Kwang-Sung Woo

Interlaminar stress distribution of laminated composites using the mixed-dimensional transition element

This article presents the efficient mixed model analysis, often called global–local approach, to obtain interlaminar stresses at free edges in the laminated composite system under extension and flexure. For the proposed analysis, first, the discrete-layer elements are adopted as three-dimensional elements in the local region. Second, the equivalent single-layer elements are considered as two-dimensional elements in the global region. Finally, the mixed-dimensional transition elements are formulated to connect two different element types used in the global as well as the local regions, respectively. All the elements have higher order shape functions derived from the Lobatto shape function. Modes of the elements are classified into nodal and nodeless modes. The nodal modes have physical meaning, while nodeless modes with respect to the increase of order of the Lobatto shape function do not have physical meaning but improve accuracy of analysis. Therefore, fixing mesh arrangement of present analysis, the quality of the analysis can be enhanced without remeshing work. Some results obtained by the proposed approach are verified with comparison with published references. Also, efficiency of the mixed model analysis using the mixed-dimensional transition element is shown through comparison with numerical results obtained by the single model analysis using only discrete-layer elements.

Kernel Integration Scheme for 2D Linear Elastic Direct Boundary Element Method Using the Subparametric Element

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.