THE USE OF OPENCAVOK FINITE ELEMENT SOFTWARE IN UNDERGRADUATED COURSES OF MECHANICAL ENGINEERING

Size: px

Start display at page:

Download "THE USE OF OPENCAVOK FINITE ELEMENT SOFTWARE IN UNDERGRADUATED COURSES OF MECHANICAL ENGINEERING"

Pierce Anderson
6 years ago
Views:

1 THE USE OF OPENCAVOK FINITE ELEMENT SOFTWARE IN UNDERGRADUATED COURSES OF MECHANICAL ENGINEERING Pierre Lamary Roberto de Araújo Bezerra Ranon Bezerra Department of Mechanical Engineering, Federal University of Ceará (UFC) Campus do Pici - Bloco CEP , Fortaleza, CE, Brazil Abner Guilherme Department of Metallurgical and Materials Engineering, Federal University of Ceará (UFC) Campus do Pici - Bloco CEP , Fortaleza, CE, Brazil Abstract. This paper relates our experience in the development of a free Finite Element code and its use in undergraduate courses of mechanical engineering. The code, named OpenCavok, was originally designed for research purpose as a prototype program to study variational formulations. First lines were written in the 90 s using, at that time, novel concepts, such as, object oriented paradigms, collaborative models and personal computers. A high level implementation of the finite element method was introduced which makes possible the formal solving of a large set of equations involved in mechanical engineering. The data model is consistent with any finite element code. It includes a list of materials, a finite element library, the definition of nodes meshes, elements meshes, boundary conditions and the definition of a solving scheme. The code mixes batch and interactive processes, batch files to define and run computations, and interactive processes to visualize the data model and the results. The code has only been recently introduced in our undergraduate teaching program. Four courses of mechanical engineering are concerned, namely, statics, dynamics, instrumentation and solid mechanics. After a short introduction to the finite element method, applied to the very case of each course, groups of students have to carry out a mini-project. Ideally, they are asked to compare analytical and numerical solutions. A training concerning the calculation of the deflection of beam is presented. The feedback from the students was very positive and, sighted from professors point of view, this experience of using a finite element code in undergraduate courses has fully increased the motivation of the students towards a better understating of the courses. Keywords: Educational, FEM, Programming, Mechanics Proceedings of the XXXV Iberian Latin-American Congress on Computational Methods in Engineering

The use of OpenCavok Finite Element software 1 INTRODUCTION The need for techniques to approximate functions arises for several reasons.

For a given differential equation, in which one cannot determine an exact solution, either because it can not be determined analytically or because it is mathematically out of the scope, numerical

The success of the FEM comes from the fact that the method is suitable for computer processing.

Increasingly, companies have a need for qualified professionals in the field of FEM, and familiar with the FE programs used in the professional market. The Fig. 1 and Fig.

2 The use of OpenCavok Finite Element software 1 INTRODUCTION The need for techniques to approximate functions arises for several reasons. This includes the ability to determine an approximate solution of some differential equations. For a given differential equation, in which one cannot determine an exact solution, either because it can not be determined analytically or because it is mathematically out of the scope, numerical methods are a way to approximate the solution. The main method used in engineering mechanics is the Finite Element Method (FEM). The success of the FEM comes from the fact that the method is suitable for computer processing. Computer codes has been developed and are improved every day to carry out simulations for various engineering applications. Increasingly, companies have a need for qualified professionals in the field of FEM, and familiar with the FE programs used in the professional market. The Fig. 1 and Fig. 2 present two commercial codes widely spread in the market, ANSYS from ANSYS Inc., and Inventor from AutoDesk company. Even if the commercial codes are paid, they generally offer free or low cost education issues. The principal interest of these codes is that they provide simple integrated solutions from the drawing of mechanical parts to the mechanical simulations. Many resources (books, papers, tutorials) are generally available. Stolarski et al. (2006), for instance, introduce at the same time, engineering analysis, the Finite Element Method and the use of ANSYS software. For free codes, we may cite Code ASTER. It is an outstanding professional code that offers a full range of multiphysical analysis and modelling methods. The recent book of Aubry (2013) should help the beginners Figure 1: ANSYS Figure 2: Inventor (AutoDesk) Figure 3: OpenCavok - Thermical equilibrium Figure 4: OpenCavok - Poroelastic foam OpenCavok code, on which we will focus in this document, is a free FE code developed at our department by the research group of the Laboratory of Vibrations. First lines were written in the 90 s, using, at that time, novel concepts, such as object oriented paradigms, collaborative models and personal computers. A high level implementation of the finite element method was Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering

3 Lamary, de Araújo Bezerra, Bezerra and Guilherme introduced which makes possible the formal solving of a large set of equations involved in mechanical engineering (Lamary and Chevalier, 2003). The Fig. 3 and Fig. 4 present, respectively, the solution of the Poisson s equation and the solution of the, so-called, Biot s equations, used to modelled poro-elastic materials. The following sections will present the main features of OpenCavok (its internal organization and its user interfaces) and training of students using OpenCavok. OpenCavok has been introduced in our undergraduate teaching program in MAIN FEATURES OF OPENCAVOK The Fig. 5 gives the general organisation of our software. The CAD-FEM model consists of a list of materials, a list of reference elements (bar, plate, solid, etc.) and a list of calculus. All these entities can be created using generators. The reference finite element generator allows the creation of new type of finite elements. It was used in order to create the proper reference elements for the applications presented in the classes. The materials generator is used to create new type of materials. A material is organized as a list of physical variables. An interpreter allows to write formulae using these variables. For each reference element, a corresponding material type is generally developed to ensure the compatibility of the data. The calculus generator allow the creation of entities named Meshes. A Mesh, in OpenCavok sense, includes groups of nodes, groups of elements, groups of boundary conditions for imposed unknowns, groups of boundary conditions for imposed loads and groups of solving schemes. In the calculus process, a real element, defined on the mesh, is associated to a reference element and to a material. Passing its coordinates to the reference element, as well as its material variables, the reference element will compute the elementary matrix of the real element. Doing this for all the real elements, and assembling the elementary matrices, leads to the global matrix K of the system. Next, the system KX = F is solved in order to get the values of nodal unknowns X for a given load F. In Fig. 5, the calculus is presented with a loop over the frequencies. This applies to harmonic problems. In the case of static problem, the frequency is set to zero and only one calculus step is performed. OpenCavok solves linear problems. OpenCavok offers two types of interfaces, the GUI (Graphic User Interface) which allows the visualization of the data and the BUI (Batch User Interface) which allows the creations of the data. The GUI is presented Fig. 6. The central region is devoted to mesh representation, the left region is devoted to the visualization of the data as trees, and the right region is devoted to the control of the calculus. The interface is interactive and allows an advanced exploration of the models. To create data, the user will have to select a batch file (script file) and run it. See the buttons Select and RUN in Fig. 6. The BUI is a set of OpenCavok functions accessible to the user. A text file, named batch file or script file, has to be written. It contains the list of the functions to be executed. Proceedings of the XXXV Iberian Latin-American Congress on Computational Methods in Engineering

4 The use of OpenCavok Finite Element software Figure 5: OpenCavok framework PSPad editor, see Fig. 7, is suggested to type the text because it offers syntax highlighting and because OpenCavok documentation can be associated to the text. Next, Python interpreter is internally used to run the instructions. 3 TRAINING USING OPENCAVOK In November 2013, an experiment was conducted in several classes taught by the authors, namely, statics, dynamics and instrumentation and solid mechanics, consisting in the use of numerical software during the lessons and in some homework. The software involved being i) FE codes and ii) programs as Matlab or Scilab. From our experience, these two kind of programs are essential tools for mechanical engineers and especially for research mechanical engineers. In the frame of undergraduate courses, our objectives were the following: make the students more familiar with the actual tools, establish a link between the theory and its use, illustrate some physical phenomena. To meet these objectives, the courses were reorganized with lessons where OpenCavok software was used by the professor, homework where the students (gathered in groups) had to use numerical software, and forums to exchange information between the professor and the students and also in between students. An example of homework is given in Appendix A. It concerns the Solid Mechanics course where the students were asked to find analytical beams deflection formulae from Hibbeler (2010) and compare the results to FE computation using OpenCavok. The Fig. 8 shows the results obtained by one group. Through this work, the students had concluded that the values found in the simulation were very close to the analytical solution, which makes the simulation valid. Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering

Batch User Interface sighted using PSPad editor Proceedings of the

5 Lamary, de Araújo Bezerra, Bezerra and Guilherme Figure 6: OpenCavok GUI - Graphic User Interface Figure 7: OpenCavok BUI - Batch User Interface sighted using PSPad editor Proceedings of the XXXV Iberian Latin-American Congress on Computational Methods in Engineering

The use of OpenCavok Finite Element software Figure 8: FE simulation using OpenCavok - Deflection and displacement field along z - Deflection max: 5.625 E-7 m (analytical) and 5.

6 The use of OpenCavok Finite Element software Figure 8: FE simulation using OpenCavok - Deflection and displacement field along z - Deflection max: E-7 m (analytical) and E-7 m (simulation) Concerning their interest, it was reported by the students i) that the images generated by the simulations fully help in a better understanding of phenomena, ii) that they would like to know better FE code and the FEM, ii) that the work served as a stimulus for learning programming languages. From the professors side, it was noticed a significant and positive change in the motivation of the students. Since then (2013), the use of FE tools in the classroom and for homework has always been renewed. Our resources concerning the use of OpenCavok for educational issues are made available. 4 CONCLUSION We have experienced in a very positive way the use of numerical codes in our undergraduate courses. FE codes seem very attractive for students and renew their interest for the theoretical background. OpenCavok is a free FE code developed at our University that could serve for this purpose. An interesting feature of OpenCavok is that it allows the creation of new types of Finite Element, thus, adapting itself to the very objective of each courses. ACKNOWLEDGEMENTS The authors would like to thank the French and Brazilian Ministries of Education through the CAPES-COFECUB program (project number 773/13) for supporting research involving OpenCavok. REFERENCES Aubry J.-P., 2013 Beginning with Code Aster. A Practical Introduction to Finite Element Method Using Code Aster, Gmsh and Salome ISBN: , first edition: December 2013, Framasoft. R. C. Hibbeler, Resistência dos materiais, 7 edição, Pearson Education do Brasil(2010). Original title: Mechanics of materiais, seventh edition, (2008) Pearson Education South Asia Pte Ltd. P. Lamary, Y. Chevalier, A Generator of Finite Elements for the solution of coupled problems - Organization and object oriented programming of CAVOK code. 16th French Congress of Mechanics, 2003, Nice. Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering

7 Lamary, de Araújo Bezerra, Bezerra and Guilherme Stolarski T., Nakasone Y. and Yoshimoto S., Engineering Analysis with ANSYS Software. ISBN: , Published: December 2006, ELSEVIER. APPENDIX A Instruction sheet given to students Solid Mechanics Beam deflection using Finite Elements Training Cavok Finite Elements, Cavok V602, TC Solid Beam, Trabalho de Casa, Document version 1, PL, December 17, A-1 Introduction This training aims to get familiar with the Finite Element Method. It is concerned by beams deflection. An example is provided and the training consists in modifying the example in order to compute some other typical cases of beams deflection. Computed values should be compared to known analytical solutions. This document is part of the Solid Mechanics II course taught at UFC/CT/DEM for graduation in mechanical engineering. A-2 Example A Finite Element model is constructed considering a rectangular cross sectional beam. H8WT solid elements are used. In the following example, the beam is clamped in one end and is submitted to a force load at the other end. The deflection is compared to the analytical formula, Uz = (F L 3 )/(3EI) as shown in Fig. A-1. The script is named: Solid Beam.py. Figure A-1: Displacement field along the z direction and deflection - Deflection max: 6.37 E-5 m (FE) - Deflection max: 6.4 E-5 m (Theoretical) Proceedings of the XXXV Iberian Latin-American Congress on Computational Methods in Engineering

8 The use of OpenCavok Finite Element software A-3 Training 1. Copy the previous model and change the boundary conditions in other to compute another known case. You can refer to the typical cases described at the end of Hibbeler s book [1], 2. Run Cavok and compare to the analytical formula, 3. Write a short report describing your model and the results obtained, 4. Prepare few slides for the oral presentation. A-4 Conclusion The Finite Element Method gives an interesting mean to compute, analyse and visualize fields in solid parts. A-5 Reference [1] R. C. Hibbeler. Resistência dos materiais, 7 edição, Pearson Education do Brasil(2010). Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering

Effectiveness of Element Free Galerkin Method over FEM

Effectiveness of Element Free Galerkin Method over FEM Remya C R 1, Suji P 2 1 M Tech Student, Dept. of Civil Engineering, Sri Vellappaly Natesan College of Engineering, Pallickal P O, Mavelikara, Kerala,