A finite element formulation based on an enhanced first order shear deformation theory for composite and sandwich structures

2008 ◽  
Vol 22 (5) ◽  
pp. 871-878 ◽  
Author(s):  
Jinho Oh ◽  
Maenghyo Cho ◽  
Jun-Sik Kim ◽  
Michel Grédiac
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Sandwich Structures ◽  
Shear Deformation Theory ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
First Order

A finite element–based assessment of free vibration behaviour of circular and annular magneto-electro-elastic plates using higher order shear deformation theory

2019 ◽  
Vol 30 (16) ◽  
pp. 2478-2501 ◽  
Author(s):  
M Vinyas ◽  
AS Sandeep ◽  
T Nguyen-Thoi ◽  
F Ebrahimi ◽  
DN Duc
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Elastic Plates ◽  
Benchmark Solutions

In this article, the free vibration behaviour of circular and annular magneto-electro-elastic plates has been investigated under the framework of higher order shear deformation theory. The three-dimensional finite element formulation has been derived with the aid of Hamilton’s principle by taking into account the coupling between elastic, electric and magnetic properties. The equations of motion are solved using condensation technique. Furthermore, the credibility of proposed finite element formulation has been validated using COMSOL software and also by comparing the results with previously published articles. Special attention has also been paid to assess the influence of parameters such as coupling effect, stacking sequences and inner-to-outer diameter ratio. The numerical results reveal that the coupled natural frequencies of the annular magneto-electro-elastic plates vary significantly with the circular hole dimensions incorporated. The circular and annular plates are considered as one of the prominent structural components in various engineering and industrial application. Therefore, the proposed finite element formulation and the results presented in this article can serve as benchmark solutions for the design and analysis of smart sensors and actuators.

scholarly journals Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

2020 ◽  
Vol 14 (3) ◽  
pp. 136-150
Author(s):  
Le Thi Ngoc Anh ◽  
Vu Thi An Ninh ◽  
Tran Van Lang ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
First Order ◽  
Various Boundary Conditions

Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

Dynamic Analysis of Plates with Cut-Out Carrying Concentrated and Distributed Mass

2020 ◽  
Vol 162 (A3) ◽  
Author(s):  
S Pal ◽  
S Haldar ◽  
K Kalita
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Formulation ◽  
Plate Bending ◽  
Mass Lumping ◽  
First Order ◽  
Side Ratio ◽  
Isotropic Plates

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

scholarly journals A COMBINED STRAIN ELEMENT TO FUNCTIONALLY GRADED STRUCTURES IN THERMAL ENVIRONMENT

2020 ◽  
Vol 60 (6) ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Element Analysis ◽  
First Order ◽  
Graded Structures

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.

Geometrically nonlinear finite element simulation of smart laminated shells using a modified first-order shear deformation theory

2019 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Hanen Mallek ◽  
Hanen Jrad ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Nonlinear Finite Element ◽  
Shear Stresses ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
First Order

This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear function through the thickness of each active sub-layer. Several numerical tests for different piezolaminated geometries are conducted to highlight the reliability and efficiency of the proposed implementation in linear and geometrically nonlinear finite element analysis.

DYNAMIC ANALYSIS OF PLATES WITH CUT-OUT CARRYING CONCENTRATED AND DISTRIBUTED MASS

2021 ◽  
Vol 162 (A3) ◽  
Author(s):  
S Pal ◽  
S Haldar ◽  
K Kalita
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Formulation ◽  
Plate Bending ◽  
Mass Lumping ◽  
First Order ◽  
Side Ratio ◽  
Isotropic Plates

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

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