A Discrete Layer Finite Element Model for Cylindrical Shells
Abstract
This paper presents a new discrete layer finite element to model thin as well as moderately thick orthotropic and laminated composite cylindrical shells. The element formulation is based on the first order shear deformation theory of shells. The twenty degrees of freedom plane stress element is modeled with inplane displacements defined at the interfaces of the element layers in addition to the, through the thickness, radial displacement. A field consistency approach is implemented to insure that the element is free from locking due to membrane tangential, membrane shear and transverse shear strains. The field consistency approach used eliminates the inconsistent terms from the original displacement shape functions that correspond to the targeted strains. The new element is validated through a series of benchmark problems and has shown accurate and fast converging results.References
Hrennikoff A, Tezcan SS. Analysis of cylindrical shells by the finite element method. Symposium on Problems of Interdependence of Design and Construction of Large-Spam Shells for Industrial and Civic Buildings 6-9 September1966, Leningrad, USSR.
Zienkiewicz OC, Cheung YK. Plate and shell problems, finite element displacement approach. International Symposium on the Use of Electrical Digital Computers in Structural Engineering July 1966, Newcastle, UK.
Bogner FK, Fox RL, Schmit LA. A cylindrical shell discrete element. AIAA Journal 1967; 5 : 745-750.
Connor JJ, Brebbia C. Stiffness matrix for shallow shell rectangular shell element. Proceedings of the American Society of Civil Engineers, Journal of Engineering Mechanics 1967; 93: 43-65.
Ahmad S, Irons BM, Zienkiewicz OC. Analysis of thick and thin shell structures by curved finite elements. International Journal for Numerical Methods in Engineering 1970; 2:419–451.
Ausserer MF and Lee SW. An eighteen node solid element for thin shell analysis. International Journal for Numerical Methods in Engineering 1988; 26, 1345-1364.
Ashwell DG and Sabir AB. A new cylindrical shell finite element based on simple independent strain functions. International Journal for Mechanical Sciences 1972; 14: 171-183
Djoudi MS and Bahai H. A cylindrical strain-based shell element for vibration analysis of shell structures. Finite Elements in Analysis and Design in 2004; 40:1947 -1961.
MacNeal RH. Derivation of element stiffness matrices by assumed strain distributions. Journal of Nuclear Engineering Design 1982; 70:3-12.
Dvorkin EN, Bathe KJ. A continuum mechanics based four-node shell element for general non-linear analysis. Engineering Computations 1984; 1:77-88.
Simo JC, Rifai S. A class of mixed assumed strain methods and the method of incompatible models. International Journal for Numerical Methods in Engineering 1990; 29:1595-1638.
Belytschko T, Leviathan I. Physical stabilization of the 4-node shell element with one point quadrature. Computer Methods in Applied Mechanics and Engineering 1994; 113:321-350.
Zienkiewicz OC, Taylor RL, Too JM. Reduced integration techniques in general analysis of plates and shells. International Journal for Numerical Methods in Engineering 1979; 3:275-290.
Stolarski H, Belytschko T. Membrane locking and reduced integration for curved elements. Journal of Applied Mechanics 1982; 49:172-176.
Kim KD, Lomboy GR, Voyiadjis GZ. A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom. International Journal for Numerical Methods in Engineering 2003; 58: 2177-2200.
Carrera E, Brischetto S. Analysis of thickness locking in classical, refined and mixed theories for layered shells. Composite Structures 2008; 85: 83–90.
Prathap G. A C0 continuous four-noded cylindrical shell element. Computers and Structures 1985; 21: 995-999.
Mohr GA. Numerically integrated triangular element for doubly curved thin shells. Computers and Structures 1980; 11: 565-571.
Mohr GA. A doubly curved isoparametric triangular shell element. Computers and Structures 1981; 14: 9-13.
Mohr GA. Application of penalty factors to a doubly curved quadratic shell element. Computers and Structures 1981; 14: 15-19.
Koziey BL, Mirza FA. Consistent thick shell element. Computers and Structures 1997; 65:531-549.
Bletzinger KU, Bischoff M, Ramm E. A unified approach for shear-locking-free triangular and rectangular shell finite elements. Computers and Structures 2000; 75: 321-334.
Koschnick F, Bischoff M, Camprub N, Bletzinger KU. The discrete strain gap method and membrane locking. Computer Methods in Applied Mechanics and Engineering 2005; 194:2444-2463.
Lee I, Oh IK, Shin WH, Cho KD, Koo KN. Dynamic characteristics of cylindrical composite panels with co-cured and constrained viscoelastic layers. JSME Internatioal Journal Series C 2002; 45:16-25.
Nayak AK, Shenoi RA. Free Vibration Analysis Of Composite Sandwich Shells Using Higher Order Shell Elements. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 18-21 April 2005, Austin, Texas.
Jeung YS, Shen Y. Development of isoparametric, degenerate constrained Layer element for plate and shell structures. AIAA Journal 2001; 39: 1997-2005.
Kulikov GM, Plotnikova SV. Geometrically exact assumed stress-strain multilayered solid-shell elements based on the 3D analytical integration. Computers and Structures 2006; 84: 1275-1287.
Arciniega RA, Reddy JN. Consistent third-order shell theory with application to composite circular cylinders. AIAA Journal 2005; 43; 2024-2038.
Alves de Sousa RJ, Natal Jorge RM, Fontes Valente RA, César de Sá JMA. A new volumetric and shear locking-free 3D enhanced strain element. Engineering Computations 2003; 20: 896-925.
Fontes Valente RA, Alves de Sousa RJ, Natal Jorge RM. An enhanced strain 3D element for large deformation elastoplastic thin-shell applications. Computational Mechanics 2004; 34: 38-52.
Moreira RAS, Alves de Sousa RJ, Fontes Valente RA. A solid-shell layerwise finite element for non-linear geometric and material analysis. Composite Structures 2010; 92: 1517-1523
Alam N, Asnani NT. Vibration and damping analysis of a multilayered cylindrical shell, Part I: theoretical analysis. AIAA Journal 1984; 22: 803-810.
Ramesh TC, Ganesan N. Vibration and damping analysis of cylindrical shells with a constrained damping layer. Computers and Structures 1993; 46: 751-758.
Wang HJ, Chen LW. Finite element dynamic analysis of orthotropic cylindrical shells with a constrained damping layer. Finite Elements in Analysis and Design 2004; 40: 737-755.
MacNeal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1985; 1: 3-20.
Simo JC, Fox DD, Rifai MS. On stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering 1989; 73:53-92.
Cheng ZQ, He LH, Kitipornaci S. Influence of imperfect interfaces on bending and vibration of laminated composite shells. International Journal of Solids and Structures 2000; 37: 2127-2150.
Reddy JN. Mechanics of laminated composite plates and shells; Theory and analysis. CRC Press, Boca Raton, FL, USA, 2003.
Liu, B, Xing YF, Qatu MS, Ferreira AJM. Exact characteristic equations for the free vibrations of thin orthotropic circular cylindrical shells. Composite Structures 2012; 94: 484-493.
Sheinman I, Greif S. Dynamic analysis of laminated shells of revolution. Journal of Composite Materials 1984; 18: 200-215.
Shariyat M. An accurate double-superposition global-local theory for vibration and bending analyses of cylindrical composite and sandwich shells subjected to thermo-mechanical loads. Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Sciences 2011; 225: 1816-1832.
Messina A, Soldatos KP. Influence of edge boundary conditions on the free vibratrions of cross-ply laminated circular cylindrical panels. Journal of the Acoustical Society of America 1999; 106: 2608-2620.
Khdeir AA, Reddy JN. Influence of the edge conditions on the modal characteristics of cross-ply laminated shells. Computers and Structures 1990; 34: 817-826.