journal article·2013-10Open access

Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory

Chien H. Thai, A.J.M. Ferreira, E. Carrera, H. Nguyen-Xuan

Abstract

We present an isogeometric finite element formulation for static, free vibration and buckling analysis of laminated composite and sandwich plates. The idea behind this work is to associate an isogeometric analysis (IGA) with a layerwise theory [A.J.M. Ferreira. Analyis of composite plates using a layerwise deformation theory and multiquadrics discretization. Mech Adv Mater Struct 2005;12(2):99–112]. Isogeometric analysis based on non-uniform rational B-spline (NURBS) basic functions were recently proposed to preserve exact geometries and to enhance very significantly the accuracy of the traditional finite elements. B-splines basic function (or NURBS) is used to represent for both geometric and field variable approximations, which provide a flexible way to make refinement and degree elevation. They enable us to achieve easily the smoothness with arbitrary continuity order compared with the traditional FEM. The layerwise theory assumes a first-order shear deformation theory in each layer and the imposition of displacement continuity at the layers interfaces. This permits to remove shear correction factors and improves the accuracy of transverse shear stresses. Intensive numerical studies have been conducted to show the highly efficient performance of the proposed formulation.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Advanced Numerical Analysis Techniques · Composite Structure Analysis and Optimization · Advanced machining processes and optimization

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (71)

Show source-provided references
1. Vinson · 1999
2. Reddy · 2004
3. Analysis of composite plates using various plate theories. Part 1. Formulation and analytical solutions10.12989/sem.1998.6.6.583 ↗
4. Shear deformation in heterogeneous anisotropic plates10.1115/1.3408654 ↗
5. A simple higher-order theory for laminated composite plates10.1115/1.3167719 ↗
6. An unsymmetric FRC laminate C0 finite element model with 12° of freedom per node10.1108/eb023749 ↗
7. Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations10.1016/0020-7683(88)90090-X ↗
8. A refined analysis of composite laminates10.1016/S0022-460X(73)80170-1 ↗
9. A generalization of two-dimensional theories of laminated composite plates10.1002/cnm.1630030303 ↗
10. Laminated composite plate theory with improved in-plane responses10.1115/1.3171828 ↗
11. Analysis of composite plates using a layerwise theory and multiquadrics discretization10.1080/15376490490493952 ↗
12. A refined laminate plate theory10.1115/1.3423032 ↗
13. Transverse shear in laminated plate theories10.2514/3.6917 ↗
14. An improved shear-deformation theory for moderately thick multilayered shells and plates10.1115/1.3173074 ↗
15. A composite plate theory for arbitrary laminate configuration10.1115/1.3172955 ↗
16. A new theory of laminated plate10.1016/0266-3538(86)90087-4 ↗
17. C0 Reissner–Mindlin multilayered plate elements including Zig–Zag and interlaminar stress continuity10.1002/(SICI)1097-0207(19960615)39:11<1797::AID-NME928>3.0.CO;2-W ↗
18. Evaluation of layer-wise mixed theories for laminated plate analysis10.2514/2.444 ↗
19. Developments, ideas and evaluations based upon the Reissner’s mixed variational theorem in the modeling of multilayered plates and shells10.1115/1.1385512 ↗
20. Historical review of zig-zag theories for multilayered plates and shells10.1115/1.1557614 ↗
21. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement10.1016/j.cma.2004.10.008 ↗
22. Studies of refinement and continuity in isogemetric analysis10.1016/j.cma.2007.04.007 ↗
23. Isogeometric analysis of structural vibrations10.1016/j.cma.2005.09.027 ↗
24. B and F projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements10.1016/j.cma.2008.01.012 ↗
25. Isogeometric structural shape optimization10.1016/j.cma.2008.01.025 ↗
26. Isogeometric shell analysis with Kirchhoff–Love elements10.1016/j.cma.2009.08.013 ↗
27. The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches10.1016/j.cma.2010.03.029 ↗
28. Rotation free isogeometric thin shell analysis using PHT-splines10.1016/j.cma.2011.08.014 ↗
29. Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS-based isogeometric approach10.1002/nme.4282 ↗
30. Isogeometric shell analysis: The Reissner–Mindlin shell10.1016/j.cma.2009.05.011 ↗
31. Thai Chien H, Nguyen-Xuan H, Bordas SPA, Nguyen-Thanh N, Rabczuk T. Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory. Mech Adv Mater Struct, 2013.10.1016/j.compositesb.2013.06.044 ↗
32. A large deformation, rotation-free, isogeometric shell10.1016/j.cma.2010.12.003 ↗
33. Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids10.1016/j.cma.2011.01.018 ↗
34. A two-dimensional isogeometric boundary element method for elastostatic analysis10.1016/j.cma.2011.08.008 ↗
35. Piegl · 1997
36. Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter10.1016/j.compstruct.2008.07.025 ↗
37. An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core10.1016/j.finel.2008.02.001 ↗
38. Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method10.1016/S0045-7825(03)00238-X ↗
39. An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape10.1016/S0263-8223(02)00034-X ↗
40. Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method10.1016/S1359-8368(03)00083-0 ↗
41. A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates10.1016/j.compstruct.2012.08.012 ↗
42. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates10.1016/j.ijsolstr.2011.09.008 ↗
43. Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory10.1016/0045-7949(94)90232-1 ↗
44. Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method10.1016/j.apm.2012.01.003 ↗
45. Exact solutions for rectangular bidirectional composites and sandwich plates10.1177/002199837000400102 ↗
46. An improved C0 FE model for the analysis of laminated sandwich plate with soft core10.1016/j.finel.2012.02.005 ↗
47. Application of a three dimensional mixed finite element model to the flexure of sandwich plate10.1016/S0045-7949(03)00289-X ↗
48. Free vibration of laminated composite and sandwich plates using global–local higher-order theory10.1016/j.jsv.2006.05.022 ↗
49. Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method10.1016/j.cma.2006.02.009 ↗
50. A high order collocation method for the static and vibration analysis of composite plates using a first-order theory10.1016/j.compstruct.2008.09.006 ↗
51. Analysis of symmetric cross-ply elastic plates using a higher-order theory: Part II: Buckling and free vibration10.1016/0263-8223(88)90048-7 ↗
52. Reddy · 1997
53. A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates10.1016/S0263-8223(02)00239-8 ↗
54. Vibration and stability of laminated plates based on a local higher-order plate theory10.1006/jsvi.1994.1448 ↗
55. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory10.1016/S0263-8223(99)00110-5 ↗
56. Free vibration of laminated rectangular plates analyzed by higher-order individual-layer theory10.1016/0022-460X(91)90112-W ↗
57. An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates10.1016/j.amc.2011.02.024 ↗
58. Noor AK, Mathers MD. Shear flexible finite element models of laminated composite plates and shells. NASA Technical Note D-8044; 1975.
59. Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates10.1016/j.compstruct.2005.08.010 ↗
60. Analysis of laminated composite plates using a higher-order shear deformation theory10.1002/nme.1620211207 ↗
61. Buckling of laminated composite plates by a new element based on higher order shear deformation theory10.1080/10759410306754 ↗
62. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory10.1016/0022-460X(85)90383-9 ↗
63. Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories10.1016/S0263-8223(98)00135-4 ↗
64. Three-dimensional solutions for initially stressed structural sandwiches10.1061/(ASCE)0733-9399(1994)120:2(284) ↗
65. Higher order piezoelectric plate theory derived from a three-dimensional variational principle10.2514/2.1618 ↗
66. Batra RC, Vidoli S, Vestroni F. Plane Waves and Modal Analysis in Higher-Order Shear and Normal Deformable Plate Theories, J Sound Vib 2002;257(1):63–88.10.1006/jsvi.2002.5029 ↗
67. Vibrations of Thick isotropic plates with higher order shear and normal deformable plate theories10.1016/j.compstruc.2004.11.023 ↗
68. Free and forced vibrations of thick rectangular plates by using higher-order shear and normal deformable plate theory and Meshless Petrov-Galerkin (MLPG) Method
69. McCarthy MA. Analysis of thick composite laminates using a Higher-Order Shear and Normal Deformable Plate Theory (HOSNDPT) and a meshless method10.1016/j.compositesb.2006.12.009 ↗
70. Analytical solutions for rectangular thick laminated plates subjected to arbitrary boundary conditions10.2514/2.624 ↗
71. The generalized plane strain deformations of thick anisotropic composite laminated plates10.1016/S0020-7683(99)00040-2 ↗