Novel higher-order zigzag theory for analysis of laminated sandwich beams

2020 ◽  
pp. 146442072095704
Author(s):  
Aman Garg ◽  
HD Chalak
Keyword(s):  
Degrees Of Freedom ◽  
Sandwich Beam ◽  
Present Theory ◽  
Higher Order ◽  
Bottom Surface ◽  
Shear Stresses ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Heaviside Step Function ◽  
Zigzag Theory

In the present work, a new higher-order zigzag theory is proposed for the analysis of laminated sandwich beams under static and free vibration conditions. Fourth-order in-plane and transverse displacement fields are chosen along with linear unit Heaviside step function. The present theory satisfies interlaminar transverse stress continuity conditions along with zero value at the top and bottom surface for transverse shear stresses. The proposed approach is also free from any kind of C-1 or penalty requirements. A three-noded one-dimensional finite element having eight degrees of freedom per node is used during analysis. The efficiency of the proposed model is carried out by comparing the present results with those available based on elasticity solutions and zigzag theories in the literature. New results are also reported in the present work, which will serve as a benchmark for future studies. The influence of boundary condition on the nature of stress distribution across the length of beam and frequencies of the beam with different end conditions is also carried out. A comparative study has also been carried out between symmetric and unsymmetric laminated sandwich beam.

Higher-Order Zig-Zag Theory for Laminated Composites With Multiple Delaminations

2000 ◽  
Vol 68 (6) ◽  
pp. 869-877 ◽  
Author(s):  
M. Cho ◽  
J.-S. Kim
Keyword(s):  
Displacement Field ◽  
Transverse Shear ◽  
Dynamic Equilibrium ◽  
Composite Plates ◽  
Present Theory ◽  
Higher Order ◽  
Bottom Surface ◽  
Shear Stresses ◽  
Equilibrium Equations ◽  
Natural Frequency Analysis

A higher-order zig-zag theory has been developed for laminated composite plates with multiple delaminations. By imposing top and bottom surface transverse shear stress-free conditions and interface continuity conditions of transverse shear stresses including delaminated interfaces, the displacement field with minimal degree-of-freedoms are obtained. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. The delaminated beam finite element is implemented to evaluate the performance of the newly developed theory. Linear buckling and natural frequency analysis demonstrate the accuracy and efficiency of the present theory. The present higher-order zig-zag theory should work as an efficient tool to analyze the static and dynamic behavior of the composite plates with multiple delaminations.

Analysis of non-skew and skew laminated composite and sandwich plates under hygro-thermo-mechanical conditions including transverse stress variations

2020 ◽  
pp. 109963622093278 ◽  
Author(s):  
Aman Garg ◽  
HD Chalak
Keyword(s):  
Displacement Field ◽  
Degrees Of Freedom ◽  
Laminated Composite ◽  
Thermal Conditions ◽  
Present Theory ◽  
Step Function ◽  
Continuity Condition ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Heaviside Step Function

A new fourth-order in-plane displacement field based refined higher-order zigzag theory is proposed for analysis of laminated sandwich plate (for both skew and non-skew shaped) subjected to hygro-thermal conditions. In order to predict behavior of thick laminated sandwich plates, third-order transverse displacement field is taken. Zig-zag effects are introduced using linear unit Heaviside step function. The theory satisfies zeros transverse normal and shear stress condition at the bottom and top surface of the plate along with continuity condition at interface. The proposed model is free from any kind of C-1 or penalty function requirements. Nine-noded isoparametric finite element having twelve degrees of freedom per node is used during analysis. Since, the present theory incorporates transverse displacement field along with continuity conditions, is able to predict the behavior of thick sandwich plates more efficiently. In literature no results are present for skew laminated composite and sandwich plates therefore, present results for skew plates are entirely new and will serve as benchmark for future studies.

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

2008 ◽  
Vol 222 (8) ◽  
pp. 1443-1452 ◽  
Author(s):  
M K Pandit ◽  
A H Sheikh ◽  
B N Singh
Keyword(s):  
Transverse Shear ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Zigzag Theory ◽  
Three Dimensional Elasticity

This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.

A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory

2015 ◽  
Vol 132 ◽  
pp. 784-803 ◽  
Author(s):  
Marco Di Sciuva ◽  
Marco Gherlone ◽  
Luigi Iurlaro ◽  
Alexander Tessler
Keyword(s):  
Sandwich Beam ◽  
Higher Order ◽  
Beam Elements ◽  
Zigzag Theory

A New Rectangular Plate Element for Vibration Analysis of Laminated Composites

1998 ◽  
Vol 120 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Guan-Liang Qian ◽  
Suong V. Hoa ◽  
Xinran Xiao
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Rectangular Plate ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Model ◽  
Higher Order ◽  
Transverse Displacement

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

scholarly journals Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal ◽  
N. S. Naik
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Bending Analysis

AbstractA trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

Wave Propagation in Sandwich Structures With Multiresonators

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
J. S. Chen ◽  
Y. J. Huang
Keyword(s):  
Wave Propagation ◽  
Timoshenko Beam ◽  
Degrees Of Freedom ◽  
Wave Attenuation ◽  
Sandwich Beam ◽  
Sandwich Beams ◽  
Central Frequency ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
In Series

A new sandwich beam with embedded multiresonators is presented. Two continuum Timoshenko beam models are adopted for modeling sandwich beams. Numerical results show that multiple resonators can lead to multiple resonant-type bandgaps with remarkable wave attenuation. The effective mass is found to become negative for frequencies in the bandgaps where the wave is greatly attenuated. With two identical resonators connected in parallel, only one single bandgap can be found. If two resonators with equal masses and springs are connected in series, the central frequency of the second bandgap is approximated twice of the central frequency of the first gap. For the beam with series-connected resonators, a simple two degrees-of-freedom system is proposed and used for predicting the initial frequencies of the bandgaps while for the beam with resonators in parallel, two separate single degree-of-freedom systems are introduced.

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