A Hybrid Finite Element Method for Calculating the Vibration of Co-Linear Beams in the Mid-Frequency Range

1999 ◽  
Author(s):  
Xi Zhao ◽  
Nickolas Vlahopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Theoretical Development ◽  
Frequency Range ◽  
Element Analysis ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
New Formulation ◽  
Element Method

Abstract The theoretical development of a hybrid finite element method is presented. It combines conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) in order to achieve a numerical solution to mid-frequency vibrations. In the mid-frequency range a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths. The former are considered long members and they are modeled by the EFEA. The latter are considered short and they are modeled by the FEA. The new formulation is based on deriving appropriate interface conditions at the joints between sections modeled by the EFEA and the FEA methods. Since the work presented in this paper constitutes a fundamental step in the development of a hybrid method for mid-frequency analysis, the formulation for one flexural degree of freedom in co-linear beams is presented. The excitation is considered to be applied on a long member and the response of the entire system is computed. Uncertainty effects are imposed only on the long members of the system. Validation cases for several configurations are presented.

A Hybrid Finite Element Formulation for Mid-Frequency Analysis of Systems With Excitation Applied on Short Members

2000 ◽  
Author(s):  
Xi Zhao ◽  
Nickolas Vlahopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Input Power ◽  
Element Formulation ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Element Method

Abstract A hybrid finite element method for computing mid-frequency vibrations is presented. In the mid-frequency region a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths within their dimensions. The former are considered long members and they are modeled by the Energy Finite Element Analysis (EFEA). The latter are considered short and they are modeled by the Finite Element Analysis (FEA). In this paper the excitation is considered to be applied on the short members. The hybrid formulation computes the response of the entire system. The characteristics of the long members affect the behavior of the short members and the amount of power flow between the members of the system. The resonant characteristics of the short members and the boundary conditions imposed by the long members determine the amount of input power into the system. The interaction between members is described by a set of equations between the FEA and the EFEA primary variables at the interfaces between long and short members. The equations for the short and the long members and the interface equations are solved simultaneously. A theoretical formulation and a numerical implementation for systems that contain one wave type is presented. Analytical solutions for several co-linear beam configurations are compared to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses.

Brain Tissue Fragility–A Finite Strain Analysis by a Hybrid Finite-Element Method

1975 ◽  
Vol 42 (2) ◽  
pp. 269-273 ◽  
Author(s):  
S. N. Atluri ◽  
A. S. Kobayashi ◽  
J. S. Cheng
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Exposed Surface ◽  
Element Analysis ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element

This paper deals with the finite-strain, finite-element analysis of the states of stress and strain in the vicinity of a blunt indenter applied to the exposed surface of the pia-arachnoid of an anesthetized rhesus monkey.

An Approach to Teaching the Finite Element Method That Uses Best Practice Techniques From Industry

2016 ◽  
Author(s):  
Michael W. Sracic
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Best Practice ◽  
Theoretical Development ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Course Structure ◽  
Approach To Teaching ◽  
Element Method

Finite element analysis has become an essential part of the formal design process since it can be used to verify the functionality and life of design components in their loading environments. For large engineering firms with numerous analysts that have varying years of experience, it can be challenging to ensure that analysis results are accurate and free of modeling errors. A finite element analysis checklist (FEA Checklist) can be used as a desktop tool to provide an auditing procedure that each analyst has to follow to prove to both supervisors and, more importantly, customers that the finite element models were created and solved correctly such that the results can be trusted. In this work, an approach to teaching an introduction to the finite element method for undergraduates is proposed. The proposed course structure includes lectures for theoretical development, where the theory is developed using familiar undergraduate mechanics and mathematics concepts, and a computational practicum, where the practicum uses approaches based on industry finite element analysis techniques. In the computational practicum, students are tasked with using a finite element analysis checklist to complete all of their analysis projects. During a recent offering of the course, the students were anonymously surveyed regarding the utility of the finite element analysis checklist. 100% of the students agreed that the checklist provided a useful tool to help them understand and execute the finite element method, and nearly half of them agreed strongly.

Tire Cornering Simulation Using an Explicit Finite Element Analysis Code

1998 ◽  
Vol 26 (2) ◽  
pp. 109-119 ◽  
Author(s):  
M. Koishi ◽  
K. Kabe ◽  
M. Shiratori
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Test System ◽  
Experimental Results ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Element Method

Abstract The finite element method has been used widely in tire engineering. Most tire simulations using the finite element method are static analyses, because tires are very complex nonlinear structures. Recently, transient phenomena have been studied with explicit finite element analysis codes. In this paper, the authors demonstrate the feasibility of tire cornering simulation using an explicit finite element code, PAM-SHOCK. First, we propose the cornering simulation using the explicit finite element analysis code. To demonstrate the efficiency of the proposed simulation, computed cornering forces for a 175SR14 tire are compared with experimental results from an MTS Flat-Trac Tire Test System. The computed cornering forces agree well with experimental results. After that, parametric studies are conducted by using the proposed simulation.

scholarly journals Modelling Plates and Shells by Means of the Rigid Finite Element Method

2015 ◽  
Vol 62 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Andrzej Nowak ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibrations ◽  
The Finite Element Method ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Rigid Finite Element Method ◽  
Plates And Shells ◽  
Single Set ◽  
Element Method

Abstract The rigid finite element method (RFEM) has been used mainly for modelling systems with beam-like links. This paper deals with modelling of a single set of electrodes consisting of an upper beam with electrodes, which are shells with complicated shapes, and an anvil beam. Discretisation of the whole system, both the beams and the electrodes, is carried out by means of the rigid finite element method. The results of calculations concerned with free vibrations of the plates are compared with those obtained from a commercial package of the finite element method (FEM), while forced vibrations of the set of electrodes are compared with those obtained by means of the hybrid finite element method (HFEM) and experimental measurements obtained on a special test stand.

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