The energy orthogonal relation between conforming and non-conforming displacements of triangular element

1999 ◽  
Vol 20 (6) ◽  
pp. 660-665
Author(s):  
Nie Yufeng ◽  
Zhou Tianxiao ◽  
Nie Tiejun
Keyword(s):  
Triangular Element ◽  
Orthogonal Relation

Damping analysis of composite plates with zig-zag triangular element

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1211-1219
Author(s):  
D. G. Lee ◽  
J. B. Kosmatka
Keyword(s):  
Composite Plates ◽  
Triangular Element

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

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.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Numerical Study on Progressive Failure of the Marble Plate Based on the Thin-Layer Tri-Node Jointed Element

2011 ◽  
Vol 255-260 ◽  
pp. 1867-1872
Author(s):  
Jing Hua Qi ◽  
Zhen Nan Zhang ◽  
Xiu Run Ge
Keyword(s):  
Crack Propagation ◽  
Thin Layer ◽  
Numerical Study ◽  
Progressive Failure ◽  
Triangular Element ◽  
Compressive Loads ◽  
Joint Element ◽  
The Common ◽  
Edge Cracks ◽  
Good Agreement

In order to model the mechanical behavior of joints efficiently, a thin-layer tri-node joint element is constructed. The stiffness matrix of the element is derived in the paper. For it shares the common nodes with the original tri-node triangle element, the tri-node joint element can be applied to model the crack propagation without remeshing or mesh adjustment. Another advantage is that the cracked body is meshed without consideration of its geometry integrity and existence of the joints or pre-existed crack in the procedure of mesh generation, and then the triangular element intersected by the crack or joint is automatically transformed into the tri-node joint element to represent pre-existed cracks. These make the numerical simulation of crack propagation highly convenient and efficient. After CZM is chosen to model the crack tip, the mixed- energy simple criterion is used to determine whether the element is intersected by the extended crack or not, the extended crack is located in the model. By modeling the marble plates with two edge cracks subjected to the uniaxial compressive loads, it is shown that the numerical results are in good agreement with the experimental results, which suggests that the present method is valid and feasible in modeling rock crack propagation.

scholarly journals Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity

2018 ◽  
Vol 2 (7) ◽  
pp. 075007 ◽  
Author(s):  
Kyu-Won Park ◽  
Songky Moon ◽  
Hyunseok Jeong ◽  
Jaewan Kim ◽  
Kabgyun Jeong
Keyword(s):  
Orthogonal Relation
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