A New Three-Dimensional Sector Element for Circular Curved Structures Analysis
الموضوعات :H. E Khiouani 1 , L Belounar 2 , M Nabil Houhou 3
1 - NMISSI Laboratory, Biskra University, BP 145 Biskra 07000, Algeria
2 - NMISSI Laboratory, Biskra University, BP 145 Biskra 07000, Algeria
3 - NMISSI Laboratory, Biskra University, BP 145 Biskra 07000, Algeria
الکلمات المفتاحية: Strain approach, plane elasticity, sector element, circular structures, field displacements,
ملخص المقالة :
In this research paper, the formulation of a new three-dimensional sector element based on the strain approach is presented for plate bending problems and linear static analysis of circular structures. The proposed element has the three essential external degrees of freedom (Ur, Vθ and W) at each of the eight corner nodes. The displacements field of the present element is based on assumed functions for the different strains satisfying the compatibility equations. The effectiveness of the present element is applied through several tests related to plate bending problems and linear static analysis of circular structures. The results of the developed element have been compared with analytical and other numerical solutions available in the literature. The obtained results show the excellent performances and precision of the present element. It is found that the new three-dimensional sector element is more accurate and efficient than the three-dimensional classical element based on displacement approach.
[1] Kim Y.H., Jones R.F., Lee S.W., 1990, Study of 20-node solid element, Communication in Applied Numerical Methods in Engineering 6: 197-205.
[2] Charhabi A., 1990, Calcul des plaques minces et épaisses a' l’aide des éléments finis tridimensionnels, Annales de l’ITBTP 486: 73-91.
[3] Trinh V.D., Abed-Meraim F., Combescure A., 2011, Assumed strain solid–shell formulation ‘‘SHB6’’ for the six- node prismatic, Journal of Mechanical Science and Technology 25(9): 2345-2364.
[4] Ayad R., Zouari W., Meftah K., Ben Zineb T., Benjeddou A., 2013, Enrichment of linear hexahedral finite elements using rotations of a virtual spacefiber, International Journal for Numerical Methods in Engineering 95(1): 46-70.
[5] Belounar L., Guerraiche K., 2014, A new strain based brick element for plate bending, Alexandria Engineering Journal 53(1): 95-105.
[6] Belarbi M.T., Charif A., 1999, Développement d'un nouvel élément hexaédrique simple basé sur le modèle en déformation pour l'étude des plaques minces et épaisses, Revue Européenne des Eléments Finis 8(2): 135-157.
[7] Guerraiche K., Belounar L., Bouzidi L., 2018, A new eight nodes brick finite element based on the strain approach, Journal of Solid Mechanics 10(1): 186-199.
[8] Messai A., Belounar L., Merzouki T., 2019, Static and free vibration of plates with a strain based brick element, European Journal of Computational Mechanics 99(1): 1-21.
[9] Dastjerdi Sh., Jabbarzadeh M., 2016, Nonlocal bending analysis of bilayer annular/circular nano plates based on first order shear deformation theory, Journal of Solid Mechanics 8(3): 645-661.
[10] Dastjerdi Sh., Jabbarzadeh M., Tahani M., 2015, Nonlinear bending analysis of sector graphene sheet embedded in elastic matrix based on nonlocal continuum mechanics, International Journal of Engineering Transactions B: Applications 28(5): 802-811.
[11] Dastjerdi Sh., Akgöz B., 2018, New static and dynamic analyses of macro and nano FGM plates using exact three-dimensional elasticity in thermal environment, Composite Structures 192: 626-641.
[12] Belarbi M. T., Charif A., 1998, Nouvel élément secteur basé sur le modèle de déformation avec rotation dans le plan, Revue Européenne de Eléments Finis 7(4): 439-458.
[13] Rebiai C., Belounar L., 2013, A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis, Archive of Civil and Mechanical Engineering 13(1): 72-81.
[14] Belounar L., Guenfoud M., 2005, A new rectangular finite element based on the strain approach for plate bending, Thin-Walled Structures 43(1): 47-63.
[15] Himeur M., Benmarce A., Guenfoud M., 2014, A new finite element based on the strain approach with transverse shear effect, Structural Engineering and Mechanic 49(6): 793-810.
[16] Rebiai C., Belounar L., 2014, An effective quadrilateral membrane finite element for plate bending analysis, Measurement 50: 263-269.
[17] Belounar A., Benmebarek S., Belounar L., 2018, Strain based triangular finite element for plate bending analysis, Mechanics of Advanced Materials and Structures 2018: 1-13.
[18] Sabir A.B., Salhi H.Y.,1986, A strain based finite element for general plane elasticity in polar coordinates, Res Mechanica 19(1): 1-16.
[19] Bouzriba A., Bouzerira C., 2015, Sector element for analysis of thick cylinders exposed to internal pressure and change of temperature, Gradevinar 67(6): 547-555.
[20] Raju I.S., Rao A.K., 1969, Stiffness matrices for sector elements, AIAA Journal 7(1): 156-157.
[21] Olson M.D., Lindberg G. M., 1970, Annular and circular sector finite element for plate bending, IJMS 12: 17-33.
[22] Timoshenko S., Woinowsky-Krieger S., 1959, Theory of Plates and Shells, London, McGraw-Hill.
[23] Choi N., 2006, A hybrid Trefftz plane elasticity element with drilling degrees of freedom, Computer Methods in Applied Mechanics Engineering 195(1): 4095-4105.
[24] Timoshenko S., Goodier J.N., 1951, Theory of Elasticity, McGraw-Hill New York.
