Frequency Response of a Three-Node Finite Element for Composite Thin and Thick Plates

2004 ◽  
Author(s):  
A. V. S. Ravi Shastry ◽  
Pramod Kumar
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Integration Scheme ◽  
Shear Locking ◽  
Triangular Finite Element ◽  
Strain Components

A shear-locking free isoparametric three-node triangular finite element is considered for the study of frequency response of moderately thick and thin composite plates. The strain displacement relationship is based on Reissner-Mindlin plate theory that accounts for transverse shear deformations into the plate formulation to circumvent the shear locking effect. The element is developed with full integration scheme; hence the element remains kinematically stable. The performance of the element for the case of static load response using the shear correction terms to shear strain components applied to a composite plate has been studied. The natural frequencies and mode shapes in accordance with varying mode numbers, are deduced and the results are compared with the available analytical and finite element solutions in literature.

Frequency Response of a Three-Node Finite Element for Thick and Thin Plates

2002 ◽  
Vol 8 (8) ◽  
pp. 1123-1153 ◽  
Author(s):  
Humayun R. H. Kabir ◽  
Abdullateef M. Al-Khaleefi
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Correction Term ◽  
Thin Plates ◽  
Mode Shapes ◽  
Integration Scheme ◽  
Element Formulation ◽  
Transverse Shear Strain ◽  
Shear Locking ◽  
Triangular Finite Element

A shear-locking free isoparametric three-node triangular finite element is presented to study the frequency response of moderately thick and thin plates. Reissner/Mindlin theory that incorporates shear deformation effects is included into the element formulation. A shear correction term is introduced in transverse shear strain components to avoid the shear-locking phenomenon. The element is developed with a full integration scheme, hence, the element remains kinematically stable. Natural frequencies and mode shapes are obtained and compared with the available analytical and finite element solutions.

Comparison of Free Flexural Vibrations of Composite Plates or Panels Stiffened by a Central and a Non-Central Plate Strip

1999 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Solution Technique ◽  
Orthotropic Plates ◽  
Bending Vibration ◽  
Central Plate ◽  
Plate Strip

Abstract The natural frequencies and the corresponding mode shapes of two classes of composite base plate or panel stiffened by a central or a non-central plate strip are analyzed and compared with each other. In each case, the base plates and the single, stiffening plate strips are assumed to be dissimilar orthotropic plates connected by a very thin, yet deformable adhesive layer. The free bending vibration problems for the two cases are formulated in terms of the Mindlin Plate Theory for orthotropic plates. The governing equations are reduced to a system of first order equations. The solution technique is the “Modified Version of the Transfer Matrix Method”. The effects of the bonded central and non-central stiffening strip on the mode shapes and the natural frequencies of the composite plate or panel system are investigated. Some important conclusions are drawn from the numerical and parametric studies presented.

Conforming shear-locking-free four-node rectangular finite element of moderately thick plate

2016 ◽  
Vol 25 (5-6) ◽  
pp. 141-152
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Smiljko Rudan ◽  
Neven Hadžić
Keyword(s):  
Finite Element ◽  
Thick Plate ◽  
Plate Theory ◽  
Shear Stiffness ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Shape Functions ◽  
Beam Shape ◽  
Stiffness Matrices ◽  
Moderately Thick Plate

AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

Free Vibration Analysis of a PEMFC Using the Finite Element Method

2010 ◽  
Author(s):  
Hasnet E. U. Ahmed ◽  
Jean W. Zu ◽  
Aimy Bazylak
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Gas Diffusion ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Maximum Displacement

In this study, a free vibration analysis of a polymer electrolyte membrane fuel cell (PEMFC) is performed by modelling the PEMFC as a composite plate structure. The membrane, gas diffusion electrodes, and bi-polar plates are modelled as composite material plies. Energy equations are derived based on the Mindlin plate theory, and natural frequencies and mode shapes of the PEMFC are calculated using finite element modelling. A parametric study is conducted to investigate how the natural frequency varies as a function of thickness, Young’s modulus, and density for each component layer. It is observed that increasing the thickness of the bi-polar plates has the most significant effect on the lowest natural frequency, with a 25% increase in thickness resulting in an 11% increase in the natural frequency. The mode shapes of the PEMFC provide insight into the maximum displacement exhibited as well as the stresses experienced by the material under various vibration conditions.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Analysis of Symmetric Angle-Ply Laminated Composite Skew Plates Using Hybrid Trefftz Finite Element

2019 ◽  
Author(s):  
Subhasankar Dwibedi
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Point Load ◽  
Shear Stresses ◽  
Skew Angle ◽  
Distributed Load ◽  
Trefftz Finite Element

Abstract Analysis of symmetric angle-ply skew laminated composite plates has been presented in the study using a newly developed hybrid Trefftz finite element (hTFE). Mindlin’s plate theory has been used to develop the present hTFE. The forms of displacement are assumed such that governing partial differential equations are satisfied a priori inside the element domain. Particular solutions of the governing equations have been ignored and Trefftz functions are derived using the homogenous solutions only. Inter-element continuity has been established by employing another displacement field along the edges of the hTFEs. The transverse shear stresses have been ignored at the top and bottom surfaces of the laminate. The angle of inclination of the width of the plate with the y-axis has been taken as the skew angle and different forms of skew plates are obtained by varying the skew angle. Sinusoidally distributed load (SDL), uniformly distributed load (UDL), and point load (PL) have been subjected to the top surface of the laminate and the non-dimensionalized center point deflection have been evaluated to assess the performance of the present hTFE. The observation from the present study further reinforce the versatility of the hTFE method for analysis of composite structures with complex shapes or geometries.

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