An improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory for static analysis of composite and sandwich plates

International Journal for Numerical Methods in Engineering

Volumn 69, Issue 9, 2007, Pages 1948-1981

  Kapuria, S ^a,b   Kulkarni, S D ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Composite plate; Discrete Kirchhoff technique; Finite element; Quadrilateral element; Sandwich plate; Zigzag theory

Indexed keywords

ABAQUS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; INTERPOLATION; NAVIER STOKES EQUATIONS; SANDWICH STRUCTURES; SHEAR STRAIN;

KIRCHHOFF CONSTRAINT TECHNIQUE; KIRCHHOFF QUADRILATERAL ELEMENT; QUADRILATERAL ELEMENT; ZIGZAG THEORY;

PLATES (STRUCTURAL COMPONENTS);

ABAQUS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; INTERPOLATION; NAVIER STOKES EQUATIONS; PLATES (STRUCTURAL COMPONENTS); SANDWICH STRUCTURES; SHEAR STRAIN;

EID: 33847397495     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1836     Document Type: Article

References (39)

1. Noor AK, Burton WS. Assessment of shear deformation theories for multilayered composite plates. Applied Mechanics Review 1989; 42:1-13.
2. Ghugal YM, Shimpi RP. A review of refined shear deformation theories of isotropic and anisotropic laminated plates. Journal of Reinforced Plastics and Composites 2002; 21:775-813.
3. Yang PC, Norris CH, Stavsky Y. Elastic wave propagation in heterogeneous plate. International Journal of Solids and Structures 1966; 2:665-684.
4. Whitney JM, Pagano NJ. Shear deformation in heterogeneous anisotropic plates. Journal of Applied Mechanics (ASME) 1970; 37:1031-1036.
5. Pai PF. A new look at shear correction factors and warping functions of anisotropic laminates. International Journal of Solids and Structures 1995; 32:2295-2315.
6. Altenbach H. On the determination of transverse shear stiffnesses of orthotropic plates. Zeitshrift für Angewandte Mathematik and Physik (ZAMP) 2000; 51:629-649.
7. Altenbach H. An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. International Journal of Solids and Structures 2000; 37:3503-3520.
8. Reddy JN. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics 1984; 51:745-752.
9. Toledano A, Murakami H. A composite plate theory for arbitrary laminate configurations. Journal of Applied Mechanics 1987; 54:181-189.
10. Lu X, Liu D. An interlaminar shear stress continuity theory for both thin and thick composite laminates. Journal of Applied Mechanics 1992; 59:502-509.
11. Robbins DH, Reddy JN. Modelling of thick composites using a layerwise laminate theory. International Journal for Numerical Methods in Engineering 1993; 36:655-677.
12. Di Sciuva M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model. Journal of Sound and Vibration 1986; 105(3):425-442.
13. Murakami H. Laminated composite plate theory with improved in-plane responses. Journal of Applied Mechanics 1986; 53:661-666.
14. Di Sciuva M. Multilayered anisotropic plate models with continuous interlaminar stresses. Composite Structures 1992; 22:149-167.
15. Cho M, Parmerter RR. Efficient higher order composite plate theory for general lamination configurations. AIAA Journal 1993; 31(7):1299-1306.
16. Shu X, Sun L. An improved simple higher-order theory for laminated composite plates. Computers and Structures 1994; 50(2):231-236.
17. Cho M, Kim JS. Higher-order zig-zag theory for laminated composites with multiple delaminations. Journal of Applied Mechanics 2001; 68:869-877.
18. Toledano A, Murakami H. A high-order laminated plate theory with improved in-plane responses. International Journal of Solids and Structures 1987; 23(1):111-131.
19. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Applied Mechanics Review 2003; 56(3):287-308.
20. Di Sciuva M. A general quadrilateral multilayered plate element with continuous interlaminar stresses. Computers and Structures 1993; 47(1):91-105.
21. Icardi U. Eight-noded zig-zag element for deflection and stress analysis of plates with general lay-up. Composites Part B 1998; 29B:425-441.
22. Cho M, Parmerter R. Finite element for composite plate bending based on efficient higher order theory. AIAA Journal 1994; 32(11):2241-2248.
23. Specht B. Modified shape functions for the three-node plate bending element passing the patch test. International Journal for Numerical Methods in Engineering 1988; 26:705-715.
24. Di Sciuva M. A third-order triangular multilayered plate finite element with continuous interlaminar stresses. International Journal for Numerical Methods in Engineering 1995; 38:1-26.
25. Chakrabarti A, Sheikh AH. Analysis of laminated sandwich plates based on interlaminar shear stress continuous plate theory. Journal of Engineering Mechanics 2005; 131(4):377-384.
26. Rao KM, Meyer-Piening HR. Analysis of thick laminated anisotropic composite plates by the finite element method. Composite Structures 1990; 15:185-213.
27. 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. International Journal for Numerical Methods in Engineering 1996; 39:1797-1820.
28. Batoz JL, Tahar MB. Evaluation of a new quadrilateral thin plate bending element. International Journal for Numerical Methods in Engineering 1982; 18:1655-1677.
29. Jeychandrabose C, Kirkhope J, Meekisho L. An improved discrete Kirchhoff quadrilateral thin-plate bending element. International Journal for Numerical Methods in Engineering 1987; 24:635-654.
30. Hinton E, Campbell JS. Local and global smoothing of discontinuous finite element functions using a least squares method. International Journal for Numerical Methods in Engineering 1974; 8:461-480.
31. Jeychandrabose C, Kirkhope J. Least squares strain smoothing for the eight-node serendipity plane stress element. International Journal for Numerical Methods in Engineering 1984; 20:1164-1166.
32. Kim JS, Cho M. Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory. International Journal for Numerical Methods in Engineering 2002; 55:1323-1343.
33. Oh J, Cho M, Kim JS. Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory. International Journal of Solids and Structures 2005; 42:6122-6140.
34. Kulkarni SD, Kapuria S. A new discrete Kirchhoff quadrilateral element based on the third-order theory. Computational Mechanics (Published online).
35. ABAQUS/STANDARD User's Manual. Vol. 1, Version 6.1, 2002.
36. Zienkiewicz OC, Taylor RL. The Finite Element Method, Vol. 2: Solid Mechanics (5th edn). Butterworth-Heinemann: Oxford, 2000.
37. Pagano NJ. Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials 1970; 4:20-35.
38. Piskunov VG, Verijenko VE, Adali S, Tabakov PY, Prisyazhnyouk VK, Buryhin SG. Rational transverse shear deformation higher-order theory of anisotropic laminated plates and shells. International Journal of Solids and Structures 2001; 38:6491-6523.
39. ChengZong Z. General analytical solution for the bending of anisotropic skew plate with first-order shear deformation theory. Mechanics Advanced Materials and Structures 2003; 10:161-181.