 42–48. http://dx.doi.org/10.15625/0866-7136/10219.

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In this paper, the finite element method has been applied to deriving the motion equation of turbine blade in coupled bending - bending - torsion vibrations. These equations permit us to develop straightforwardly digital computer programs for studying vibration problems of turbine blades in turbo machinery as well as in other structural dynamic applications.

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5

Marufiy, A., and E. Rysbekova. "Specific Design Solution for Covering Large Areas With Spatial Metal Truss." Bulletin of Science and Practice 7, no. 12 (December 15, 2021): 160–68. http://dx.doi.org/10.33619/2414-2948/73/22.

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. The relevance of the research results given in the article lies in the need to apply new constructive solutions for large spaces. The purpose of this work is to search for new design solutions for covering large areas with spatial metal trusses. The problems of forming a computational spatial bar finite element model of a steel spatial truss of a dome-shaped radial-ring structure were solved. The calculation of the spatial system was carried out using the finite element method of current computer programs, new constructive solutions for spatial metal trusses were adopted. The stress-strain states of the model from a given load have been determined. The calculation of the spatial system was carried out using the finite element method of current computer programs, new constructive solutions for spatial metal trusses were adopted. The research results can be used in the formation of architectural and structural solutions of a building using a new structural arrangement of the elements of a spatial truss.

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6

Serrette, R. L. "An introduction to the finite element method using basic programs." Mechanism and Machine Theory 27, no. 6 (November 1992): 751. http://dx.doi.org/10.1016/0094-114x(92)90073-q.

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7

Kosasih, P. B. "Learning Finite Element Methods by Building Applications." International Journal of Mechanical Engineering Education 38, no. 2 (April 2010): 167–84. http://dx.doi.org/10.7227/ijmee.38.2.7.

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This paper describes how programming projects are used to help students understand the theory of finite element (FE) methods in the author's class. The implementation of FE theory in FE-based commercial software is made clearer through programming simple FE analysis codes. From the experience gained in the coding, students have a better understanding of the theory and numerical processes used in FE commercial software. As a result, they have more confidence in using commercial software, knowing that the computer programs are not simply ‘black boxes’ that process data and produce colourful results. More importantly, they understand the limitations of the programs, how to use them correctly and interpret the generated output correctly. Two projects are described in which students develop codes and then compare the results with those from commercial software.

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Choporov, S. V., M. S. Ihnatchenko, O. V. Kudin, A. G. Kryvokhata, and S. I. Homeniuk. "IMPLEMENTATION OF A FINITE ELEMENT CLASS LIBRARY USING GENERALIZED PROGRAMMING." Radio Electronics, Computer Science, Control, no. 2 (July 10, 2021): 164–73. http://dx.doi.org/10.15588/1607-3274-2021-2-17.

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Context. For computer modeling of complex objects and phenomena of various nature, in practice, the numerical finite element method is often used. Its software implementation (especially for the study of new classes of problems) is a rather laborious process. The high cost of software development makes the development of new approaches to improving the efficiency of programming and maintenance (including the addition of new functions) urgent. Objective. The aim of the work is to create a new effective architecture of programs for finite element analysis of problems in mathematical physics, which makes it easy to expand their functionality to solve new classes of problems. Method. A method for developing programs for finite element analysis using generalized programming is proposed, which makes it possible to significantly simplify the architecture of the software and make it more convenient for maintenance and modification by separating algorithms and data structures. A new architecture of classes that implement finite element calculation is proposed, which makes it possible to easily expand the functionality of programs by adding new types of finite elements, methods for solving systems of linear algebraic equations, parallel computations, etc. Results. The proposed approach was implemented in software as a class library in C ++. A number of computational experiments have been carried out, which have confirmed its efficiency in solving practical problems. Conclusions. The developed approach can be used both to create general-purpose finite element analysis systems with an open architecture, and to implement specialized software packages focused on solving specific classes of problems (fracture mechanics, elastomers, contact interaction, etc.).

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Verbovoy, A. Y., M. L. Sieryk, I. V. Pavlenko, and A. A. Rudenko. "CALCULATION OF THE CENTRIFULAL PUMP CRITICAL FREQUENCIES BASED ON ITS DISCRETE MATHEMATICAL MODEL." Journal of Numerical and Applied Mathematics, no. 1 (135) (2021): 43–52. http://dx.doi.org/10.17721/2706-9699.2021.1.05.

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Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.

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PLENGKHOM, K., and W. KANOK-NUKULCHAI. "AN ENHANCEMENT OF FINITE ELEMENT METHOD WITH MOVING KRIGING SHAPE FUNCTIONS." International Journal of Computational Methods 02, no. 04 (December 2005): 451–75. http://dx.doi.org/10.1142/s0219876205000594.

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This paper presents an enhancement of the finite element method (FEM) by adopting the moving Kriging (MK) interpolation as a substitute for the traditional hat functions. The MK shape functions can be referred as element-free because their construction is not tied to the element geometry. Kriging interpolation is a geostatistical technique for spatial interpolation. The basic idea of Kriging is that any unknown point can be interpolated from known scatter points in a specific domain. Using the moving Kriging interpolation, shape functions can be generated over any finite set of nodes. This leads to an idea to extend the influence of a node beyond the layer of surrounding elements to enhance the global smoothness of the field variable and its derivatives. The present paper thus proposes a concept of layered domain of influence. Hence, characteristic arrays of an element, such as the element stiffness, have contributions from all visible nodes that include a set of satellite nodes unattached to the element. The validation of the method was confirmed through numerical tests of one and two-dimensional problems. The results show remarkable accuracy and global smoothness. Existing general-purposed FE programs can be easily modified to accommodate this new element concept; thus, the method has a higher chance to be accepted in practice.

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Plesha, Michael E. "An illustrative computer program for instruction in the finite element method." Computers & Education 10, no. 3 (January 1986): 353–58. http://dx.doi.org/10.1016/0360-1315(86)90005-9.

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Nazaruddin, N., and Richard Siallagan. "Software Engineering Development of Finite Element Method Programming Applications in 2D Frame Structures Using Python Programs." Journal of Physics: Conference Series 2049, no. 1 (October 1, 2021): 012031. http://dx.doi.org/10.1088/1742-6596/2049/1/012031.

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Abstract The application of the Finite Element Method as one of the numerical methods to solve various engineering problems is of course inseparable from the development of computers with various other related fields such as Computer Aided Design (CAD) and Computer Aided Engineering (CAE) which continuously becomes a concentration of interest in the engineering field. Element analysis has so far been in great demand by various industries due to its reliability and speed in terms of optimization in the world of design and analysis. There are many finite element software such as Abaqus, Nastran, Ansys, CosmosWork, LS-Dyna, Pro-Mecanica, SAP2000. However, the application is paid at a relatively high cost and has quite strict licensing rules, of course this is an obstacle for students at the University of Riau who want to use it. From these problems the author is interested in developing a programming application that can be an alternative to analyzing a structure. The solution that the author can propose is to develop an application using the python programming language to analyze a two-dimensional (2D) frame structure that is under load and is in an elastic condition. From the results of the research that has been carried out, the simulation results of the frame A model obtained data on the 2nd frame model of frame A, the horizontal displacement of -0.06098 m, the vertical displacement of -0.00002857 m, and the angular displacement of 0.00762 rad. These results are compared with manual solutions, analytical solutions, and previous research, it can be concluded that the results of calculations in the developed application show values that are close to that comparison, where the percentage error is not more than 3%, with the highest percentage difference of 2.5%.

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13

Cai, Song Bai, Da Zhi Li, Chang Wan Kim, and Pu Sheng Shen. "A Simple Numerical Solution Procedure for Equations of Nonlinear Finite Element Method." Advanced Materials Research 889-890 (February 2014): 187–90. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.187.

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The conventional solution strategy for nonlinear FEM of structural analysis is usually based on Newton-Raphson iteration under an additional constraint equation. So far a lot of nonlinear finite element solution procedures have been devised to provide the basis for most nonlinear finite element computer programs. In order to produce effective, robust solution algorithms, additional constraint equations for nonlinear FEM calculations in the load-displacement space of has been extensively investigated for the last a few decades. However, it is widely believed that due to the additional computations in the controlling of steps and directions of the iteration procedure, there will be more round-off errors accumulated to influence the convergence of solution. In this work, a more simplified solution procedure is presented, which is featured to be with neither iterations nor constraints. A Fortran computer program of the algorithm presented has been implemented in combining with a space truss element of co-rotational procedure. Verification of the procedure has been done by numerical example and a good result achieved.

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Светличный, С. П. "ОГЛЯД МОЖЛИВОСТЕЙ СІТКОВОГО ПРЕПРОЦЕСОРА ANSYS MESHING ДЛЯ СТВОРЕННЯ ВИСОКОЯКІСНИХ СКІНЧЕННО-ЕЛЕМЕНТНИХ СІТОК". Open Information and Computer Integrated Technologies, № 95 (26 жовтня 2022): 83–113. http://dx.doi.org/10.32620/oikit.2022.95.07.

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The finite element method is one of the most widely used numerical methods for solving problems of solid mechanics, heat transfer, hydrodynamics and electrodynamics. It refers to approximate methods for solving partial differential equations, as well as integral equations that arise in solving applied problems of mechanics. One of the steps of the method’s implementation is discretization: the process of replacing a real physical object with its discrete model, consisting of a set of elements of a certain geometric shape and finite sizes. As a result of this transition, a reduction in the overall dimension of the problem being solved is achieved, which makes it possible to practically implement this method on a computer in the form of a package of applied programs. One of the strategic issues of the method under consideration is the accuracy of the resulting solution, which depends on the degree of discretization of the computational model. Building a finite element mesh is one of the most time-consuming steps and its effectiveness is largely determined by the methods used to build the mesh and, of course, the practical experience of the user with a particular calculation program. The issue of creating a high-quality and economical finite element mesh is a key issue in solving resource-intensive problems of solid mechanics and computational fluid dynamics in conditions of limited computing resources. The quality of the created mesh largely determines the outcome of the computer simulation process and affects the accuracy of the resulting solution, its stability and convergence, as well as the required computing resources and time costs. The article provides an overview of the methods for constructing finite element meshes implemented in the ANSYS Workbench system, describes individual functions that improve the quality of the mesh, as well as reduce the dimension of the finite element model. The capabilities of the Mesh Metric tool used to assess the quality of the mesh are described and practical recommendations for its use are given. A number of practical examples show that the use of methods that make it possible to create finite element meshes containing predominantly hexahedral elements makes it possible to increase individual metric data that determine the quality of the mesh and reduce the model dimension.

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15

Truong, Thien Tich, and Bang Kim Tran. "APPLICATION OF QUARTER-POINT SINGULAR ELEMENT IN FINITE ELEMENT METHOD TO SIMULATION OF CRACK TIP BEHAVIOR." Science and Technology Development Journal 13, no. 2 (June 30, 2010): 5–13. http://dx.doi.org/10.32508/stdj.v13i2.2113.

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Fracture mechanics is a new branch in engineering. The development of modern mathematical background with different numerical methods has supported fracture mechanics to solve many complex fracture problems in practice effectively. This article introduces the application of quarter - point singular element in finite element method to simulate crack tip behavior in two dimensional problems. The ANSYS and FRANC2D programs are used to compute stress intensity factor, simulate the stress and displacement fields near crack tip and simulate crack propagation. The calculation results are compared with analytical results and the results in other articles.

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PHAN-DAO, H. H., H. NGUYEN-XUAN, C. THAI-HOANG, T. NGUYEN-THOI, and T. RABCZUK. "AN EDGE-BASED SMOOTHED FINITE ELEMENT METHOD FOR ANALYSIS OF LAMINATED COMPOSITE PLATES." International Journal of Computational Methods 10, no. 01 (February 2013): 1340005. http://dx.doi.org/10.1142/s0219876213400057.

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This paper promotes a novel numerical approach to static, free vibration and buckling analyses of laminated composite plates by an edge-based smoothed finite method (ES-FEM). In the present ES-FEM formulation, the system stiffness matrix is established by using the strain smoothing technique over the smoothing domains associated with the edges of the triangular elements. A discrete shear gap (DSG3) technique without shear locking is combined into the ES-FEM to give a so-called edge-based smoothed discrete shear gap method (ES-DSG3) for analysis of laminated composite plates. The present method uses only linear interpolations and its implementation into finite element programs is quite simple. Numerical results for analysis of laminated composite plates show that the ES-DSG3 performs quite well compared to several other published approaches in the literature.

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Pandelea, Alexandrina Elena, Mihai Budescu, Lucian Soveja, and Maria Solonaru. "Determination of Internal Forces Using Artificial Neural Networks." Advanced Engineering Forum 21 (March 2017): 151–57. http://dx.doi.org/10.4028/www.scientific.net/aef.21.151.

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Design and verification of engineering structures require knowing the numerical values of sectional internal forces as close to reality, considering that the intervention construction works are correlated with these values.Most of the computer programs are working with finite element method, which was designed by engineers and founded by mathematicians. After running the computer program, stresses and deformations maps are generated as results.Considering these results, using artificial neural networks, a computer program has been designed, which is able to determine internal forces of a section, namely axial force, shear force and bending moment.Neural network input parameters consist of color maps resulted from numerical modeling, numerical values of the normal and tangential tensions and dimensions of the structural element.This procedure is particularly useful when using finite element programs that do not have the ability to determine sectional internal forces.

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18

Dahlblom, Ola, Anders Peterson, and Hans Petersson. "CALFEM — a program for computer‐aided learning of the finite element method." Engineering Computations 3, no. 2 (February 1986): 155–60. http://dx.doi.org/10.1108/eb023653.

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Song, Weidong, H. P. Tang, and X. N. Mao. "Finite element analysis on hot deformation behavior of TiC-particle-reinforced titanium matrix composite." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 6 (July 29, 2014): 1301–11. http://dx.doi.org/10.1108/hff-03-2013-0097.

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Purpose – The purpose of this paper is to investigate tensile properties of TiC particle-reinforced titanium matrix composites (PRTMC) using the elasto-plastic finite element (FE) programs and the homogenization method and the fixed point iteration method. Design/methodology/approach – Two quasi-static and dynamic transient programs of elasto-plastic FE were coded by using FORTRAN. Based on the FE programs, the FE model of the TiC PRTMC with typical microstructures was established by using the fixed point iteration method and the homogenization theory. The hot deformation behavior of TiC PRTMC under different temperatures were analyzed by using the above model and programs. Findings – Calculation results are presented to investigate the influence of different temperatures on the hot deformation behavior of TiC PRTMC. Based on the experimental data, a good agreement was obtained between the numerical predictions and the experimental results, and the feasibility of this method was verified. Originality/value – The work is original and findings are new, which demonstrates this FE frame combined with the homogenization method and the fixed point iteration method can be used to investigate the tensile behavior of particle-reinforced metal matrix composites.

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20

Owerko, Piotr. "The stochastic finite element method in the assessment of bridge infrastructure objects - review." E3S Web of Conferences 45 (2018): 00062. http://dx.doi.org/10.1051/e3sconf/20184500062.

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The stochastic finite element method (SFEM) is an extension of classical FEM which allows the representation of various types and sources of uncertainty in one computational system. This review paper presents information regarding SFEM implementation in the assessment of bridge objects. A concise theoretical background of the three most commonly used branches of SFEM is also presented. This technique is used in the assessment of bridge structures with regards to, e.g. load in motion problems, wind and seismic excitation analysis, random material property analysis, reliability and fatigue reliability analysis. However, it seems that the main feasibility concern is the lack of proper SFEM implementation into general purpose FEM systems which are used by bridge engineers. This is why, arguably, one of the most effective ways to introduce SFEM in real-life bridge engineering problems is with the methods that rely on multiple calculations of classical deterministic FEM e.g. Monte Carlo Simulation, or Response Function Method. To introduce randomness directly into individual finite elements of the model in a complete SFEM procedure it is usually necessary to develop proprietary computer programs.

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21

Niering, E. "Simulation of Bird Strikes on Turbine Engines." Journal of Engineering for Gas Turbines and Power 112, no. 4 (October 1, 1990): 573–78. http://dx.doi.org/10.1115/1.2906207.

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External components of aeroengines, such as casings and intake blades, must be capable of withstanding bird strikes. Various methods of computer simulation that have been developed are presented in summary. The most accurate and meaningful results are obtained with finite element programs specifically developed for impact events. Bird and component are divided into finite elements. The component model must allow for great elastic-plastic deformation, where the yield strength is a function of the strain rate. A model shape and a homogeneous substitute material must be defined for the complicated and nonhomogeneous structure of the bird. Bird strikes on a rotating spinner and an intake blade are investigated with the finite element program DYNA3D.

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Agapov, Vladimir P., and Kurban R. Aidemirov. "Designing of the blades of aircraft propellers by the finite element method, taking into account the strength of structure." RUDN Journal of Engineering Researches 22, no. 1 (August 27, 2021): 65–71. http://dx.doi.org/10.22363/2312-8143-2021-22-1-65-71.

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The blades of contemporary turboprop engines have a complex spatial configuration. They can be classified as shells. Methods for the shells calculation are well known. A number of computer programs have been created on their basis. However, these programs do not take into account the peculiarities associated with the mutual influence of deformations of the blade and the aerodynamic and inertial loads acting on it. The aim of this work is to develop a method of finite element calculation of aircraft propeller blades taking into account aeroelastic effects and to create a computer program on its basis that is available to a wide range of designers and engineers. The finite element method is used in a geometrically nonlinear formulation. As the initial one, the equilibrium equation is used, which includes a complete nonlinear stiffness matrix and takes into account both conservative and non-conservative loads. The blade of one of the serial propellers was calculated. The effect of deformations on the magnitude of the aerodynamic load and, as a result, on the stresses in the design sections was found and analyzed. The proposed technique and the program compiled on its basis can be used in the design of aircraft propeller blades.

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Davids, William G., George M. Turkiyyah, and Joe P. Mahoney. "EverFE: Rigid Pavement Three-Dimensional Finite Element Analysis Tool." Transportation Research Record: Journal of the Transportation Research Board 1629, no. 1 (January 1998): 41–49. http://dx.doi.org/10.3141/1629-06.

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The interactive and computational features of EverFE, a new rigid pavement three-dimensional (3D) finite element (FE) analysis tool, are presented. To date, the use of 3D FE analysis has been hampered by (a) the difficulty of model generation and result interpretation, (b) the inability of many programs to adequately model joint shear transfer due to aggregate interlock and dowel action, and (c) the large computational requirements of conventional solution techniques employed by available programs. The development of EverFE is motivated by the desire to make 3D FE analysis feasible for routine analysis of rigid pavements. The intuitive graphical user interface employed by EverFE, which greatly simplifies model generation and result interpretation, is demonstrated using a sample problem. A novel technique for modeling aggregate interlock joint shear transfer that rationally incorporates nonlinearities is developed and presented, as is a new method for modeling dowel joint shear transfer. The solution strategy employed by EverFE that allows realistic 3D models to be simulated on desktop computers is briefly described, and its performance is presented.

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Read, D. T., and G. K. Lucey. "Automated Finite-Element Mesh Generation for Surface Mount Technology Solder Joints." Journal of Electronic Packaging 113, no. 2 (June 1, 1991): 178–85. http://dx.doi.org/10.1115/1.2905384.

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The ultimate goal of this work is an improved method to assess the significance of anomalies in surface mount technology (SMT) solder joints, by relating them to field performance and reliability. The fitness-for-purpose approach can be applied to SMT solder joints by relating specific characteristics or flaw indications in individual solder joints to their likelihood of failure, through finite element analysis. An effort is underway to automate the finite element modeling of actual solder joints by generating meshes from optical and X-ray inspection data in the form of thousands of surface points. Computer programs have been written to convert these surface points to finite element meshes. Two trial data sets have been meshed, one from an X-ray laminography system and one from a machine vision system.

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25

D’yachenko, D. Yu, A. A. Vorob’ev, Iu A. Makedonova, О. N. Kurkina, S. V. D’yachenko, O. Yu Afanas’eva, and S. A. Vargina. "Analysis of the lower jaw exoskeleton in finite element programs." Medical alphabet, no. 24 (September 26, 2021): 88–92. http://dx.doi.org/10.33667/2078-5631-2021-24-88-92.

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A special place in the methods of surgical treatment of bone fractures is occupied by transosseous osteosynthesis using external fixation devices of various designs.Objective: to analyze the lower jaw exoskeleton in finite element programs.Materials and research methods. During the research, 36 human lower jaws were involved from the museum of the Department of Oper-ative Surgery and Topographic Anatomy of the Volgograd State Medical University. They were scanned in 3D. All obtained images were loaded into a virtual scene reconstruction program. Fractures of the lower jaws in the corner area were modeled, an apparatus for external fixation of the lower jaw exoskeleton was installed, and the chewing load on the lower jaw was simulated. The place of application of the force was an area on a small fragment of a repositioned 3D model of the mandibular bone corresponding to the place of attachment of the masseter muscle. The evaluation of virtual studies was carried out according to the results of the stress-strain states of the bones and apparatus, the schedule of displacements of objects and the results of the analysis of the safety factor.Research results and discussion. In the course of evaluating the virtual placement of the mini-fixator wires of the apparatus for external fixation of the lower jaw exoskeleton, it was revealed that the main load is applied to the mini-fixator wires on a large fragment and the bone in the area of the wires. For the possibility of precise positioning of the osteofixers of the external fixation device, a device for the safe installation of the spokes of the lower jaw exoskeleton was also developed.Conclusion. Thus, on the basis of computer mathematical analysis, it can be argued that the developed design of the apparatus for external fixation of the lower jaw exoskeleton works under conditions of the maxillofacial region, performs reposition and fixation of bone fragments of the lower jaw under conditions of chewing functioning of the restored fracture of the lower jaw.

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Matsievskiy, S. V., V. I. Kaminskii, A. A. Gorchakov, M. V. Lalayan, M. A. Gusarova, and N. P. Sobenin. "Linaccalc: software for accelerating structure characteristics simulation based on equivalent circuit method." Cybernetics and Physics, Volume 10, 2021, Number 1 (June 30, 2021): 22–26. http://dx.doi.org/10.35470/2226-4116-2021-10-1-22-26.

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Nowadays design of accelerating structures is almost exclusively done using 2.5D and 3D codes based on finite elements method. Equivalent circuit method is frequently considered limited and inconvenient to use in real-life projects. However, low resource requirements make this method attractive for wide range sweep calculations.This paper describes LinacCalc application — a user friendly accelerating structure simulation software based on the equivalent circuit method. It allows calculating characteristics of the accelerating sections with large number of cells in short time on machines with moderate amount of computational power. Core application modules are validated by comparing calculation results with ones obtained by a conventional finite element method based programs.

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27

Sun, Pengtao, Su Zhou, Qiya Hu, and Guoping Liang. "Numerical Study of a 3D Two-Phase PEM Fuel Cell Model Via a Novel Automated Finite Element/Finite Volume Program Generator." Communications in Computational Physics 11, no. 1 (January 2012): 65–98. http://dx.doi.org/10.4208/cicp.051010.180311a.

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AbstractNumerical methods of a 3D multiphysics, two-phase transport model of proton exchange membrane fuel cell (PEMFC) is studied in this paper. Due to the coexistence of multiphase regions, the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC [49,50]. By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach, we efficiently achieve a fast convergence and reasonable solutions for this multiphase, multiphysics PEMFC model. Numerical implementation is done by using a novel automated finite element/finite volume program generator (FEPG). By virtue of a high-level algorithm description language (script), component programming and human intelligence technologies, FEPG can quickly generate finite element/finite volume source code for PEMFC simulation. Thus, one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods. Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D, multiphysics PEMFC model with multicomponent and multiphase mechanism.

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28

Padmaja, R., R. Ravinder Rao, B. Kotiveerachari, and P. B. Godbole. "Comparative Evaluation of Finite Element Models and Types of Analyses for a Bolted Joint." Journal of Mechanical Design 127, no. 6 (February 9, 2005): 1207–10. http://dx.doi.org/10.1115/1.2118647.

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The present work is aimed at evaluating different ways in which a given joint can be analyzed using the Finite Element Method. The bolt is modeled using line elements (link) or area elements (continuum) and a comparative evaluation is carried out. Each of these types is further subdivided into three categories viz., plane stress, axisymmetric, and three-dimensional models. Thus a total of six models are proposed to be analyzed and compared. As the bolt shares only a small fraction of external load in a well-tightened joint, the relative flexibility of a bracket is also studied as an example in the present work. Comparing the results of these analyses it was found that the type of model used for the bolt is more important than the type of analysis. This aspect is probed further to find the essential difference between bolt as link and bolt as continuum. The analysis is carried out using ANSYS, which enables writing many parametric programs.

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29

Faflei, О. Ya, V. V. Mykhailiuk, R. V. Rachkevych, R. О. Deynega, А. І. Riznychuk, and R. S. Kravchuk. "Features of the study of threaded joints using the finite element method." Scientific Bulletin of Ivano-Frankivsk National Technical University of Oil and Gas, no. 1(50) (September 7, 2021): 62–69. http://dx.doi.org/10.31471/1993-9965-2021-1(50)-62-69.

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A significant number of computer programs exist today for various engineering calculations, research and development of equipment elements. The SolidWorks software has become widespread for such work, which allows you to minimize time, facilitate the performance of the necessary work, as well as analyze the strength, stiffness, stability and endurance of products of a wide range of complexity and purpose. The program uses the finite element method, which has both a number of advantages and certain disadvantages. To investigate the possibilities of such a program, a model of a threaded connection of sucker rods has been built. Simulation of make-up torque for threaded connections remains problematic when modeling in SolidWorks Simulation. There are several ways to simulate the make-up moment during the study of the stress-strain state of threaded connections. To solve problems in an axisymmetric setting, the optimal method is to overlap the ends of the nipple and coupling by the required amount. The use of an axisymmetric model in the process of simulation does not impair the results obtained in comparison with 3D models. But it speeds up the calculation process, allows you to build a fine mesh of finite elements and get more accurate results. The paper presents an algorithm for calculating the tension of the threaded connections of sucker rods, which can be applied to threaded connections of drill string elements with some adjustments. The only difference will be in the formula for determining the make-up moment, from which the value of the pre-tightening force and the areas of dangerous sections are derived. Also, in the work, a simulation study was carried out using the selected method using the example of a threaded connection of sucker rods with a diameter of 19 mm. A diagram of displacements and distribution of equivalent stresses in a threaded connection was obtained and the possibility of determining specific parameters at certain points of the model under study was shown with subsequent automated construction of their graphical dependencies.

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30

Marek, Pavel, Milan Gušntar, Mauricio Sanchez-Silva, and Michal Micka. "Comments on the Development of SBRA method considering application of Finite Elements Method and corresponding computer programs." IABSE Symposium Report 92, no. 6 (January 1, 2006): 1–7. http://dx.doi.org/10.2749/222137806796185418.

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31

Tamayo, Jorge Luis Palomino, Armando Miguel Awruch, and Inácio Benvegnu Morsch. "Numerical modeling of reinforced concrete structures: static and dynamic analysis." Rem: Revista Escola de Minas 66, no. 4 (December 2013): 425–30. http://dx.doi.org/10.1590/s0370-44672013000400004.

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A numerical model using the Finite Element Method (FEM) for the nonlinear static and dynamic analysis of reinforced concrete (RC) beams, plates and shells is presented in this work. For this purpose, computer programs based on plasticity theory and with crack monitoring capabilities are developed. The static analysis of RC shells up to failure load is carried out using 9-node degenerated shell finite elements while 20-node brick finite elements are used for dynamic applications. The elasto-plastic constitutive law for concrete is coupled with a strain-rate sensitive model in order to take into account high loading rate effect when transient loading is intended. The implicit Newmark scheme with predictor and corrector phases is used for time integration of the nonlinear system of equations. In both cases, the steel reinforcement is considered to be smeared and represented by membrane finite elements. Various benchmark examples are solved with the present numerical model and comparisons with other published data are performed. For all examples, the path failure, collapse loads and failure mechanism is reproduced with great accuracy.

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32

Walton, D., and S. Prayoonrat. "A computerised design aid for drive shafts with some fatigue considerations." Journal of Strain Analysis for Engineering Design 21, no. 2 (April 1, 1986): 85–98. http://dx.doi.org/10.1243/03093247v212085.

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A method of designing power transmission drive shafts is described based on two interactive computer programs. The first program can model shafts of any configuration and under any system of loads and supports. The program is based on the finite element method. Reducing the size of the stiffness matrix by storing only the parameters in the matrix bandwidth and by overlaying the stiffness matrices, the problem of using finite element analysis on small memory microcomputers can be solved. A menu allows the designer to specify machine elements, such as spur or bevel gears or pulleys, to be positioned at any point along the shaft. The user can give information of the power transmitted, speed, and details of the physical dimensions of the machine elements which then enables the program to determine the force vectors and apply these to the shaft nodes. The second program determines the design factors of safety on the basis of both static and cyclic loads. For cyclic loads the factors of safety are based on infinite-life design, using Soderberg and Goodman criteria. The program contains extensive built-in data on endurance strengths, factors influencing the endurance limit, and stress concentration factors.

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Dirr, B. O., and B. K. Schmalhorst. "Crack Depth Analysis of a Rotating Shaft by Vibration Measurement." Journal of Vibration and Acoustics 110, no. 2 (April 1, 1988): 158–64. http://dx.doi.org/10.1115/1.3269493.

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The increasing development of measurement techniques for monitoring rotor plants requires improved possibilities for the interpretation of vibration response. Therefore, computer programs that have been used will have to be constantly updated. This especially concerns the modelling of a rotor for calculation purposes. This paper deals with a propagating crack that causes the slender uniform round shaft to vibrate about its main axis. Experiments using a stationary shaft are also performed. Beach marks are used to measure the crack depth and the actual shape of the cracked cross section. These results are compared with those obtained using the dc-potential method, applied to the same cracked cross-section. A finite element model for the cracked region of the rotor is then deduced from the experimental results. Three-dimensional 20-node elements are applied, so a single edge crack of the rotor can be described and varying forms of the cross section—as shown by the beach marks—can be modelled. The additional installation of nonlinear truss elements to the finite element structure permits the breathing of the cracked rotor to be calculated.

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34

OLARU, IONEL. "SOFTWARE INTEGRATION TYPE CAD-CAM-CAE IN PRODUCT LIFECYCLE MANAGEMENT." Journal of Engineering Studies and Research 28, no. 2 (September 1, 2022): 57–61. http://dx.doi.org/10.29081/jesr.v28i2.006.

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Abstract: Using the CAD-CAM-CAE type programs, case studies can be carried out to analyze some industrial tasks that may occur in the realization, manufacture, and operation of certain industrial components, before they are manufactured and put into operation under normal conditions. operation. Computer programs that perform a virtual modeling and an analysis of them based on the finite element method, help reduce launch and production times, control, and review of industrial products, before making the physical model. All this information resulting from simulations with specialized programs will be analyzed in detail, and the design team within the company can take the right measures to improve the final product.

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35

Kotova, K. S., and G. S. Slavcheva. "Foam Concrete and Composite Fittings Cohesion Parameters: Experimental Result and Numerical Simulation." Materials Science Forum 992 (May 2020): 836–42. http://dx.doi.org/10.4028/www.scientific.net/msf.992.836.

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The article presents the computer simulation results and real experiment of foam concrete cohesion with glass-composite, basalt-composite and metal fittings in bending elements. Numerical simulation of beams implemented with software package “Lira-SAPR 2013” using finite element method for modeling. For real experiment used bending beam test method according to ISO 10406-1:2015. As a result, the influence of the loading level and foam concrete density on the reinforcement slipping value and foam concrete cohesive strength with reinforcement in the bending elements. The foam concrete cohesive strength with glass-composite fittings meets the standard requirements, so it can be recommended for the foam concrete bending elements reinforcement. Verification of the computer simulation results with the real experiment data allowed to establish the efficiency of the used numerical model and revealed the need to use the cohesion parameters in the "foam concrete – reinforcement" system for foam concrete structures calculations in specialized programs.

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36

Li, Hong, Guang Lei Li, and Da Lu Qiu. "Analysis of Stress Concentration for Curvilinear Holes by Complex Variable Function Method." Advanced Materials Research 314-316 (August 2011): 1052–55. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1052.

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A solving method with complex variable function which is fit for numerical calculation for stress concentration phenomena on an infinite plate where there are curvilinear holes is described in this paper. According to the method, the computer programs are made to study the stress concentration problems with curvilinear holes (hexagonal form and oblate form) that are often used in ship and other engineering structures. The maximum of the stresses at the edge of the holes and the distribution of the stresses under axial loading and pure bending moment are calculated respectively. Furthermore, the variations of factors of stress concentration with the different proportions of length and width for oblate holes are considered. The influence on factors of stress concentration due to the change of plate width is indicated. The solutions are consistent with the numerical results of boundary element method, finite element method and related articles.

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37

Palyvoda, Roman, Vladyslav Malanchuk, Mykola Kryschuk, and Oksana Volovar. "THREE-DIMENSIONAL COMPUTER MODELLING AND STRESS-STRAIN ANALYSIS OF TEMPOROMANDIBULAR JOINT." EUREKA: Health Sciences 2 (March 31, 2016): 11–17. http://dx.doi.org/10.21303/2504-5679.2016.00088.

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The main purpose of the study is to build 3D model of temporomandibular joint and mandible using programs for modelling and design, research stress and strain in cartilage and bone of model depending on different contraction of chewing muscles (especially lateral pterygoid muscle). There were used such methods as computer tomography data, finite element method and analysis topography of lateral pterygoid muscle on cadavers. In results of study was obtained maximal stress in anterior and distal parts of articular disc between 1,4–3 MPa and 0,4–1 MPa. Thus, static loads of articular disc were different, depends on force of contraction lateral pterygoid muscle. Muscle disturbances (hyperfunctioning, atrophy etc.) should be considered in treatment of temporomandibular dysfunction and examined on magnetic resonance investigation if it is present in the same patient.

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38

Hussin, A. A. M., P. Hartley, C. E. N. Sturgess, and G. W. Rowe. "Non-linear finite-element analyis on microcomputers for metal forging." Journal of Strain Analysis for Engineering Design 21, no. 4 (October 1, 1986): 197–203. http://dx.doi.org/10.1243/03093247v214197.

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In recent years microcomputers have become more powerful and for some purposes are now able to compete with minis and mainframe computers. It is now possible to implement a wide variety of CAD packages and linear finite-element stress analysis programmes on microcomputers, but the solution of non-linear problems - for example, forging - is more complex. This paper shows that a microcomputer can, nevertheless, be used for the analysis of a bulk metal forming process where there are both geometric and material non-linearities. The programs give reliable estimates of metal flow, grid distortions, stress, and strain distributions in the workpiece, as well as the forming force. An elastic-plastic finite-element method is used, with SSS-Fortran as the computing language. The results of such simulations can be used in-house to form the basis of improved forging die design, and, hence, a better final product, without the need for much of the expensive and time-consuming experimental trials currently practiced in industry.

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39

Zhang, Jia Wei, Zhi Guo Yang, Ya Ping Wu, Shi Jun Zhou, and Jian Chang Zhao. "Finite Element Analysis for Effect of Initial Load on Dynamic Characteristic of Beams." Advanced Materials Research 368-373 (October 2011): 2031–40. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.2031.

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Based on nonlinear elastic theory and Hamilton’s principle, a generalized element stiffness matrix, which incorporates the effects of flexural as well as axial stresses induced by initial load, is given. A finite element method for dynamic analysis considering the effect of initial load is presented, with corresponding computer programs produced to facilitate the analysis. The formula is validated through a comparison in results with the analytical solution. The effects of key physical factors, including the type and magnitude of initial load, and stiffness parameters such as sectional inertia moment, inertia radius and span, on the dynamic characteristics of the beams with various restraint conditions are discussed with the effect of initial flexural stress considered. The results suggest that the natural frequency of the beam would be enhanced due to the existence of flexural stress induced by initial load and such as effect relates to the magnitude of initial load and stiffness parameters of the beam.

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40

LI, Shuting. "Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear." Journal of Mechanical Design 124, no. 3 (August 6, 2002): 511–17. http://dx.doi.org/10.1115/1.1485290.

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This paper performs loaded tooth contact analysis of a three-dimensional, thin-rimmed gear (3DTRG) by presenting a method that combines the mathematical programming method with the three-dimensional, finite element method (3DFEM). Also, a face-contact and whole gear deformation model is used for the 3DTRG. 3DFEM programs for the contact analysis and strength calculation of the 3DTRG are developed successfully in a personal computer. By using this program, 3D tooth load distributions, tooth root strains and the tooth contact pattern of the 3DTRG are obtained. Calculation results are proved to be correct by experiments.

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41

Manea, Marius Costin, Damian Timofte, and Stefan Velicu. "Prediction of Forces and Damage at Forming Sheet on Multipoint Die." Applied Mechanics and Materials 656 (October 2014): 215–22. http://dx.doi.org/10.4028/www.scientific.net/amm.656.215.

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This paper presents aspects of a simulation based on multi-point die optimization sheet metal deformation using for types of materials: titanium grade 1, aluminium 2024, carbon steel 1010 and 1137. Due to processing methods of the sheet metal appeared, multi-point deformation is a very interesting process industry. For the finite element simulation of sheets metal using multi-point die was chosen Deform 3D software. Simulations were performed for four types of materials used in the construction industry. With the development of computer software, specialized programs appeared on the market forming process simulation, for determining the stresses and strains of the deformed material, the distribution of temperature field, how the material is flowing, the final form of the product, etc. Modeling and numerical simulation of deformation processes can be viewed at any time of their deployment, which allows rethinking solutions for problems arising in the process. Also by this method of finite element simulation can be optimized in the design engineering processes and tools.

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42

Au-Yang, M. K. "Dynamics of Coupled Fluid-Shells." Journal of Vibration and Acoustics 108, no. 3 (July 1, 1986): 339–47. http://dx.doi.org/10.1115/1.3269348.

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The hydrodynamic mass approach to the solution of dynamic problems in coupled fluid-cylindrical shells is reviewed; simplified equations for computing the hydrodynamic masses and for the subsequent solution of the eigenvalue problem are given in several commonly encountered special cases. Methods of incorporating the hydrodynamic mass concept into finite element structural analysis computer programs for the more general cases are discussed.

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43

Mahammed, Isam M. "Evaluation of Method of Line (MOL) for Solution of Soil Water Flow Equations and Comparison with Finite Element Method (FEM)." Tikrit Journal of Engineering Sciences 19, no. 1 (March 31, 2012): 44–53. http://dx.doi.org/10.25130/tjes.19.1.13.

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The objective of this research is to evaluate Method of Line (MOL) used for solution of water flow equations through porous media using MATLAB package functions for solution of ordinary differential equations ODE,s , instead of writing long programs codes. sink & source term to MOL model were included. Then Comparing MOL model with another model that uses finite element method in solving water flow equations(FEM) in one dimensional flow using computer program code in FORTRAN. Two cases were examined for evaluation and comparison of these two models. Firstly, infiltration phenomena using sandy soil was studied with the same parameter for both models. Results show that there is a divergence between the two models along time of 60 minutes of infiltration. Changes of moisture content with soil depth were sharp with FEM model. Second case, data of the volume of water content for wheat field where used taking irrigation and evaporation into account, along the growth period of wheat crop and different depths up to 100 cm. Results show that output of FEM model has high degree of agreement with the measured data for all depths and along all period of growth. Data given by MOL model were less in values than measured data for all depths and along all period of wheat growth time.

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44

Wintersberger, E., D. Kriegner, N. Hrauda, J. Stangl, and G. Bauer. "Algorithms for the calculation of X-ray diffraction patterns from finite element data." Journal of Applied Crystallography 43, no. 6 (October 1, 2010): 1287–99. http://dx.doi.org/10.1107/s0021889810032802.

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A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

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45

Azarnejad, A., and T. M. Hrudey. "A numerical study of thermal ice loads on structures." Canadian Journal of Civil Engineering 25, no. 3 (June 1, 1998): 557–68. http://dx.doi.org/10.1139/l97-119.

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A numerical model is presented for the prediction of the three-dimensional stress field in an ice sheet due to temperature changes, as a function of time, under a variety of conditions. The model relies on two separate computer programs for the thermal and mechanical aspects of the problem. The thermal program uses the finite difference method to calculate the temperature distribution through the thickness of the ice cover under a variety of meteorological input conditions. The mechanical part of the analysis is conducted using the finite element method. A degenerate shell element is used, which is capable of modeling both bending and membrane behaviors of the ice cover. Relevant features of the finite element model include variable temperature and properties through the thickness, an elastic foundation representation of the underlying water, nonlinear constitutive behavior of the ice, temperature-dependent mechanical properties, flexibility of resisting structures, and boundary conditions representing a variety of shoreline types. Results are presented from simulations conducted during verification of the model. Included are simulations of uniaxial and biaxial laboratory tests on the thermal expansion of ice as well as three thermal events for which field data were available. Conclusions are presented concerning the analytical prediction of thermal ice forces.Key words: ice loads, thermal loads, ice mechanics, hydraulic structures, dams.

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46

Wiryadi, I. Gede Gegiranang. "3-DIMENTIONAL MODELING OF CYLINDRICAL CONCRETE UNDER AXIAL COMPRESSION WITH VARIATIONS OF MESH ELEMENT TECHNIC AND EFFECT OF REDUCED INTEGRATION." Jurnal Ilmiah Teknik Sipil 25, no. 1 (January 29, 2021): 49. http://dx.doi.org/10.24843/jits.2021.v25.i01.p06.

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Research with numerical methods using computer programs has increased in recent years in various fields including the field of structural materials. However, this numerical analysis still needs to be developed in terms of modeling techniques in order to get the results according to the real condition. In this paper, modeling of concrete-cylinder with numerically method using a finite element based computer program, Abaqus®, presented.. Modeling technique to inventigate the mesh element technique and the reduced integration on hourglass control. Modeling specimen is in the form of cylindrical concrete measuring 150 mm x 300 mm with a quality of 25 MPa. Concrete plastic behavior is modeled with the concrete damage plasticity (CDP) feature. The results of the analysis show that the reduction-integration of hourglass control gives a lower peak load effect when the material passes the elastic limit. Meanwhile, a better mesh technique is to use 8-noded hexahedral because it is more stable and the reduction-integration effect of hourglass control can work.

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47

Naito, Yoshitaka, Ryuji Kawamura, Yukio Tokuno, and Shin-Ichiro Tsuruta. "A computer program for solving the three-dimensional multigroup diffusion equation by finite element method with 20-node isoparametric element (FEM3DJAR)." Progress in Nuclear Energy 18, no. 1-2 (January 1986): 207–14. http://dx.doi.org/10.1016/0149-1970(86)90027-2.

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48

Bathe, Klaus-Ju¨rgen. "Fluid-structure Interactions." Mechanical Engineering 120, no. 04 (April 1, 1998): 66–68. http://dx.doi.org/10.1115/1.1998-apr-4.

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This article reviews finite element methods that are widely used in the analysis of solids and structures, and they provide great benefits in product design. In fact, with today’s highly competitive design and manufacturing markets, it is nearly impossible to ignore the advances that have been made in the computer analysis of structures without losing an edge in innovation and productivity. Various commercial finite-element programs are widely used and have proven to be indispensable in designing safer, more economical products. Applications of acoustic-fluid/structure interactions are found whenever the fluid can be modeled to be inviscid and to undergo only relatively small particle motions. The interplay between finite-element modeling and analysis with the recognition and understanding of new physical phenomena will advance the understanding of physical processes. This will lead to increasingly better simulations. Based on current technology and realistic expectations of further hardware and software developments, a tremendous future for fluid–structure interaction applications lies ahead.

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49

Bai, Xin Li, Gui Rong Liu, and Song An Zhang. "Optimal Design of a Scroll Case with Natural Frequency Constraints." Applied Mechanics and Materials 94-96 (September 2011): 1719–22. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1719.

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In this paper, sensitivity formula with analytical method is derived for calculating structural natural frequency, and the partial derivative of plate element stiffness matrix and mass matrix with respect to design variables are gained respectively. Computer programs for computing frequency sensitivity with analytical method are developed. And combining it with large finite element structural analysis software ADINA, the optimal design software based on genetic algorithms, a structural dynamic optimization program system is constituted for computing structural natural frequency sensitivity with analytical method. Finally, the program system is applied to the optimal design of a turbine scroll case of a hydropower station (taking into account the natural frequency constraints). Calculation results show that analytical method presented in the paper is of higher computational precision, good stability, convenient to use, and can be popularized. Calculation results obtained the approval of client and used in real engineering.

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SUÁREZ, BENJAMIacute;N, ELENA BLANCO, LLUÍS GIL, PERE ZAPATA, and EUGENIO OÑATE. "ED-Elas2D: An Educational Program for Computer-aided Training in Structural Analysis Using the Finite Element Method." European Journal of Engineering Education 23, no. 2 (June 1998): 243–54. http://dx.doi.org/10.1080/03043799808923502.

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