A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells

Abstract

In this paper, a combined scheme of edge-based smoothed finite element method (ES-FEM) and node-based smoothed finite element method (NS-FEM) for triangular Reissner–Mindlin flat shells is developed to improve the accuracy of numerical results. The present method, named edge/node-based S-FEM (ENS-FEM), uses a gradient smoothing technique over smoothing domains based on a combination of ES-FEM and NS-FEM. A discrete shear gap technique is incorporated into ENS-FEM to avoid shear-locking phenomenon in Reissner–Mindlin flat shell elements. For all practical purpose, we propose an average combination (aENS-FEM) of ES-FEM and NS-FEM for shell structural problems. We compare numerical results obtained using aENS-FEM with other existing methods in the literature to show the effectiveness of the present method

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

“…Nguyen-Hoang và cs. đã áp dụng phương pháp làm trơn biến dạng kết hợp cho phần tử vỏ phẳng DGS3 để phân tích tĩnh và dao động tự do các kết cấu vỏ đồng nhất theo lý thuyết biến dạng cắt bậc nhất [18]. Kết quả nghiên cứu cho thấy phần tử sử dụng phương pháp làm trơn biến dạng kết hợp có kết quả nằm giữa kết quả của phần tử chỉ sử dụng một phương pháp làm trơn biến dạng trên cạnh hoặc trên nút.…”

Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method

“…in which T is the transformation matrix between the local coordinate system Oxyz and the global coordinate systemÔxŷẑ [14].…”

“…in which Λ k m1 , Λ k b1 , and Λ k s1 are strain transformation matrices between the global coordinate systemÔxŷẑ and the virtual coordinate system O x y z, respectively; Λ i m2 , Λ i b2 and Λ i s2 are the strain transformation matrices between the local coordinate system Oxyz of ith adjacent triangular elements and the virtual coordinate system O x y z, respectively; T i j is the transformation matrix between the local coordinate system Oxyz at the jth node of the ith adjacent triangular element and the global coordinate systemÔxŷẑ. More detailed information about these strain transformation matrices can be found in [14]. The area A k of the smoothing domain Ω k is computed by…”

A Smoothed Finite Element‐Based Elasticity Model for Soft Bodies

“…Similar to ES-FEM, the FS-FEM is more accurate than the standard FEM using the same T4 mesh for dynamic problems [39] and both linear and nonlinear problems [36]. Because of its excellent properties, S-FEM has been applied to a wide range of practical mechanics problems such as fracture mechanics and fatigue behavior [40][41][42][43], nonlinear material behavior analysis [35,38,[44][45][46][47][48], plates and shells [49][50][51][52], piezoelectric structures [43,[53][54][55], heat transfer and thermomechanical problems [56][57][58][59], vibration analysis and acoustics problems [39,58,[60][61][62], and fluid and structure interaction problems [63][64][65][66]. We refer the reader to [67,68] for recent in-depth reviews of S-FEM.…”