A high-order three-dimensional numerical manifold method enriched with derivative degrees of freedom

2017 ◽  
Vol 83 ◽  
pp. 229-241 ◽  
Author(s):  
Huo Fan ◽  
Jidong Zhao ◽  
Hong Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
High Order ◽  
Numerical Manifold Method ◽  
Numerical Manifold

Novel Insight into High-Order Numerical Manifold Method Using Complex Fourier Element Shape Functions in Statics and Dynamics

2019 ◽  
Vol 11 (06) ◽  
pp. 1950058
Author(s):  
M. Malekzadeh ◽  
S. Hamzehei-Javaran ◽  
S. Shojaee
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
High Order ◽  
Numerical Manifold Method ◽  
Shape Functions ◽  
Linear Complex ◽  
Statics And Dynamics ◽  
Vibration Problems ◽  
Numerical Manifold ◽  
Discontinuous Problems

In this paper, the high-order numerical manifold method (HONMM) with new complex Fourier shape functions is developed for the simulation of elastostatic and elastodynamic problems. NMM uses two separate covers which give it the ability to analyze continuous and discontinuous problems in a unified way. The new shape functions are derived using constant and linear complex Fourier shape functions. These shape functions are able to satisfy exponential and trigonometric function fields in addition to polynomial ones, unlike classic Lagrange shape functions. Compared to the Lagrange shape functions, the proposed shape functions show much more accurate results with fewer degrees of freedom. The superiority of the proposed method over the conventional HONMM in static analysis is demonstrated through a special beam example. As cases of dynamic analysis, four free and forced vibration problems are illustrated. The results of the HONMM with the use of constant and linear complex Fourier shape functions are compared with the classic HONMM results and available analytical and other numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic HONMM.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Theoretical study of three-dimensional numerical manifold method

2005 ◽  
Vol 26 (9) ◽  
pp. 1126-1131 ◽  
Author(s):  
Luo Shao-ming ◽  
Zhang Xiang-wei ◽  
Lü Wen-ge ◽  
Jiang Dong-ru
Keyword(s):  
Theoretical Study ◽  
Three Dimensional ◽  
Numerical Manifold Method ◽  
Numerical Manifold

Research on Fault Cutting Algorithm of the Three-Dimensional Numerical Manifold Method

2017 ◽  
Vol 17 (5) ◽  
Author(s):  
Yanqiang Wu ◽  
Guangqi Chen ◽  
Zaisen Jiang ◽  
Long Zhang ◽  
Hong Zhang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Numerical Manifold Method ◽  
Cutting Algorithm ◽  
Numerical Manifold

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.

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