Chien H. Thai

Isogeometric Analysis of Laminated Composite Plates Using the Higher-Order Shear Deformation Theory

Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown fields (Analysis). IGA can be based on a variety of CAD descriptions, the most widely used today being non-uniform rational B-splines (NURBS). In this article, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated. The method employs NURBS basis functions to both represent the geometry (exactly) and the unknown field variables. One of the main advantages of the present method is directly inherited from IGA, that is to easily increase the approximation order. To avoid using a shear correction factor, a third-order shear deformation theory (TSDT) is introduced. It requires C1-continuity of generalized displacements and the NURBS basis functions are well suited for this requirement. Several numerical examples are used to demonstrate the performance of the present method compared with other published ones.

An Edge-Based Smoothed Discrete Shear Gap Method Using the C0-Type Higher-Order Shear Deformation Theory for Analysis of Laminated Composite Plates

The edge-based smoothing discrete shear gap method (ES-DSG3) using three-node triangular elements is combined with a C0-type higher-order shear deformation theory (HSDT) to give a new linear triangular plate element for static, free vibration, and buckling analyses of laminated composite plates. In the ES-DSG3, only the linear approximation is necessary, and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are calculated relying on smoothing domains associated with the edges of the triangular elements through an edge-based strain smoothing technique. Using the C0-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. The numerical examples demonstrated that the ES-DSG3 show remarkably excellent performance compared to several other published elements in the literature.

A generalized unconstrained theory and isogeometric finite element analysis based on Bézier extraction for laminated composite plates

This work presents an isogeometric finite element formulation based on Bézier extraction of the non-uniform rational B-splines (NURBS) in combination with a generalized unconstrained higher-order shear deformation theory (UHSDT) for laminated composite plates. The proposed approach relaxes zero-shear stresses at the top and bottom surfaces of the plates and no shear correction factors are required. A weak form of static, free vibration and transient response analyses for laminated composite plates is then established and is numerically solved using isogeometric Bézier finite elements. NURBS can be written in terms of Bernstein polynomials and the Bézier extraction operator. IGA is implemented with the presence of C°-continuous Bézier elements which allow to easily incorporate into existing finite element codes without adding many changes as the former IGA. As a result, all computations can be performed based on the basis functions defined previously as the same way in finite element method (FEM). Numerical results performed over static, vibration and transient analysis show high efficiency of the present method.

A Naturally Stabilized Nodal Integration Meshfree Formulation for Thermo-Mechanical Analysis of Functionally Graded Material Plates

This chapter presents naturally stabilized nodal integration (NSNI) meshfree formulations for thermo-mechanical analysis of functionally graded material (FGM) plates. The effective material properties of FGM plates are homogenized by a rule of mixture. Gradient strains from the present approach are directly computed at nodes, the same as the direct nodal integration (DNI). The current approach is to alleviate the instability of solutions in the DNI and to significantly decrease computational cost when compared to the high-order Gauss quadrature scheme. The enforcement of essential boundary conditions is completely similar to the finite element method (FEM) due to satisfying the Kronecker delta function property of moving Kriging integration shape functions. Numerical validations are given to show the efficiency of the present approach.