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In this article, the bending properties of functionally graded material (FGM) sandwich beams are analyzed by using the scaled boundary finite element method (SBFEM) for the first time. The model of FGM sandwhich beams is realized by using high order spectral elements, and only the axial dimension of the beam needs to be discretized. The analytical formula along the thickness direction can better satisfy the properties of the FGM. More importantly, only a small number of the high order spectral element is used to discretize the FGM sandwich beam model, which greatly improves the computational efficiency. [ABSTRACT FROM AUTHOR]

Functionally graded materials have widespread applications for the practical engineering and industry of design and development. In the present work, free vibration and transient dynamic behaviors of functionally graded material (FGM) sandwich plates are semi-analytically investigated by the scaled boundary finite element method (SBFEM). A layerwise approach based on the three-dimensional (3D) theory of elasticity is adopted for the simulation of FGM sandwich plates, and the material properties involving Young's modulus and mass density are assumed to be continuously graded in the thickness direction according to a power law function while Poisson's ratio is taken to be constant in each individual layer. In order to obtain the global equilibrium equations for the dynamic problem of FGM sandwich plates, the SBFEM governing equation associated with a single layer is derived based on the principle of virtual work in the first step. Subsequently, they are assembled for the whole FGM sandwich plate by imposing the continuity conditions of the layer interface in the displacement fields. Natural frequencies are determined by eigenvalue analysis, and the transient dynamic equilibrium equation is solved on the basis of the Newmark's method. One of the advantages of present technique is the capability of reducing the spatial dimension and no discretizations in the thickness direction are needed, which results in a considerable reduction in the computational costs of the project. Furthermore, dynamic responses can be obtained directly from the semi-analytical solutions without shear correction factors or special treatments for the shear-locking effect as some high-order shear deformation plate theories. Excellent adaptability in mesh distortion, thickness ratio and boundary condition of proposed formulations for the dynamic analysis of FGM sandwich plates are confirmed and comprehensive parametric investigations are also carried out. Numerical results show that the dynamic responses obtained by the proposed approach converge rapidly and excellent agreement can be achieved between SBFEM results and the available solutions with a small number of computational costs, which indicates high accuracy and efficiency of the proposed formulations in dynamic analyses of FGM sandwich plates. • First comprehensive investigation of transient dynamics for FGM sandwich plates using the SBFEM. • Accurate solutions in dynamic simulations with severely distorted meshes. • High accuracy for arbitrary thickness of FGM sandwich plates. • Computational cost is significantly reduced due to the semi-analytical characteristic. • Shear correction factors and special treatments for the shear-locking effect are not required. [ABSTRACT FROM AUTHOR]

A novel semi-analytical plate formulation based on the isogeometric analysis (IGA) and scaled boundary element method (SBFEM) is proposed in this paper, and aims to solving the static bending and free vibration problems of functionally graded material (FGM) plates. The modulus of elasticity and density of the material are assumed to vary continuously along the thickness direction with a power-law distribution. The proposed formulation is derived on the basis of 3D theory of elasticity, while only the 2D in-plane dimension of reference surface needed to be discretized with three degrees of freedom (Dofs) per control points, and the non-uniform rational B-spline (NURBS) basis functions are adopted for both the representation of exact geometry and mechanical analysis. The system equations are obtained by using the principle of virtual work. A set of dual variables involving the displacements and nodal forces are introduced to reduce the system equations into first order ordinary differential equations (ODEs), which can be solved by conventional methods. The proposed approach possesses many advantages, such as the problem dimension is successfully reduced by one due to that the physical fields in the thickness direction are expressed analytically as Padé expansion associated with the material property distributed in gradient form, which are able to predict the stress through the thickness more precisely then traditional formulations. The IGSBFEM meshes can maintain exact geometry at any level without further communication with the computer-aided design (CAD) model, which enables the proposed method a flexible method in simulation of FGM plates with complex geometries. The NURBS basis functions can reach to C ∞ continuous within a knot span, which means that the discontinuity between adjacent elements on the same patch will vanish naturally. Numerous numerical examples are performed to evaluate the superior accuracy, convergence, locking-free, grid adaptability based on the comparison with other references. Effects of gradient index and several aspect ratios on the static and free vibration responses of FGM plates are investigated. [ABSTRACT FROM AUTHOR]