Using the exact element method and modal frequency changes to identify distributed damage in beams

2013 ◽  
Vol 51 ◽  
pp. 60-72 ◽  
Author(s):  
Yiska Goldfeld ◽  
Dikla Elias
Keyword(s):  
Modal Frequency ◽  
Exact Element Method ◽  
Frequency Changes ◽  
Element Method

scholarly journals GBT-Based Buckling Analysis Using the Exact Element Method

2017 ◽  
Vol 17 (10) ◽  
pp. 1750125 ◽  
Author(s):  
Rui Bebiano ◽  
Moshe Eisenberger ◽  
Dinar Camotim ◽  
Rodrigo Gonçalves
Keyword(s):  
Finite Elements ◽  
Beam Theory ◽  
Computational Effort ◽  
Power Series Method ◽  
Half Wave ◽  
Governing Differential Equation ◽  
Exact Element Method ◽  
Deformation Modes ◽  
Element Method

Generalized Beam Theory (GBT), intended to analyze the structural behavior of prismatic thin-walled members and structural systems, expresses the member deformed configuration as a combination of cross-section deformation modes multiplied by the corresponding longitudinal amplitude functions. The determination of the latter, usually the most computer-intensive step of the analysis, is almost always performed by means of GBT-based conventional 1D (beam) finite elements. This paper presents the formulation, implementation and application of the so-called “exact element method” in the framework of GBT-based linear buckling analyses. This method, originally proposed by Eisenberger (1990), uses the power series method to solve the governing differential equation and obtains the buckling eigenvalue problem from the boundary terms. A few illustrative numerical examples are presented, focusing mainly on the comparison between the combined accuracy and computational effort associated with the determination of buckling solutions with the exact and standard GBT-based (finite) elements. This comparison shows that the GBT-based exact element method may lead to significant computational savings, particularly when the buckling modes exhibit larger half-wave numbers.

GBT-Based Vibration Analysis Using the Exact Element Method

2018 ◽  
Vol 18 (05) ◽  
pp. 1850068 ◽  
Author(s):  
Rui Bebiano ◽  
Moshe Eisenberger ◽  
Dinar Camotim ◽  
Rodrigo Gonçalves
Keyword(s):  
Finite Elements ◽  
Beam Theory ◽  
Computational Effort ◽  
Power Series Method ◽  
Half Wave ◽  
Exact Element Method ◽  
Deformation Modes ◽  
Generalized Beam Theory ◽  
Element Method

Generalized Beam Theory (GBT), intended to analyze the structural behavior of prismatic thin-walled members and structural systems, expresses the member deformed configuration as a combination of cross-section deformation modes multiplied by the corresponding longitudinal amplitude functions. The determination of the latter, often the most computer-intensive step of the analysis, is almost always performed by means of GBT-based “conventional” 1D (beam) finite elements. This paper presents the formulation, implementation and application of the so-called “exact element method” in the framework of GBT-based elastic free vibration analyses. This technique, originally proposed by Eisenberger (1990), uses the power series method to solve the governing differential equations and obtains the vibration eigenvalue problem from the boundary terms. A few illustrative numerical examples are presented, focusing mainly on the comparison between the combined accuracy and computational effort associated with the determination of vibration solutions with the exact and conventional GBT-based (finite) elements. This comparison shows that the GBT-based exact element method may lead to significant computational savings, particularly when the vibration modes exhibit large half-wave numbers.

An exact element method for plane problem

1990 ◽  
Vol 11 (5) ◽  
pp. 413-420
Author(s):  
Yeh Kai-yuan ◽  
Ji Zhen-yi
Keyword(s):  
Plane Problem ◽  
Exact Element Method ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document