scholarly journals Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xin Qu ◽  
Lijun Su ◽  
Zhijun Liu ◽  
Xingqian Xu ◽  
Fangfang Diao ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Displacement Function ◽  
Thin Plates ◽  
Irregular Domain ◽  
Interpolation Accuracy ◽  
Mixed Order ◽  
Convergence Performance ◽  
Nonconforming Elements ◽  
Numerical Manifold ◽  
Thin Plate Bending

As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM.

scholarly journals Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ding Jun ◽  
Chen Song ◽  
Wen Wei-Bin ◽  
Luo Shao-Ming ◽  
Huang Xia
Keyword(s):  
Dynamic Equation ◽  
Degrees Of Freedom ◽  
Solution Process ◽  
Thin Plates ◽  
Numerical Manifold Method ◽  
Bending Vibration ◽  
Linear Elastic ◽  
Spline Basis ◽  
Generalized Degrees Of Freedom ◽  
Numerical Manifold

A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method.

On Improved Thin Plate Bending Rectangular Finite Element Based on the Strain Approach

2016 ◽  
Vol 27 ◽  
pp. 76-86 ◽  
Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Djamal Hamadi
Keyword(s):  
Finite Element ◽  
Thin Plate ◽  
Degrees Of Freedom ◽  
Body Motion ◽  
Thin Plates ◽  
Elastic Behavior ◽  
Transverse Displacement ◽  
Plate Bending ◽  
Linear Elastic ◽  
Thin Plate Bending

We propose in this paper the development of a new rectangular finite element for thin plate bending based on the strain approach with linear elastic behavior. An analytical integration is used to evaluate the element stiffness matrix. The present element possesses the three main degrees of freedom (d.o.f) per node, namely, one transverse displacement (w) and two normal rotations about x and y axis respectively (Ɵx, Ɵy). The proposed displacement field represents exactly the rigid body motion and satisfies the compatibility equations. The numerical results converges rapidly to the Kirchhoff solution for thin plates, this makes the present element robust, better suitable for computations, and particularly interesting in modeling this type of structures.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

The Transverse Shear Effect of a New Plate Bending Finite Element Based on the Strain Approach

2018 ◽  
Vol 35 ◽  
pp. 1-10
Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Djamal Hamadi
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Plate Bending ◽  
Shear Effect ◽  
Thin Plate Bending ◽  
Kirchhoff Theory ◽  
Three Degrees Of Freedom

In this paper, we present a comparative study of the transverse shear effect on the plate bending. The element used is a rectangular finite element called SBRPK (Strain Based Rectangular Plate-Kirchhoff Theory-), it used for the numerical analysis of thin plate bending, and it based on the strain approach. This element has four nodes and three degrees of freedom per node (w, θx, θy). Through the numerical applications with different loading cases and boundary conditions; the numerical results obtained are in close agreement with the analytical solution.

NONLINEAR THIN-PLATE BENDING ANALYSES USING THE HERMITE REPRODUCING KERNEL APPROXIMATION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240012 ◽  
Author(s):  
SATOYUKI TANAKA ◽  
SHOTA SADAMOTO ◽  
SHIGENOBU OKAZAWA
Keyword(s):  
Thin Plate ◽  
Reproducing Kernel ◽  
Geometrical Nonlinearity ◽  
Mathematical Formulation ◽  
Thin Plates ◽  
Plate Bending ◽  
Kernel Approximation ◽  
Hermite Reproducing Kernel Approximation ◽  
Lagrange Strain ◽  
Thin Plate Bending

This study analyzed thin-plate bending problems with a geometrical nonlinearity using the Hermite reproducing kernel approximation and sub-domain-stabilized conforming integration. In thin-plate bending analyses, the deflections and rotations satisfy so-called Kirchhoff mode reproducing conditions. It is then possible to solve large deflection analyses of thin plates, such as elastic bucking problems, with high accuracy and efficiency. Total Lagrangian method is applied to solve the geometrical nonlinearity of the thin plates' deflections and rotations. The Green–Lagrange strain and second Piola–Kirchhoff stress forms are adopted to represent the strains and stresses in the thin plates. Mathematical formulation and some numerical examples are also demonstrated.

Smooth 3D manifolds based on thin plates

2016 ◽  
Vol 22 (3) ◽  
pp. 477-490
Author(s):  
VA Grachev ◽  
YS Neustadt
Keyword(s):  
Degrees Of Freedom ◽  
3D Structure ◽  
Three Dimensional ◽  
Small Diameter ◽  
Thin Plates ◽  
Mechanics Of Solids ◽  
Dimensional Manifold ◽  
Initial State ◽  
Rigid Plastic ◽  
Definition Of

This paper demonstrates a fractal system of thin plates connected with hinges. The system can be studied using the methods of the mechanics of solids with internal degrees of freedom. The structure is deployable, and initially, it is similar to a small-diameter one-dimensional manifold, which occupies significant volume after deployment. The geometry of solids is studied using the method of the moving hedron. The relationships enabling the definition of the geometry of the introduced manifolds are derived based on the Cartan structure equations. The proof substantially makes use of the fact that the fractal consists of thin plates that are not long compared to the sizes of the system. The mechanics are described for solids with rigid plastic hinges between the plates, and the hinges are made of shape memory material. Based on the ultimate load theorems, estimates are performed to specify the internal pressure that is required to deploy the package into a three-dimensional (3D) structure and the heat input needed to return the system into its initial state. Some possible applications of the smooth 3D manifolds are demonstrated.

The Transverse Shear Effect of a New Strain Based Sector Finite Elements for Plate Bending Problems

2020 ◽  
Vol 50 ◽  
pp. 103-112
Author(s):  
Sifeddine Abderrahmani
Keyword(s):  
Finite Element ◽  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Plate Bending ◽  
Shear Effect ◽  
Sector Plate ◽  
Bending Problems ◽  
Thin Plate Bending ◽  
Kirchhoff Theory ◽  
Three Degrees Of Freedom

In this paper, we present the transverse shear effect on the plate bending. The element used is a sector finite element called SBSP (Strain Based Sector Plate-Kirchhoff Theory-), it used for the numerical analysis of circular thin plate bending., and it based on the strain approach. This element has four nodes and three degrees of freedom per node. Through the numerical applications with different loading cases and boundary conditions; This makes the present element robust, better suitable for computations.

OPTIMAL NODE LOCATION IN TRIANGULAR PLATE BENDING ELEMENTS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350075 ◽  
Author(s):  
MOHAMMAD REZAIEE-PAJAND ◽  
MOHAMMAD KARKON
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Tests ◽  
Optimal Node ◽  
Node Location ◽  
Triangular Elements ◽  
Plate Analysis ◽  
Nonconforming Elements ◽  
Bending Plates ◽  
Element Shape ◽  
Better Than

Many triangular elements have been formulated for bending plate analysis so far. In this type of element, researchers generally considered the same distance between the side nodes. The present study will show that these types of node locations are not the best. To clarify the effect of side node locations, three new triangular elements will be formulated for the analysis of thin bending plates. These are nonconforming elements and have 10, 15, and 21 degrees of freedom, respectively. Merits and disadvantages of these proposed elements will be revealed by solving different structures. Optimal side nodes' location will be positioned by changing the place of element nodes. Numerical tests will confirm that element accuracy in the best possible situation is much better than the state in which side nodes have the same distance. Moreover, this study will reveal that the presented optimal locations of nodes have no significant dependence on the load cases, boundary conditions, distortion of element shape, and variation of the meshes.

Docetaxel (Taxotere® Trihydrate) Forms: Crystal Structure Determination from XRPD & XRSCD Data

2004 ◽  
Vol 443-444 ◽  
pp. 411-0 ◽  
Author(s):  
L. Zaske ◽  
M.-A. Perrin ◽  
C. Daiguebonne ◽  
O. Guillou
Keyword(s):  
Crystal Structure ◽  
Crystal Growth ◽  
Degrees Of Freedom ◽  
Atomic Scale ◽  
Thin Plates ◽  
Water Molecules ◽  
Ambient Conditions ◽  
Strong Anisotropy ◽  
Growth Study ◽  
Space Method

Docetaxel (form A), a stoichiometric hydrate containing three water molecules per molecule of drug substance (Taxotere®), is thermodynamically stable under ambient conditions of pressure, temperature and relative humidity. In order to gain a better understanding of docetaxel system at the atomic scale a structural study was performed. Due to strong anisotropy of crystals (thin plates), the crystal structure of docetaxel (29 degrees of freedom) was solved and refined using high resolution XRPD data applying an ab initio direct space method. In parallel, an in-depth crystal growth study was carried out until single crystals suitable for XRSCD structural resolution were obtained: surprisingly, a new polymorph of docetaxel, called form B, was isolated.

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