Thermal Analysis of a Functionally Graded Coating/Substrate System Using the Approximated Transfer Approach

As a heterogeneous material, functionally graded material (FGM) behaves as continuously changed material properties in certain directions from one composition to another, and hence it has received much more attention for biomedical applications and thermal protections to achieve innovative functions that conventional homogeneous material cannot accomplish. However, due to the particularly small thickness ratio of coating to substrate in practice, the conventional mesh discretization of the coating region is inefficient. To simplify the meshing procedure and increase the efficiency of analysis, the approximated transfer algorithm based on the concept of finite difference is developed for transferring boundary conditions applied on the coating surface to the interface of coating and substrate. As a result, only the substrate with transferred convection boundary conditions needs to be solved numerically, i.e., by the fundamental-solution based hybrid finite element method (HFS-FEM) with high accuracy and feasible polygonal element construction, in which only integrals along the element boundary are evaluated because of the application of fundamental solutions of the problem as kernel functions of interior approximated fields. Finally, numerical experiments including the single-layered, multi-layered and functionally graded coatings are carried out to verify the accuracy and applicability of the present method.

Nonlinear analysis for the polygonal element

As an important method for solving boundary value problems of differential equations, the finite element method (FEM) has been widely used in the fields of engineering and academic research. For two dimensional problems, the traditional finite element method mainly adopts triangular and quadrilateral elements, but the triangular element is constant strain element, its accuracy is low, the poor adaptability of quadrilateral element with complex geometry. The polygon element is more flexible and convenient in the discrete complex geometric model. Some interpolation functions of the polygon element were introduced. And some analysis was given. The numerical calculation accuracy and related features of different interpolation function were studied. The damage analysis for the koyna dam was given by using the polygonal element polygonal element of Wachspress interpolation function. The damage result is very similar to that by using Xfem, which shows the calculation accuracy of this method is very high.

Parasitic Capacitance Extraction Using Finite Element Method on Polygonal Mesh through Piecewise Interpolation

Parasitic capacitance extraction is a critical issue in the area of integrated circuit (IC), its performance heavily depends on the electromagnetic field solver involved. To improve the computation accuracy and efficiency, the interpolation finite element methods (FEM) have been investigated to deal with polygonal elements. Such methods are based on the thinking of generalized barycentric coordinates, such as mostly used mean value coordinates, Sibson coordinates, andetc. They have demonstrated good convergence and accuracy. However, they are time consuming during processing shape functions for Galerkin-schema FEM. A kind of piecewise interpolation method within convex polygonal element is presented. The polygon is divided into triangular sub-regions utilizing its barycenter, where the shape functions related to the whole polygon are conveniently and quickly acquired. The method has excellent performance in computation speed and shows good convergence and high accuracy. A comparison between different FEMs is performed with a typical electrostatic capacitance extraction example.

A Novel Shape-Free Plane Quadratic Polygonal Hybrid Stress-Function Element

A novel plane quadratic shape-free hybrid stress-function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy stress function. Without construction of displacement interpolation function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and stress solutions.