Aims: In this work, an improved control Volume finite element method (ICVFEM) is proposed and implemented for thermoelastic analysis in functionally graded materials (FGMs) at a steady state.
Methods and Results: Different from the conventional CVFEM, the sub-control Volume used in the proposed method is circular in the intrinsic coordinate. The advantages of the new integral domain are: (i) the complex integration path can be avoided: (ii) the method is very suitable for many types of elements. High-order shape functions of eight quadrilateral (Q8) elements are used to obtain the unknown variables and their derivatives. Besides, material properties in a functionally graded structure are calculated by the high-order shape functions based on the properties defined at the node.
Conclusion: To verify the convergence and accuracy of the proposed method, three numerical examples with analytical solutions are illustrated by using the conventional CVFEM and FEM at the same time.