scholarly journals Dynamic finite element formulation for Cosserat elastic plates

2014 ◽  
Vol 101 (13) ◽  
pp. 992-1018 ◽  
Author(s):  
Michele Godio ◽  
Ioannis Stefanou ◽  
Karam Sab ◽  
Jean Sulem
Keyword(s):  
Finite Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Elastic Plates ◽  
Dynamic Finite Element

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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 A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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 A New Dynamic Finite Element Formulation with Applications to Composite Aircraft Wings

2021 ◽  
Author(s):  
Stephen R. Bomeman
Keyword(s):  
Finite Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Aircraft Wings ◽  
Dynamic Finite Element

A New Dynamic Finite Element Formulation with Applications to Composite Aircraft Wings

scholarly journals A New Dynamic Finite Element Formulation with Applications to Composite Aircraft Wings

2021 ◽  
Author(s):  
Stephen R. Bomeman
Keyword(s):  
Finite Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Aircraft Wings ◽  
Dynamic Finite Element

A New Dynamic Finite Element Formulation with Applications to Composite Aircraft Wings

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MATLAB® software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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