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

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.

scholarly journals The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ge Tian ◽  
Xiang-Rong Fu ◽  
Ming-Wu Yuan ◽  
Meng-Yan Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Problem ◽  
Efficient Method ◽  
Complex Variables ◽  
Numerical Examples ◽  
Element Method

This paper presents a novel way to calculate the characteristic solutions of the anisotropy V-notch plane problem. The material eigen equation of the anisotropy based on the Stroh theory and the boundary eigen equation of the V-notch plane problem are studied separately. A modified Müller method is utilized to calculate characteristic solutions of anisotropy V-notch plane problem, which are employed to formulate the analytical trial functions (ATF) in the associated finite element method. The numerical examples show that the proposed subregion accelerated Müller method is an efficient method to calculate the solutions of the equation involving the complex variables. The proposed element ATF-VN based on the analytical trial functions, which contain the characteristic solutions of the anisotropy V-notch problem, presents good performance in the benchmarks.

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