Haitian Yang

An Element-Free Galerkin Scaled Boundary Method for Steady-State Heat Transfer Problems

This article develops an element-free Galerkin scaled boundary method (EFG-SBM) for solving steady-state heat transfer problems. The SBM weakens the governing differential equations along the circumferential coordinate direction and solves analytically in the radial direction. Unlike the conventional scaled boundary finite-element method (SBFEM), an EFG approach is used in the circumferential direction in this article. The proposed method is verified via numerical examples including problems with thermal singularity and unbounded domain, and satisfactory results are obtained in comparison with analytical and SBFEM solutions.

Interval Estimation of Convection-Diffusion Heat Transfer Problems

This article presents two approaches to tackle the steady-state convection-diffusion heat transfer problem with interval uncertainty. The finite-element method and expansion techniques are combined in the modeling process, and the lower and upper bounds of the uncertain intervals of temperatures are estimated by solving two sets of deterministic equations in terms of central values and the radius of the intervals. A 2-D numerical example is provided to verify the proposed approaches. In comparison with the combinatorial and probabilistic methods, the estimated bounds are reasonable.

An EFG-SBM based partitioning algorithm for two-dimensional elastic analysis of cyclically symmetrical structures

Purpose – The purpose of this paper is to exploit the cyclic symmetry to reduce the computational expense of scaled boundary method (SBM) which may cumber its further application. Design/methodology/approach – A partitioning EFG-SB (Element-free Galerkin-SB) algorithm is proposed for the two-dimensional elastic analysis of cyclically symmetric structures. Findings – By utilizing the cyclic symmetry and partitioning algorithm, the whole computational cost can be significantly reduced. Three numerical examples are given to illustrate the advantages of the proposed algorithm. Originality/value – It is proved that the matrices of eigenvalue and system equations of EFG-SBM for cyclically symmetric structures are block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted. No matter whether displacement constraints are cyclically symmetric or not, the partition is available for the eigenvalue equations. Therefore the major computational cost can be saved via the proposed partiti...

A NODE-BASED ERROR ESTIMATOR FOR THE ELEMENT-FREE GALERKIN (EFG) METHOD

Meshless methods are suitable for adaptive analysis, as the nodes are unstructured, and can be added or deleted freely. However, the smooth shape functions may produce spurious oscillation away from the region containing error, which may result in addition of unnecessary nodes. In order to avoid the influence of spurious oscillation on adaptive analysis, a node-based error estimator is presented. The recovered nodal stress value is obtained from a reference solution using a double refinement technique. Numerical tests are presented illustrating the effectiveness of the proposed approach in the terms of the number and distribution of nodes compared with traditional approaches.