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.

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.

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded
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