Geometrically nonlinear analysis of 3D structures by HH20 element with new numerical integration schemes

Nguyen Dinh Du, MSc - Nguyen Khanh Hung, MSc

Faculty of Civil Engineering, Lac Hong University, Viet Nam

ABSTRACT. Gaussian integration is an integral part of the hardness matrix as well as force vectors in most numerical methods. The high-order quadrilateral (Q8 and Q9) in FEM needs a minimum number of 3 × 3 Gaussian integral points while the higher-order cube (HH20) needs a minimum of 3 × 3 × 3 to ensure stability and accuracy. However, in geometric nonlinear analysis, many loops are needed, so it takes time to calculate. Therefore, in this study, a new integral method based on published by Jeyakarthikeyan P.V authors will be improved for 3D called 3D-EM with nine integral points. The 3D-EM replacement integral model is applied to the HH20 element to shorten the calculation time but still ensure stability and accuracy. Two numerical examples will be presented to evaluate the efficiency of the new integral method compared to the traditional Gaussian integral in the HH20 element.

KEYWORDS: Geometrically nonlinear analysis, FEM, numerical integration, quadratic hexahedral, nearly incompressible

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