scholarly journals The displacement view of a multilayered HSDT plate

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Priyaranjan Pal
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Shear Deformation Theory ◽  
Mesh Size ◽  
Finite Element Formulation ◽  
Computational Time ◽  
Element Formulation ◽  
Maximum Deflection ◽  
Suitable Combination ◽  
Optimal Mesh

This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the center of plate for both fixed and simply supported edges is verified with reported literature and a good conformity is found. An attempt has been made to observe the minimum value of maximum deflection in the laminate for attaining the maximum strength of laminate with a suitable combination of stacking sequences with a constant volume of material.

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

2017 ◽  
Vol 29 (7) ◽  
pp. 1430-1455 ◽  
Author(s):  
Vinyas Mahesh ◽  
Piyush J Sagar ◽  
Subhaschandra Kattimani
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Elastic Plate ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Elastic Plates

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

scholarly journals Generalized finite element formulation for efficient first-order plastic hinge analysis

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983636
Author(s):  
Dae-Jin Kim ◽  
Hong-Jun Son ◽  
Yousun Yi ◽  
Sung-Gul Hong
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Plastic Hinge ◽  
Computational Cost ◽  
Finite Element Formulation ◽  
Solution Technique ◽  
Element Formulation ◽  
Plastic Hinges ◽  
First Order ◽  
Generalized Finite Element

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

scholarly journals Effect of Mesh on Springback in 3D Finite Element Analysis of Flexible Microrolling

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Feijun Qu ◽  
Zhengyi Jiang ◽  
Haina Lu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Study ◽  
Mesh Size ◽  
Computational Time ◽  
Element Analysis ◽  
3D Finite Element ◽  
Forming Quality ◽  
The Finite Element Analysis ◽  
Optimal Mesh

In flexible microrolling, springback in thickness direction is a critical indicator to determine the forming quality. Accurate prediction of springback is one of the significant aspects in the finite element analysis of flexible microrolling. Meshing is a step of great importance in finite element analysis of manufacturing process as it directly determines the accuracy of the FEA results as well as the requested computational time. This paper presents a numerical study on revealing the mesh effects on the accuracy of springback estimation utilising ABAQUS/Standard for modelling and analyses. Two types of meshes with six mesh sizes for each mesh type are considered in this study and the optimal mesh type and mesh size have been found to obtain accurate value of springback while saving as much computational time as possible.

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.

Influence of Joint Flexibility on Vibration Analysis of Free-Free Beams

2014 ◽  
Vol 3 (4) ◽  
Author(s):  
Jagadish Babu Gunda ◽  
Y. Krishna
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Joint Stiffness ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Joint Flexibility ◽  
Rotational Spring ◽  
Finite Element Software ◽  
Joint Location

AbstractIn present work, joint flexibility (or looseness) of the free-free beam is investigated by using a two noded beam finite element formulation with transverse displacement and joint rotations as the degrees of freedom per node at joint location. Flexibility of the joint is primarily represented by means of a rotational spring analogy, where the stiffness of the rotational spring characterizes the looseness of the flexible joint for an applied bending moment. Influence of joint location as well as joint stiffness on modal behavior of first five modes of slender, uniform free-free beams are discussed for various values of non-dimensional rotational spring stiffness parameter. Numerical accuracy of the results obtained from the present finite element formulation are validated by using the commercially available finite element software which shows the confidence gained on the numerical results discussed in the present study.

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.

scholarly journals A \(C^1\) bending element for composite plates based on a high-order shear deformation theory

2008 ◽  
Vol 30 (4) ◽  
Author(s):  
Tran Ich Thinh ◽  
Ngo Nhu Khoa ◽  
Do Tien Dung
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Degrees Of Freedom ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Formulation ◽  
Element Analysis ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A new \(C^1\) rectangular element is proposed and the finite element formulation based on Reddy’s higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy’s plate theory is successfully implemented. It has nine nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability.

Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method

2012 ◽  
Vol 585 ◽  
pp. 44-48 ◽  
Author(s):  
Ajay Kumar ◽  
Pradeep Bhargava ◽  
Anupam Chakrabarti
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Element Formulation

In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the present results of problems with those available in the published literature. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, new results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.

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