A combined strain element to functionally graded structures in thermal environment

Abstract

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.