Tinh Quoc Bui

NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

An efficient meshfree method for analysis of two-dimensional piezoelectric structures

Further application of an efficient novel meshfree technique based on the moving kriging (MK) interpolation for static and dynamic analyses of two-dimensional piezoelectric structures is presented. The MK scheme is used for constructing the shape functions which satisfy the Kronecker delta property. Hence, the burdensome task of enforcing the essential boundary conditions as in the moving least-squares approximation is avoided. The mechanical displacements, electric potential and natural frequencies of structures are investigated in detail through a series of numerical examples that are to demonstrate the applicability and the efficiency of the proposed method. The results obtained are then compared with those of other available reference solutions with very good agreement.

Numerical modeling of wave propagation in functionally graded materials using time-domain spectral Chebyshev elements

Numerical modeling of the Lamb wave propagation in functionally graded materials (FGMs) by a two-dimensional time-domain spectral finite element method (SpFEM) is presented. The high-order Chebyshev polynomials as approximation functions are used in the present formulation, which provides the capability to take into account the through thickness variation of the material properties. The efficiency and accuracy of the present model with one and two layers of 5th order spectral elements in modeling wave propagation in FGM plates are analyzed. Different excitation frequencies in a wide range of 28-350 kHz are investigated, and the dispersion properties obtained by the present model are verified by reference results. The through thickness wave structure of two principal Lamb modes are extracted and analyzed by the symmetry and relative amplitude of the vertical and horizontal oscillations. The differences with respect to Lamb modes generated in homogeneous plates are explained. Zero-crossing and wavelet signal processing-spectrum decomposition procedures are implemented to obtain phase and group velocities and their dispersion properties. So it is attested how this approach can be practically employed for simulation, calibration and optimization of Lamb wave based nondestructive evaluation techniques for the FGMs. The capability of modeling stress wave propagation through the thickness of an FGM specimen subjected to impact load is also investigated, which shows that the present method is highly accurate as compared with other existing reference data. Spectral time-domain Chebyshev element is developed for wave propagation in FGMs.Phase velocity dispersion properties of FGM structures are studied using one and two layers of 5th order spectral elements.Different excitation frequencies in a wide range of 28-350 kHz are analyzed.Impact stress wave propagation through the thickness of FGM specimen is investigated.

ISOGEOMETRIC SIMULATION FOR BUCKLING, FREE AND FORCED VIBRATION OF ORTHOTROPIC PLATES

Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.

MESHFREE GALERKIN KRIGING MODEL FOR BENDING AND BUCKLING ANALYSIS OF SIMPLY SUPPORTED LAMINATED COMPOSITE PLATES

Further development of the novel meshfree Galerkin Kriging method for bending and buckling analysis of laminated composite plates is the main objective of the present work. The present formulation follows the classical plate theory while the discrete equations are derived from the standard Galerkin weak form. The moving Kriging interpolation technique is used for constructing shape functions, which possess the delta property and thus no special techniques are required for imposing the essential boundary conditions. Various numerical examples with different geometries of plates for both bending and buckling analysis are solved to demonstrate the applicability and the effectiveness of the present approach. The calculated results are compared with reference solutions available in the literature and very good agreements are obtained. It obviously illustrates that the proposed method can be considered as an alternative numerical approach for buckling and bending of laminated plates.

EIGENVALUE ANALYSIS OF THIN PLATE WITH COMPLICATED SHAPES BY A NOVEL MESH-FREE METHOD

Further development of a novel mesh-free method for eigenvalue analysis of thin plate structures with complicated shapes is presented in this paper. A mesh-free method used the moving Kriging interpolation technique for constructing the shape functions, which possess the Kroneckers delta property, is formulated. Thus, it makes the present method efficient in enforcing the essential boundary conditions and none of any special techniques are required. The present plate theory followed the classical Kirchhoffs assumption and the deflection is in general approximated through the moving Kriging interpolation. Also, the mesh-free formulations for the vibration problem are formed in a simple way as finite element methods. The orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. A standard weak form is adopted to discrete the governing partial differential equation of plates. Some numerical examples are attempted to demonstrate the applicability, the effectiveness, and the accuracy of the method.

Buckling analysis of simply supported composite laminates subjected to an in-plane compression load by a novel mesh-free method

Buckling analysis of composite laminates under an in-plane compression load based on the mesh free Galerkin Kriging method is presented. The moving Kriging interpolation (MK) technique possessing the delta property is employed to construct the shape functions, and thus no special techniques for imposing the essential boundary conditions are required. The present formulation is based on the Krichhoff plate theory. The applicability, the accuracy and the effectiveness of the method are illustrated through a number of numerical examples. The results calculated by the proposed method are compared with those of existing reference solutions available in the literature and very good agreements are observed. It can be said that the proposed method can be considered as an alternative numerical technique in terms of meshfree methods.

Recent Advances in Computational Mechanics

Computational mechanics deals with the use of computational methods in engineering to study physical phenomena governed by the principles of mechanics. It has got huge potential for the future growth and applications by incorporating new models of physical and biological systems based on quantum, molecular, biomechanics, and so on. The computational mechanics spans to several areas of mechanics, mathematics, computer science, and many others. Over the years, it has made a significant contribution in the design and development of new process and products due to the availability of effective computational resources. Nowadays, the computationalmethods are applied in all areas of engineering and sciences. This special issue covers the papers from various topics including thermal, fluid, solid mechanics, vibration, and vehicle dynamics. In totality, these papers provide the reader with an overall picture of the computational mechanics along with engineering and industrial applications. In this special issue, the editors received 38 manuscripts on various topics of computational mechanics. After peer review and based on the comments from reviewers, only 16 manuscripts have been accepted for publication.