Analysis of mechanical structures using plate finite element method under different boundary conditions

• Autorzy: Hamrit F. , Necib B.

Identyfikatory

DOI

10.29354/diag/86257

• Języki publikacji: EN

Abstrakty

EN

The mechanical discrete or continuum structures are actually of great importance in the application field of contemporary modern industry. However, during their life time these structures are often subjected to considerable external stresses or to high amplitudes of vibrations which can cause them large deformations and internal stresses which can cause them internal cracking or even their total destruction. In order to avoid these types of problems, the concept of static and dynamic analysis of these structures is recommended, and due to the complexity of their shape and size, the finite element method is the most used. The latter is currently recognized as a very powerful technique for the static and dynamic analysis of discrete or continuous structures of complicated form applied in the field of mechanics, aeronautics, civil engineering, maritime or robotics. Consequently, the calculation and dimensioning of these mechanical systems by the finite element method plays an important role at the service of the industry for possible sizing and prediction of their lifetime. Our work consists of static and dynamic analysis of two-dimensional discrete and continuous mechanical systems using the finite element method based on the main elements of bars, beams and plates, under the effect of external excitations with different boundary conditions. The discrete structures considered are two-dimensional in metallic framework interconnected to the nodes by welding, riveting or bolted under various boundary conditions. Their elements are modeled comparatively by bar elements and beam elements, while for continuous structures the elements are rectangular thin plates with different boundary conditions. The excitation forces are based on periodic, random or impulsive forces and a numerical solution by development of a program to describe the behavior of these structures is realized. The mass and stiffness matrices of all the structures are determined respectively by assembling the bars, beam and plate elements based on the kinetic and deformation energy for each element. The displacements, the node reactions and the axial forces in all the elements as well as the transverse stresses and the eigenvalues of the structures under different boundary conditions were also calculated and good results were obtained compared to those obtained using other software already existing. In fact, analysis using the finite element method will allow the proper dimensioning and design of complex industrial mechanical structures according to different boundary conditions, their internal loading and their vibratory level.

Słowa kluczowe

EN

structures; vibration modes; finite elements; plate element; assembly; deformation energy; deformation; stress

PL

struktura; drgania; elementy skończone; element płytowy; montaż; energia deformacji; naprężenie

• Wydawca: Polskie Towarzystwo Diagnostyki Technicznej
• Czasopismo: Diagnostyka
• Rocznik: 2018
• Tom: Vol. 19, No. 2
• Strony: 3--9
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Hamrit F.

• Laboratory of Mechanics, University of Constantine 1, Algeria

autor

Necib B.

• Laboratory of Mechanics, University of Constantine 1, Algeria
• Mechanical Engineering Department, Faculty of Technology Sciences, University of Constantine 1, Algeria

Bibliografia

• 1. Fortin A, Garon A. Les éléments finis de la théorie à la pratique, cours école polytechnique de Montréal, 2011. https://moodle.polymtl.ca/pluginfile.php/357690/mod _resource/content/1/Fortin-Garon-elements-finis.pdf
• 2. El Ghazi A, El Hajji S. Guide d’utilisation du logiciel MATLAB, département mathématiques et informatique, Université Mohammed V, Maroc 2004.
• 3. Spiteri P. Présentation générale de la méthode des éléments finis. Ed. Techniques Ingénieur, 2002.
• 4. Sauer RA, Mergel JC. A geometrically exact finite beam element formulation for thin film adhesion and debonding, Finite Elements in Analysis and Design 2014;86:120-135. https://doi.org/10.1016/j.finel.2014.03.009
• 5. Alotta G, Failla G, Zingales M. Finite element method for a nonlocal Timoshenko beam model, Finite Elements in Analysis and Design 2014; 89:77-92. https://doi.org/10.1016/j.finel.2014.05.011
• 6. Ghoneim A, A mesh free interface-finite element method for modeling isothermal solutal melting and solidification in binary systems, Finite Elements in Analysis and Design 2015; 95:20-41. https://doi.org/10.1016/j.finel.2014.10.002
• 7. Kim JG, Lee JK, Yoon HJ. Free vibration analysis for shells of revolution based on p-version mixed finite element formulation, Finite Elements in Analysis and Design 2015; 95:12-19 https://doi.org/10.1016/j.finel.2014.10.006
• 8. Brighenti R, Bottoli S. A novel finite element formulation for beams with composite cross-section, International Journal of Mechanical Sciences 2014; 89:112-122. ttps://doi.org/10.1016/j.ijmecsci.2014.08.023
• 9. Donà M, Palmeri A, Lombardo M, Cicirello A. An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia, Computers and Structures 2015;147:96-106. https://doi.org/10.1016/j.compstruc.2014.10.002
• 10. Teng JG, Fernando D, Yu T. Finite element modelling of debonding failures in steel beams flexurally strengthened with CFRP laminates, Engineering Structures 2015; 86:213-224. https://doi.org/10.1016/j.engstruct.2015.01.003
• 11. Gao D Y, Machalová J, Netuk H. Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation, Nonlinear Analysis: Real World Applications 2015; 22:537-550. https://doi.org/10.1016/j.nonrwa.2014.09.012
• 12. Lalanne M, Berthier P, Der Hagobian J. Mécanique des vibrations linéaires, MASSON Edition 1995.
• 13. Yang T Y, Finite element structural analysis, Prentice-Hall, 1986.
• 14. Trompette P. Mécanique des structures par la méthode des éléments finis (Statique et dynamique), 1992.
• 15. Abdi M, Mohamed K. Numerical simulation and active vibration control of piezoelectric smart structure. International Review of Mechanical Engineering 2009; (3)2:175-181.
• 16. Zienkiewiez OC. The finite element method in engineering analysis, courses, Paris 1991. http://civil.dept.shef.ac.uk/current/module/CIV8130.pdf
• 17. Lebeid A, Necib B. Analysis and numerical modelling of ceramic piezoelectric beam, International Review of Mechanical Engineering 2011; 3:454-456.
• 18. Brie N. Mise en œuvre d'un calcul de modes propres d'une structure, cours, EDF R&D 2014. https://www.codeaster.org/V2/doc/v11/fr/man_u/u2/u2.06.01.pdf

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).