Smoothing Technique Based Beta FEM (βFEM) for Static and Free Vibration Analyses of Reissner–Mindlin Plates

Abstract

Recently, the edge-based and node-based smoothed finite element method (ES-FEM and NS-FEM) has been proposed for Reissner–Mindlin plate problems. In this work, in order to utilize the numerical advantages of both ES-FEM and NS-FEM for static and vibration analysis, a hybrid smoothing technique based beta FEM ([Formula: see text]FEM) is presented for Reissner–Mindlin plate problems. A tunable parameter [Formula: see text] is introduced to tune the proportion of smoothing domains calculated by ES-FEM or NS-FEM, which controlled the accuracy of the results. Numerical illustrations in both static and free vibration analysis are conducted. The shear locking free property, converge property and dynamic stability are carefully examined via several well-known benchmark examples. Moreover, an experimental test is carefully designed and conducted for validations, in which the mode values and shape of a rectangular steel plate is tested. Numerical examples demonstrate the advantages of [Formula: see text]FEM, in comparison with the standard FEM, ES-FEM and NS-FEM using the same meshes. The numerical and experimental results are in good agreement with each other and the [Formula: see text]FEM achieves the best accuracy among all the methods for the static or free vibration analysis of plates.

Phân tích tĩnh kết cấu vỏ bằng phần tử vỏ phẳng có biến dạng trơn kết hợp ES+NS-MITC3

“…Nhờ hệ số β ∈ [0, 1] tỉ lệ tham gia vào độ cứng phần tử của phương pháp làm trơn biến dạng trên cạnh và trên nút được hiệu chỉnh. PP β-PTHH đã được phát triển cho các phần tử tấm sử dụng kỹ thuật khử khóa cắt DSG3 [16] hoặc MITC3 [17]. Nguyen-Hoang và cs.…”

Static analysis of Reissner-Mindlin plates using ES+NS-MITC3 elements

“…It means that if β = 0, the ES+NS-domains become the ES-domains, and if β = 1, the ES+NS-domains are purely NS-ones. This approach is also called the βFEM [12,13].…”

“…In contrast, the NS-FEM causes overly soft behaviors in comparison with analytical solutions. To narrow the gap in results provided by the SFEM and the analytical solutions, the hybrid SFEM or βFEM has been suggested [12,13] by reconstructing a new smoothed strain fields which includes the ES-and NS-strain fields. In this approach, a scale factor β ∈ [0,1] is used to tune the contribution ratio of ES-and NS-domains into the hybrid smoothed strain fields.…”

“…In this approach, a scale factor β ∈ [0,1] is used to tune the contribution ratio of ES-and NS-domains into the hybrid smoothed strain fields. The βFEM for the DSG3 plate element has demonstrated the superior performance when analyzing statics and vibration of the Reissner-Mindlin plates [12,13]. Therefore, the βFEM will be developed for the MITC3 triangular plate element in this work.…”