A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

A bridging transition technique for the combination of meshfree method with finite element method in 2D solids and structures

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration—Part I : Modeling methodology and strategy

This paper aims to develop the methodology and strategy for concurrent finite element modeling of civil infrastructures at the different scale levels for the purposes of analyses of structural deteriorating. The modeling strategy and method were investigated to develop the concurrent multi-scale model of structural behavior (CMSM-of-SB) in which the global structural behavior and nonlinear damage features of local details in a large complicated structure could be concurrently analyzed in order to meet the needs of structural-state evaluation as well as structural deteriorating. In the proposed method, the “large-scale” modeling is adopted for the global structure with linear responses between stress and strain and the “small-scale” modeling is available for nonlinear damage analyses of the local welded details. A longitudinal truss in steel bridge decks was selected as a case to study how a CMSM-of-SB was developed. The reduced-scale specimen of the longitudinal truss was studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details, while the multi-scale models using constraint equations and substructuring were developed for numerical simulation. The comparison of dynamic and static response between the calculated results by different models indicated that the proposed multi-scale model was found to be the most efficient and accurate. The verification of the model with results from the tested truss under the specific loading showed that, responses at the material scale in the vicinity of local details as well as structural global behaviors could be obtained and fit well with the measured results. The proposed concurrent multi-scale modeling strategy and implementation procedures were applied to Runyang cable-stayed bridge (RYCB) and the CMSM-of-SB of the bridge deck system was accordingly constructed as a practical application.