US-FE-LSPIM TRI3 Element for Free Vibration Analysis

2012 ◽  
Vol 246-247 ◽  
pp. 1278-1282 ◽  
Author(s):  
Hui Hui Chen ◽  
Cheng Jia
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Shape Functions ◽  
The Individual ◽  
Element Shape

For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.

scholarly journals Buckling and Free Vibration Analysis of Laminated Sandwich Beams under Hygrothermal Conditions

2021 ◽  
Vol 2070 (1) ◽  
pp. 012170
Author(s):  
A Garg ◽  
S Gupta ◽  
HD Chalak
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Fourth Order ◽  
Vibration Analysis ◽  
Loading Condition ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Sandwich Beams ◽  
Proposed Model ◽  
Zigzag Theory

Abstract In present work, an attempt has been made for carrying out free vibration and buckling analysis of laminated sandwich beams under hygrothermal conditions. The analysis is carried out using fourth order zigzag theory based on finite element formulation. The efficiency of proposed model is validated by comparing the present results with those available in literature. Geometric properties and loading condition widely affect the behavior of the laminated sandwich beams.

FREE VIBRATION ANALYSIS OF ROTATING FLEXIBLE BEAMS BY USING THE FOURIER p-VERSION OF THE FINITE ELEMENT METHOD

2005 ◽  
Vol 02 (02) ◽  
pp. 255-269 ◽  
Author(s):  
S. M. HAMZA-CHERIF
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
P Element ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Flexible Beams ◽  
Element Method

A p-version of the finite element method is applied to free vibration analysis of rotating beams in conjunction with the modeling dynamic method using the arc-length stretch deformation. In this study the flexible and the rigid body degrees of freedom (d.o.f.) are supposedly uncoupled, the linear equations of motion are derived for flapwise and chordwise bending with the integration of the gyroscopic effect. The hybrid displacements are expressed as the combination of the in-plane and out-of-plane shape functions. These are formulated in terms of linear and cubic polynomial functions used generally in FEM in addition to a variable number of trigonometric shape functions which represent the internal d.o.f. for the rotating flexible beams. The convergence properties of the rotating beam Fourier p-element and the influence of angular speed, boundary conditions and slenderness ratio on the dynamic response are studied. It is shown that using this element the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effort.

An Efficient Three Nodded Finite Element Formulation for Free Vibration Analysis of Sandwich Arches with Graded Metallic Cellular Core

2020 ◽  
Vol 12 (06) ◽  
pp. 2050069
Author(s):  
Mohammad Amir ◽  
Mohammad Talha
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Finite Element Model ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Element Model ◽  
Element Formulation ◽  
Present Formulation ◽  
Porosity Coefficient

An efficient finite element model based on three nodded element has been developed for the vibration analysis of sandwich arches with graded metallic cellular (GMC) core. The present formulation is based on the higher-order shear deformation theory and orthogonal curvilinear coordinate axes. The arch consists of two isotropic face sheets and a GMC core layer. The internal pores in the core layer follow the different types of distributions. The material properties of the GMC core layer of the sandwich arches vary in the thickness direction as a function in terms of porosity coefficient and mass density. Three types of porosity distributions have been considered to accomplish the vibration responses of sandwich arches. The present formulation is validated with limited results available in the literature. Few new results are computed and the effects of different influencing parameters such as porosity coefficient [Formula: see text], porosity distribution type, the thickness-to-length ratio [Formula: see text], boundary conditions and opening angle [Formula: see text] on the free vibration characteristics of sandwich arches with the GMC core are observed. The present finite element model gives better convergence and more accurate results than a conventional two nodded element-based finite element model.

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