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Paper 43

Transient Analysis of Laminated Composite Plates using Isogeometric Analysis

N. Valizadeh1, S.Sh. Ghorashi2, H. Yousefi3, T.Q. Bui4 and T. Rabczuk2
1Department of Civil Engineering, University of Kerman, Iran
2Institute of Structural Mechanics, Department of Civil Engineering, Bauhaus-Universität Weimar, Germany
3School of Civil Engineering, University of Tehran, Iran
4Department of Civil Engineering, University of Siegen, Germany

Keywords: transient analysis, laminated composite plates, classical laminated plate theory, isogeometric analysis, NURBS, Newmark integration.

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Isogeometric analysis (IGA) has been recently introduced for unifying computer aided design (CAD) and the computer aided engineering (CAE) to benefit from the operation of geometrical exactness in engineering problems. In this context, the CAD-shape functions, commonly the non-uniform rational B-splines (NURBS), are substituted for the Lagrange polynomial based shape functions in the CAE. Some main superiorities of the IGA compared with the conventional finite element method (FEM), are: (1) the computational cost is decreased significantly as the meshes are generated within the CAD in the CAE; (2) isogeometric analysis gives higher accuracy results because of the smoothness and the higher order continuity between elements; and (3) mesh refinement is simple by re-indexing the parametric space without any interaction with the CAD system.

In this paper, an isogeometric finite element method based on NURBS basis functions is developed for transient analysis of laminated composite plates using the classical laminated plate theory (CLPT). The finite element formulation based on the classical laminated plate theory requires elements with at least C1-inter-element continuity. It is quite difficult to achieve such elements for free-form geometries when using the standard Lagrangian polynomials as basis functions. In terms of the isogeometric analysis, however, higher order NURBS basis functions with an increased inter-element continuity can be easily obtained. The NURBS are thus suited for such CLPT elements. As a result, the parameterization of the geometry and the approximation of the solution space for the plate deflection are utilized using the NURBS basis functions. The governing equations of the laminated composite plate are transformed into a standard weak-form, which is then discretized into an isogeometric system of time-dependent equations to be solved by the unconditionally stable Newmark time integration scheme. The essential boundary conditions are enforced by a direct approach. In this method, the clamped boundary condition is simply imposed by fixing the z-component of the first two rows of the control points from the desired boundary while the simply supported one is enforced by fixing the z-component of the first row of the control points. Some numerical examples of the laminated composite plates with different boundary conditions, fibre orientations and lay-up number are presented, discussed and compared with the analytical and other reference numerical solutions. Consequently, they show that the results derived from the IGA are efficient and accurate for transient analysis of the laminated composite plates.