Practical Applications of Scale Independent Elements

1995 ◽  
Author(s):  
Mohammed M. Ettouney ◽  
Raymond P. Daddazio ◽  
Najib N. Abboud
Keyword(s):  
Finite Element ◽  
Energy Methods ◽  
Great Flexibility ◽  
New Approach ◽  
Practical Applications ◽  
Deterministic Methods ◽  
Computer Resources ◽  
Single Coordinate ◽  
General Method ◽  
Vibrating Systems

Abstract Discrete deterministic methods such as finite elements offer great flexibility in analyzing the dynamic response of vibrating systems. However, these methods can easily grow beyond available computer resources as frequencies of interest grow higher. In this paper we present a new approach for the frequency domain dynamic analysis of structures. A theory is developed for the analysis of systems which are uniform along a single coordinate axis but otherwise arbitrary in geometry and material composition. This approach, termed the Scale Independent Element, is shown to be an accurate, efficient and general method for the analysis of vibrating systems. This technique extends the applicability of discrete deterministic finite element based modeling to higher frequencies and is capable of bridging the gap to frequency regimes where statistical energy methods become applicable.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Application of QR Method for Analysis of Spatial-Mega Frame Structure

2011 ◽  
Vol 243-249 ◽  
pp. 6049-6052
Author(s):  
Wen Jun Pan ◽  
Xian Guo Ye ◽  
Lei Chang
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Reliable Method ◽  
Frame Structure ◽  
New Approach ◽  
Nodal Displacement ◽  
Simplified Calculation ◽  
Node Displacement

With the generalized displacement parameters of spline knots chosen as basic unknowns, the node displacement functions of spatial mega frames were built up, then element node displacements could be expressed by these parameters. New stiffness equation of spatial mega frame was deduced according to energy variational principle. The nodal displacement and nodal forces were worked out by the displacement parameters of spline knots. Process of block assembling for spline-discretization matrix was introduced briefly. One spatial mega frame was calculated by QR method and different finite element softwares. Comparation among the results and those of references proves that QR method is exactly an economical, effective and reliable method for computation of spatial mega frames. It provides a new approach for simplified calculation to spatial mega structures, so has good theoretical and practical value.

The Flattening Behaviour of Angle Section Beams Subjected to Pure Bending

2014 ◽  
Vol 501-504 ◽  
pp. 2479-2483
Author(s):  
Wei Bin Yuan ◽  
Chang Yi Chen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Analytical Solutions ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Experimental Results ◽  
Energy Methods ◽  
Pure Bending ◽  
Angle Section ◽  
Nonlinear Finite Element Model

The flattening behaviour of angle section beams subjected to pure bending is studied in this paper. Analytical solutions for static instabilities of angle section beams subjected to pure bending about its weak axis are derived using energy methods. Nonlinear finite element model using the code ANSYS is developed to simulate nonlinear snap-through instability of angle section beams under pure bending. The optimization assumption about flattening shape of the leg is proposed, through comparison of between the present solutions, experimental results, and the finite element results.

A Size-Dependent Coupled Symplectic and Finite Element Method for Steady-State Forced Vibration of Built-Up Nanobeam Systems

2019 ◽  
Vol 19 (07) ◽  
pp. 1950081 ◽  
Author(s):  
Zhenhuan Zhou ◽  
Junhai Fan ◽  
C. W. Lim ◽  
Dalun Rong ◽  
Xinsheng Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
New Approach ◽  
Size Dependent ◽  
Numerical Result ◽  
Proper Comparison ◽  
Element Method

A novel size-dependent coupled symplectic and finite element method (FEM) is proposed to study the steady-state forced vibration of built-up nanobeam system resting on elastic foundations. The overall system is modeled as a combination of nonlocal Timoshenko beams. A new analytical subsystem modeling with formulation and another numerical subsystem modeling are developed and discussed. In the analytical subsystem model, the uniform nanobeams are modeled and solved by a new approach based on a series of analytical symplectic eigensolutions. The numerical subsystem model applies a nonlocal FEM to solve nonuniform nanobeams. Analytical and numerical solutions are presented, and a proper comparison between the two approaches is established. Comprehensive and accurate numerical result is subsequently presented to illustrate the accuracy and reliability of the coupled method. The new results established are expected to have reference values for future studies.

scholarly journals Bolt-Grout Interactions in Elastoplastic Rock Mass Using Coupled FEM-FDM Techniques

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Debasis Deb ◽  
Kamal C. Das
Keyword(s):  
Finite Element ◽  
Rock Mass ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Experimental Validation ◽  
Yield Criterion ◽  
Numerical Procedure ◽  
Practical Applications ◽  
Finite Element Procedure

Numerical procedure based on finite element method (FEM) and finite difference method (FDM) for the analysis of bolt-grout interactions are introduced in this paper. The finite element procedure incorporates elasto-plastic concepts with Hoek and Brown yield criterion and has been applied for rock mass. Bolt-grout interactions are evaluated based on finite difference method and are embedded in the elasto-plastic procedures of FEM. The experimental validation of the proposed FEM-FDM procedures and numerical examples of a bolted tunnel are provided to demonstrate the efficacy of the proposed method for practical applications.

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