On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach

• Published in: International journal of mechanical sciences Vol. 110; pp. 242 - 255
• Main Authors: Nguyen, Tuan N., Thai, Chien H., Nguyen-Xuan, H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2016
• Subjects: A unified formulation; Composite structures; Higher order shear deformation theory; Isogeometric analysis; Laminated composite plates; Mathematical models; Plates (structural members); Polynomials; Quasi-3D theory; Readers; Shear deformation; Shear stress; Stretching; Isogeometric analysis; Higher order shear deformation theory; A unified formulation; Laminated composite plates; Quasi-3D theory
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2016.01.012

This paper brings to the readers a unified framework on higher order shear deformation theories (HSDTs), modelling and analysis of laminated composite plates. The major objective of this work is to (1) unify all higher order shear deformation theories in a unique formulation by a polynomial form; (2) propose the new higher shear deformation models systematically based on a unified formulation. In addition, the effect of thickness stretching is taken into account by considering a quasi-3D theory. The principle of virtual displacements is exploited to derive a weak form based on the generalized displacement fields of the higher order shear deformation theories. Numerical results are computed by using isogeometric analysis and verified to show the accuracy and reliability of the present approach. It is found that the unique formulation of a polynomial form can theoretically cover all existing HSDTs models and is thus sufficient to describe the nonlinear and parabolic variation of transverse shear stress. Moreover, the proposed higher order shear deformation theories predict the proper responses for laminated composite plates in comparison with the available ones in the literature. •We unify all HSDTs in a unique formulation by a polynomial form.•* We then propose several new HSDTs systematically based on a unified formulation.•The higher-order continuity requirement is solved by isogeometric analysis.•The proposed method is insensitive to shear locking.•Two numerical examples are given to show the performance of the present method.