Finite Element Modeling of Dynamic Behavior of Some Basic Structural Members

1992 ◽  
Vol 114 (1) ◽  
pp. 3-9 ◽  
Author(s):  
R. C. Engels
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Modeling ◽  
Mass Matrix ◽  
Matrix Approach ◽  
Structural Members ◽  
Shape Functions ◽  
Generalized Coordinates ◽  
Stiffness Matrices ◽  
Consistent Mass Matrix

A method is described to model the dynamics of finite elements. The assumed modes method is used to show how static shape functions approximate the element mass distribution. The deterioration of the modal content of a model can be linked to the neglect of interface restrained assumed modes. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates compared to the standard consistent mass matrix approach. Also, no need exists for subdivision of basic elements such as rods and beams. The mass and stiffness matrices for several basic elements are derived and used in demonstration problems.

Analysis of Dynamic Response for Piezoelectric Vibration Converter by Finite Element Simulation

2007 ◽  
Vol 336-338 ◽  
pp. 335-337
Author(s):  
Xiang Cheng Chu ◽  
Ren Bo Yan ◽  
Wen Gong ◽  
Long Tu Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Dynamic Response ◽  
Finite Element Modeling ◽  
Three Dimensions ◽  
Dynamic Motion ◽  
Element Simulation ◽  
Piezoelectric Coupling ◽  
Piezoelectric Vibration

The dynamic behavior of a vibration converter of an ultrasonic motor is described using finite element method. Tetrahedral finite elements with three dimensions are formulated with the effects of piezoelectric coupling. And the solution of the coupled electroelastic equations of dynamic motion is presented. The simulated response of the vibration converter is calculated, and shows excellent consistency with experimental results, which proved that finite element modeling is a good approach to optimize piezoelectric apparatus design. A gradual optimized method is employed to ascertain the most compatible structure.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Karin Nachbagauer ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Continuum Mechanics ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Finite Element Software ◽  
High Order Convergence ◽  
Dynamics Problems ◽  
Transverse Slope ◽  
Shear Deformable

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

scholarly journals Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping

2007 ◽  
Vol 17 (3) ◽  
pp. 375-393 ◽  
Author(s):  
Sébastien Jund ◽  
Stéphanie Salmon
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Elements ◽  
Taylor Expansion ◽  
High Order ◽  
Computational Time ◽  
Mass Lumping ◽  
Stiffness Matrices ◽  
High Order Time ◽  
Finite Element Schemes

Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of orderkand show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up toP5elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

New Insight Into Viscoelastic Finite Element Modeling of Time-Dependent Material Creep Problems Using Spherical Hankel Element Framework

2018 ◽  
Vol 10 (08) ◽  
pp. 1850085 ◽  
Author(s):  
M. Bahrampour ◽  
S. Hamzeh Javaran ◽  
S. Shojaee
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Finite Element Modeling ◽  
Degrees Of Freedom ◽  
Shape Functions ◽  
Element Modeling ◽  
Hankel Functions ◽  
Material Creep ◽  
New Formulation ◽  
Insight Into

In this study, a new formulation of finite element method (FEM) has been extracted to analyze 2D viscoelastic problems. As there has not been enough accuracy and not sufficient literature in classical finite element modeling of viscoelastic problems, using a new set of shape functions founded on radial basis functions (RBFs) is recommended. Applying these new, RBF-based shape functions instead of the classical Lagrangian ones, results in subtler answers and conducts a reconsideration over the usual numerical method. Hankel functions are chosen, enriched and summed up with polynomial terms. Therefore, they satisfy not only polynomial terms, but also the first- and second-order Bessel functions simultaneously; which, in the case of classic shape functions, happens only for the polynomial function field. This method illustrates an approach with faster convergence rate and better robustness in different manners. Hence, it is less time-consuming and economical. Finally, various numerical examples are provided for the comparison of analytical solution, classic FEM and Hankel-based FEM, which show the much better agreement of the proposed method with analytical solution in comparison to classic FEM. Also, the number of nodes and degrees of freedom are reduced noticeably while maintaining accuracy in the interpolation of the adopted procedure.

Frequency-Dependent Element Mass Matrices

1992 ◽  
Vol 59 (1) ◽  
pp. 136-139 ◽  
Author(s):  
N. J. Fergusson ◽  
W. D. Pilkey
Keyword(s):  
Stiffness Matrix ◽  
Shape Function ◽  
Mass Matrix ◽  
Power Series Expansion ◽  
Shape Functions ◽  
Frequency Dependent ◽  
Mass Matrices ◽  
The Matrix ◽  
Matrix Expansion ◽  
Consistent Mass Matrix

This paper considers some of the theoretical aspects of the formulation of frequency-dependent structural matrices. Two types of mass matrices are examined, the consistent mass matrix found by integrating frequency-dependent shape functions, and the mixed mass matrix found by integrating a frequency-dependent shape function against a static shape function. The coefficients in the power series expansion for the consistent mass matrix are found to be determinable from those in the expansion for the mixed mass matrix by multiplication by the appropriate constant. Both of the mass matrices are related in a similar manner to the coefficients in the frequency-dependent stiffness matrix expansion. A formulation is derived which allows one to calculate, using a shape function truncated at a given order, the mass matrix expansion truncated at twice that order. That is the terms for either of the two mass matrix expansions of order 2n are shown to be expressible using shape functions terms of order n. Finally, the terms in the matrix expansions are given by formulas which depend only on the values of the shape function terms at the boundary.

scholarly journals The Inf-Sup Condition Tests for Shell/Plate Finite Elements / Testy Warunku Inf-Sup Do Oceny Płytowych I Powłokowych Elementów Skonczonych

2011 ◽  
Vol 57 (4) ◽  
pp. 425-447 ◽  
Author(s):  
W. Gilewski ◽  
M. Sitek
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
High Performance ◽  
Point Of View ◽  
Numerical Verification ◽  
Shell Elements ◽  
Numerical Tests ◽  
Stiffness Matrices ◽  
Finite Element Technology ◽  
Selection Of

Abstract Development of high-performance finite elements for thick, moderately thick, as well as thin shells and plates, was one of the active areas of the finite element technology for 40 years, followed by hundreds of publications. A variety of shell elements exist in the FE codes, but “the best” finite element is still to be discovered. The paper deals with an evaluation of some existing shell finite elements, from the point of view of the third of three requirements to be satisfied by the element: ellipticity, consistency and inf-sup condition. It is difficult to prove the inf-sup condition analytically, so, a numerical verification is proposed. A set of numerical tests is considered for shell and plate problems. Two norm matrices and a selection of the stiffness matrices (bending, shear and membrane dominated) are analysed. Finite elements from various computer systems can be evaluated and compared with the use of the proposed tests.

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