Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Abstract

In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references. Lee et al. 2009). Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al. 2012;Wali et al. 2014Wali et al. , 2015Frikha et al. 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories. KeywordsIt is certainly plausible that linear finite element (FE) models cannot be able to accurately predict the structural response presenting large elastic deformations and finite rotations. Indeed, according to Yu et al. (2015), several practical problems of FG structures require a geometrically non-linear formulation, such as the post-buckling behavior of structures used in aeronautical, aerospace as well as in mechanical and civil engineering. In such cases, it becomes crucial to develop efficient and accurate nonlinear FE models.It is well known that analytical solutions of shell problems are very limited. Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al. 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al. 2014;Kim et al. 2008;Hajlaoui et al. 2017;Frikha and Dammak 2017;Asemi et al. 2014 andAnsari et al. 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.Hosseini Kordkheili and Naghdabadi (2007) derived a FE formulation for the geometrically nonlinear thermoelastic analysis of FGM plates and shells using the updated Lagrangian approach. Later, Zhao and Liew (2009) conducted a geometrically non-linear analysis of FGM shells under mechanical and thermal loading using the element-free kp-Ritz method. The formulation was based on the modified version of Sander's non-li...

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Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

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Three-Dimensional Free Vibration Analysis of Thermally Loaded FGM Sandwich Plates

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