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Another six-node triangular element for structural analysis

Ton-That Hoang Lan

Engineering Transactions

2022

Vol. 70, iss. 3

221--238

A six-node triangular element is presented in this paper for structural analysis. With this approach, the approximation functions of the interpolation strategy are given by using the double interpolation procedure, which includes nodal values as well as averaged nodal gradients. The numerical results are, therefore, achieved following the proposed element. The efficiency of this element and its comparison is described by some fundamental examples. Better numerical solutions and smoother distributions of stresses not achieved by the standard elements will be provided when using this element. The computational time is also presented to overview the pros and cons of the proposed element. In fact, the new element’s computational time is higher than that based on the standard element because of the double interpolation procedure, but one does not need post-processing of any smoothing operation.

Plate structural analysis based on a double interpolation element with arbitrary meshing

Ton-That Hoang Lan

Acta Mechanica et Automatica

2021

Vol. 15, no. 2

91--99

This paper presents the plate structural analysis based on the finite element method (FEM) using a double interpolation element with arbitrary meshing. This element used in this research is related to the first-order shear deformation theory (FSDT) and the double interpolation procedure. The first stage of the procedure is the same with the standard FEM for the quadrilateral element, but the averaged nodal gradients must be computed for the second stage of this interpolation. Shape functions established by the double interpolation procedure exhibit more continuous nodal gradients and higher-order polynomial contrast compared to the standard FEM when analysing the same mesh. Note that the total degrees of freedom (DOFs) do not increase in this procedure, and the trial solution and its derivatives are continuous across inter-element boundaries. Besides, with controlling distortion factors, the interior nodes of a plate domain are derived from a set of regular nodes. Four practical examples with good results and small errors are considered in this study for showing excellent efficiency for this element. Last but not least, this element allows us to implement the procedure in an existing FEM computer code as well as can be used for nonlinear analysis in the near future.