Finite Element Analysis on Modal Parameters of Anisotropic Laminated Plates

1988 ◽  
Vol 110 (4) ◽  
pp. 473-477 ◽  
Author(s):  
C. Z. Xiao ◽  
D. X. Lin ◽  
F. Ju
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Mode Shapes ◽  
Transverse Shear Deformation ◽  
Element Technique

This paper is concerned with the finite element technique for predicting the dynamic properties of anisotropic fiber-reinforced composite laminated plates. Considering the effect of transverse shear deformation, a higher order shear deformation theory which satisifes the zero shear stress conditions at the upper and bottom surfaces is assumed. The natural frequencies and mode shapes of a rectangular plate with all free edges are obtained by finite element method and the modal damping values by finite damped element technique. An equivalent stiffness method is introduced to reduce computation time. Four different theoretical predictions of natural frequencies and damped values of a laminated plate are compared with experimental results. Discussions on the effect of transverse shear deformation to the dynamic properties of composite plates are given.

Comparative perspective of various shear deformation theories with experimental verification for modal analysis of hybrid laminates

2015 ◽  
Vol 23 (8) ◽  
pp. 1321-1333 ◽  
Author(s):  
Dhiraj Biswas ◽  
Chaitali Ray
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Modal Analysis ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Mode Shapes ◽  
Glass Fibres ◽  
Hybrid Laminates

The present paper deals with the free vibration modal analysis of hybrid laminates using a finite element model based on the third order shear deformation theory (TSDT) and the first order shear deformation theory (FSDT). A computer code has been developed using MATLAB, 2013. The experimental investigation on the free vibration of hybrid laminates made of carbon and glass fibres has been conducted. The hybrid laminate is prepared by placing carbon fibres in the outermost laminae and glass fibres in the rest of the laminate. The bi-directional glass and carbon fabrics and the epoxy resin are used for the preparation of laminates in the laboratory. The experimental models of laminates have been prepared by the resin infusion process using vacuum bagging technique. The natural frequencies of hybrid laminates for different modes are determined and the mode shapes are plotted for the corresponding frequencies by experiment and numerical procedure. The finite element formulations based on TSDT and FSDT for the composite laminates predict the natural frequencies and are validated by comparing with the experimental results.

scholarly journals Natural Frequency Analysis of Functionally Graded Orthotropic Cross-Ply Plates Based on the Finite Element Method

2019 ◽  
Vol 24 (2) ◽  
pp. 52 ◽  
Author(s):  
Michele Bacciocchi ◽  
Angelo Tarantino
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Mode Shapes ◽  
Thickness Direction ◽  
Thick Plates ◽  
Natural Frequency Analysis

This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is the modelling of the reinforcing fibers of the orthotropic layers assuming a non-uniform distribution in the thickness direction. The Halpin–Tsai approach is employed to define the overall mechanical properties of the composite layers starting from the features of the two constituents (fiber and epoxy resin). Several functions are introduced to describe the dependency on the thickness coordinate of their volume fraction. The analyses are carried out in the theoretical framework provided by the first-order shear deformation theory (FSDT) for laminated thick plates. Nevertheless, the same approach is used to deal with the vibration analysis of thin plates, neglecting the shear stiffness of the structure. This objective is achieved by properly choosing the value of the shear correction factor, without any modification in the formulation. The results prove that the dynamic response of thin and thick plates, in terms of natural frequencies and mode shapes, is affected by the non-uniform placement of the fibers along the thickness direction.

scholarly journals Non-linear analysis of laminated plates

2002 ◽  
Vol 24 (4) ◽  
pp. 197-208
Author(s):  
Dao Huy Bich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Linear Analysis ◽  
Laminated Plates ◽  
Transverse Shear Deformation ◽  
Governing Equations ◽  
Non Linear

The governing equations of laminates plates taking into account the transverse shear deformation effects for large deformation are given. The formulation of Ritsz method and finite element method for non-linear analysis of this problem is presented

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.

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

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