scholarly journals A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Yadong Xu ◽  
Guangsong Chen ◽  
Jinsong Tang
Keyword(s):  
Variational Principle ◽  
Free Vibration ◽  
Weak Form ◽  
Stable Node ◽  
Shear Locking ◽  
Numerical Examples ◽  
System Equations ◽  
Triangular Elements ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking

In this paper, a gradient stable node-based smoothed discrete shear gap method (GS-DSG) using 3-node triangular elements is presented for Reissner–Mindlin plates in elastic-static, free vibration, and buckling analyses fields. By applying the smoothed Galerkin weak form, the discretized system equations are obtained. In order to carry out the smoothing operation and numerical integration, the smoothing domain associated with each node is defined. The modified smoothed strain with gradient information is derived from the Hu–Washizu three-field variational principle, resulting in the stabilization terms in the system equations. The stabilized discrete shear gap method is also applied to avoid transverse shear-locking problem. Several numerical examples are provided to illustrate the accuracy and effectiveness. The results demonstrate that the presented method is free of shear locking and can overcome the temporal instability issues, simultaneously obtaining excellent solutions.

A Parametric Study for Four Node Bilinear EAS Shell Elements

2010 ◽  
Vol 26 (4) ◽  
pp. 431-438
Author(s):  
Cengiz Polat
Keyword(s):  
Variational Principle ◽  
Transverse Shear ◽  
Strain Field ◽  
Shell Element ◽  
Shell Structures ◽  
Shear Locking ◽  
Shell Elements ◽  
Assumed Strain ◽  
Dependent Strain ◽  
Transverse Shear Locking

ABSTRACTA locking free formulation of 4-node bilinear shell element and its application to shell structures is demonstrated. The Enhanced Assumed Strain (EAS) method based on three-field variational principle of Hu-Washizu is used in the formulation. Transverse shear locking and membrane locking are circumvented by means of enhancing the displacement-dependent strain field with extra assumed strain field. Several benchmark shell problems are analyzed.

Static and Free Vibration Analysis of Stiffened Flat Shells by a Cell-Based Smoothed Discrete Shear Gap Method (CS-FEM-DSG3) Using Three-Node Triangular Elements

2018 ◽  
Vol 15 (06) ◽  
pp. 1850056 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Bui-Xuan ◽  
G. R. Liu ◽  
T. Vo-Duy
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Triangular Element ◽  
Plate Element ◽  
Smoothing Technique ◽  
A Cell ◽  
Triangular Elements ◽  
Discrete Shear Gap

A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular element was recently proposed for static, free vibration and buckling analyses of stiffened Mindlin plates. The CS-FEM-DSG3 element is a significant improvement of the original DSG3 element by using smoothing technique to soften the stiffness of the DSG3 element while it has still inherited the locking-free feature of the former. In this paper, the CS-FEM-DSG3 is further extended for the static and free vibration analyses of stiffened flat shells by combining the original plate element CS-FEM-DSG3 with Allman’s plane stress element and a linearly isotropic two-node stiffened beam element. The compatibility of displacement field of stiffeners and shell is applied at the contact positions. Numerical results of the proposed element are compared with those of some existing methods to demonstrate the accuracy and reliability of the proposed method.

MESHFREE CELL-BASED SMOOTHED POINT INTERPOLATION METHOD USING ISOPARAMETRIC PIM SHAPE FUNCTIONS AND CONDENSED RPIM SHAPE FUNCTIONS

2011 ◽  
Vol 08 (04) ◽  
pp. 705-730 ◽  
Author(s):  
G. Y. ZHANG ◽  
G. R. LIU
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Shape Functions ◽  
Generalized Gradient ◽  
Singularity Problem ◽  
Numerical Examples ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
System Equations ◽  
Gradient Smoothing

This paper presents two novel and effective cell-based smoothed point interpolation methods (CS-PIM) using isoparametric PIM (PIM-Iso) shape functions and condensed radial PIM (RPIM-Cd) shape functions respectively. These two types of PIM shape functions can successfully overcome the singularity problem occurred in the process of creating PIM shape functions and make the constructed CS-PIM models work well with the three-node triangular meshes. Smoothed strains are obtained by performing the generalized gradient smoothing operation over each triangular background cells, because the nodal PIM shape functions can be discontinuous. The generalized smoothed Galerkin (GS-Galerkin) weakform is used to create the discretized system equations. Some numerical examples are studied to examine various properties of the present methods in terms of accuracy, convergence, and computational efficiency.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

2019 ◽  
Vol 17 (03) ◽  
pp. 1850133 ◽  
Author(s):  
T. Truong-Thi ◽  
T. Vo-Duy ◽  
V. Ho-Huu ◽  
T. Nguyen-Thoi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Numerical Solutions ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Discrete Shear Gap

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

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