Development of Finite Element Model based on Carrera Unified Formulation for Laminated Composites

Pegallapati, Abhijith and Raju, Gangadharan (2019) Development of Finite Element Model based on Carrera Unified Formulation for Laminated Composites. Masters thesis, Indian institute of technology Hyderabad.

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Abstract

Laminated composite structures are increasingly being used in the aerospace, automobile and wind energy sectors due to their superior specific mechanical properties, fatigue life and design tailorability. Accurate stress analysis of composite laminates has become crucial for safe design under realistic loads and boundary conditions. Different approaches based on analytical, experimental and numerical techniques are available for stress analysis. The classical theories like Euler-Bernoulli Beam Theory, Timoshenko Beam Theory, Kirchhoff plate theory and Reissner-Mindlin Plate Theory, respectively for beams and plates/shells are inaccurate for stress analysis of thick laminates as the effects such as transverse shear and normal deformations are neglected. Further, these models are limited by assumptions of material heterogeneity, structural geometry and Saint-Venant’s principle, which limits the accuracy of the stress field solution away from supports, discontinuities and singularities in the structures. For accurate evaluation of 3D stress / strain fields in the composite structures, computationally expensive 3D finite element analyse is usually carried out. New computationally efficient approaches are required for 3D evaluation of stresses in laminated composite structures. Recently, an advanced structural theory, namely Carrera Unified Formulation (CUF), has been proposed to accurately evaluate 3D stress / strain fields in slender beam-like and plate-like composite structures. CUF permits us to develop higher order displacement based beam and plate theories in a generic way. CUF provides a systematic approach for implementing the higher order theories. In this work, 1D and 2D CUF is implemented in a finite element framework to determine the 3D displacement, strain and stress fields of laminated composite structures. In the case of 1D CUF finite element formulation, the Lagrange shape functions of cubic and quadratic orders is used along the beam length and cross-section respectively. In the case of 2D CUF finite element formulation, the Lagrange shape functions are used to define the mid-surface deformation of the laminate and Taylor shape functions are used to define the thickness deformation of the laminate. In 2D CUF finite elements, the MITC plate formulation is followed to avoid the locking problems. The developed CUF finite element framework is validated against benchmark problems available in the literature and also with 3D finite element solutions. The convergence and accuracy of the stress field solution obtained using CUF finite elements are studied by varying the element order, element size and mesh distribution.

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