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The thermo-elastic behaviour induced by temperature in composite structures has become a significant factor in structural design. In this paper, a three-dimensional thermo-elastic theory for composite cross-ply laminated plates was discretized by a differential quadrature hierarchical finite element method (DQHFEM). The DQHFEM is a weak-form differential quadrature method using hierarchical bases that can provide highly accurate results using only a few sampling points. Flexible and efficient wedge (triangular prism) and hexahedron elements were constructed and applied to three-dimensional (3D) analyses of cross-ply laminated plates and shells for the first time. Compared with various models in literatures, the DQHFEM showed very good agreements with exact solutions based on 3D elastic theory. The thermo-mechanical analyses of cross-ply laminated plates and shells based on 3D theory indicate that the DQHFEM is an effective method for high accuracy analyses with low computational costs, because the DQHFEM can provide results with high accuracy by using only several nodes on the thickness direction.

The interface of composite structures is usually modeled by assuming displacement continuous. However, the reality is that the interface is another type of material with different elastic constants and is generally of different scale compared with the matrix of the composites. This work uses a differential quadrature hierarchical finite element method (DQHFEM) to analyze the interface of composite structures. The DQHFEM allows a great number of nodes on the boundary of elements but only a few nodes inside the elements, or the reverse. Therefore, the method is very convenient for the two scale analysis of the problem. Interfaces of two types of materials are analyzed in this work: (1) the interaction of grains and grain boundaries of metals that are composites in microscale and (2) the interface of nanoparticles and the matrix of nanoparticle composites. The elastic constants of the components of composite structures are obtained from test results or by molecular dynamic simulations. Numerical analysis of the two types of composite structures shown that the DQHFEM is of high accuracy and efficiency and is suitable for two-scale analysis.

This paper presents a differential quadrature hierarchical finite element method (DQHFEM) for dynamic analyses of functionally graded material (FGM) sandwich shallow shells in thermal and non-thermal environments. A layer-wise theory based on the first-order shear deformation theory (FSDT) for each layer was adopted. Effective material properties of the FGM are estimated according to Voigt’s rule of mixture (ROM) and/or Mori–Tanaka (MT) scheme. For the shells in thermal environment, a nonlinear temperature distribution in thickness direction is considered and the elastic properties are assumed to be temperature dependent. The results obtained from the proposed formulation are validated with those available in literatures. Natural frequencies obtained from Sander’s, Love’s and Donnell’s shell theories for different geometric and boundary conditions are compared with each other first to assess the performance of different shell theories for FGM sandwich shells under non-thermal environment. Then the effects of volume fraction index, core thickness and temperature gradient on natural frequencies of FGM sandwich shells are investigated. The presented DQHFEM is much like the fixed interface mode synthesis method but does not need modal analysis and is of high accuracy. This work is the first application of the method to functionally graded sandwich shells in thermal environments .