Free vibration and transient dynamic response of functionally graded sandwich plates with power-law nonhomogeneity by the scaled boundary finite element method

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Functionally graded material sandwich plates were analyzed for their dynamic behaviors using the SBFEM method with a layerwise approach and continuously graded material properties. The proposed method showed high accuracy and efficiency in dynamic analysis.