Vibration of laminated sandwich beams having soft core

2011 ◽  
Vol 18 (10) ◽  
pp. 1422-1435 ◽  
Author(s):  
Hanuman Devidas Chalak ◽  
Anupam Chakrabarti ◽  
Mohamad Asharaf Iqbal ◽  
Abdul Hamid Sheikh
Keyword(s):  
Shear Stress ◽  
Free Vibration ◽  
Transverse Shear ◽  
Soft Core ◽  
Future Research ◽  
Transverse Displacement ◽  
Beam Model ◽  
Sandwich Beams ◽  
Transverse Shear Stress ◽  
The Core

Free vibration response of laminated sandwich beams having a soft core is studied by using a recently developed C0 finite element beam model. The model has been developed based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. Numerical examples on free vibration covering different features of laminated composite and sandwich beams are presented. Many new results are also presented which should be useful for future research.

VIBRATION AND BUCKLING ANALYSIS OF LAMINATED SANDWICH PLATE HAVING SOFT CORE

2013 ◽  
Vol 13 (08) ◽  
pp. 1350034 ◽  
Author(s):  
RAVI PRAKASH KHANDELWAL ◽  
ANUPAM CHAKRABARTI ◽  
PRADEEP BHARGAVA
Keyword(s):  
Shear Stress ◽  
Free Vibration ◽  
Displacement Field ◽  
Transverse Shear ◽  
Sandwich Plate ◽  
Soft Core ◽  
Transverse Displacement ◽  
Fe Model ◽  
Transverse Shear Stress ◽  
The Core

Free vibration and buckling of laminated sandwich plate having soft core is studied by using an efficient C0 continuous finite element (FE) model based on higher-order zigzag theory (HOZT). In this theory, the in-plane displacement field for both the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly varying displacement field with a different slope in each layer. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the plate. The nodal field variables are chosen in an efficient manner to overcome the problem of C1 continuity requirement of the transverse displacement. Numerical examples on free vibration and buckling covering different geometric and material features of laminated composite and sandwich plates are presented. Many new results are also presented which should be useful for future research.

scholarly journals A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate

2013 ◽  
Vol 18 (2) ◽  
pp. 395-423 ◽  
Author(s):  
R.P. Khandelwal ◽  
A. Chakrabarti ◽  
P. Bhargava
Keyword(s):  
Shear Stress ◽  
Displacement Field ◽  
Transverse Shear ◽  
Sandwich Plate ◽  
Higher Order ◽  
Least Square ◽  
Soft Core ◽  
Fe Model ◽  
Transverse Shear Stress ◽  
The Core

An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.

Free Vibration Analysis of Laminated Soft Core Sandwich Plates

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
H. D. Chalak ◽  
Anupam Chakrabarti ◽  
Mohd. Ashraf Iqbal ◽  
Abdul Hamid Sheikh
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Soft Core ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Fe Model ◽  
The Core

Free vibration behavior of laminated soft core sandwich plates with stiff laminated face sheets is investigated using a new C0 finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement variations are considered to be cubic for both the face sheets and the core, while the transverse displacement is assumed to vary quadratically within the core and remains constant in the faces beyond the core. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for an accurate modeling of laminated sandwich plates. As very few elements based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to develop this new element. The nodal field variables are chosen in such a manner to overcome the problem of continuity requirement of the derivatives of transverse displacements, i.e., no need to impose any penalty stiffness in the formulation. A nine node C0 quadratic plate finite element is implemented to model the HOZT for the present analysis. A new C0 element has been utilized to study some interesting problems on free vibration analysis of laminated sandwich plates. Many new results are also presented which should be useful for future research.

Bending and free vibration response of sandwich laminate under hygrothermal load using improved zigzag theory

2017 ◽  
Vol 52 (5) ◽  
pp. 288-297 ◽  
Author(s):  
Ansuman Padhi ◽  
Mihir K Pandit
Keyword(s):  
Shear Stress ◽  
Free Vibration ◽  
Transverse Shear ◽  
Vibration Response ◽  
Element Formulation ◽  
Transverse Shear Stress ◽  
Plate Model ◽  
Aspect Ratios ◽  
Moisture Variation ◽  
Free Vibration Response

In this work, the effects of variations in temperature and moisture concentrations on the static and free vibration response of sandwich laminated plates with low-density core have been studied. A higher order zigzag laminate theory is used which satisfies the continuity in transverse shear stress at the layer interfaces and zero transverse shear stress condition at the top and bottom surfaces of the laminate . The displacement field in this theory suitably allows for the quadratic distribution of transverse shear stress across the thickness and transverse compressibility effect of the core. An effective finite element formulation is carried out by employing a nine-node C0 isoparametric element for the above plate model. Numerical examples of composite and sandwich laminates with different material properties, effect of temperature and moisture variation, aspect ratios, boundary conditions, number of layers and ply orientations are considered for the analysis. Efficiency of the present plate model in predicting various responses subjected to hygrothermal loading is verified by comparing with the available published results.

Determination of the transverse shear stress in layered composites

2020 ◽  
Vol 86 (2) ◽  
pp. 44-53
Author(s):  
Yu. I. Dudarkov ◽  
M. V. Limonin
Keyword(s):  
Shear Stress ◽  
Transverse Shear ◽  
Composite Beam ◽  
Layered Composite ◽  
Equivalent Model ◽  
Shear Stresses ◽  
Transverse Shear Stress ◽  
Layered Composites ◽  
Laminate Composites ◽  
Transverse Shear Stresses

An engineering approach to estimation of the transverse shear stresses in layered composites is developed. The technique is based on the well-known D. I. Zhuravsky equation for shear stresses in an isotropic beam upon transverse bending. In general, application of this equation to a composite beam is incorrect due to the heterogeneity of the composite structure. According to the proposed method, at the first stage of its implementation, a transition to the equivalent model of a homogeneous beam is made, for which the Zhuravsky formula is valid. The transition is carried out by changing the shape of the cross section of the beam, provided that the bending stiffness and generalized elastic modulus remain the same. The calculated shear stresses in the equivalent beam are then converted to the stress values in the original composite beam from the equilibrium condition. The main equations and definitions of the method as well as the analytical equation for estimation of the transverse shear stress in a composite beam are presented. The method is verified by comparing the analytical solution and the results of the numerical solution of the problem by finite element method (FEM). It is shown that laminate stacking sequence has a significant impact both on the character and on the value of the transverse shear stress distribution. The limits of the applicability of the developed technique attributed to the conditions of the validity of the hypothesis of straight normal are considered. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in the obtained equation. The classical theory of laminate composites is based on the similar assumptions, which gives ground to use this equation for an approximate estimation of the transverse shear stresses in in a layered composite package.

Transverse shear stress within surface layer and its effects

2019 ◽  
Vol 25 (2) ◽  
pp. 166-180
Author(s):  
Ge Yan ◽  
Zaixing Huang
Keyword(s):  
Shear Stress ◽  
Surface Layer ◽  
Hydrostatic Pressure ◽  
Transverse Shear ◽  
Transverse Shear Stress ◽  
Middle Section ◽  
Nanoscale Solids ◽  
Maximal Stress

When the transverse shear stress within a surface layer is taken into account, what happens in the deformation of micro- or nanoscale solids? The relevant problems are investigated by analyzing the deformation of a micro- or nanosized solid ellipsoid. The results show that both the stress and the deformation of a micro- or nanosized ellipsoid increase after the transverse shear stress within the surface layer is introduced, and that the maximal stress always occurs at both ends of the long axis of the ellipsoid. Unlike the prediction given by the Gurtin–Murdoch model, the calculation coming from the model of this paper predicts that the micro- or nanosized ellipsoid subjected to hydrostatic pressure contracts radially in the middle section and expands radially on both sides of the middle section. This difference provides an experimental standard to verify two models.

Analytical and Experimental Study of Free Vibration Response of Soft-core Sandwich Beams

2004 ◽  
Vol 6 (3) ◽  
pp. 239-261 ◽  
Author(s):  
Vladimir S. Sokolinsky ◽  
Hubertus F. Von Bremen ◽  
J. André Lavoie ◽  
Steven R. Nutt
Keyword(s):  
Experimental Study ◽  
Free Vibration ◽  
Vibration Response ◽  
Soft Core ◽  
Sandwich Beams ◽  
Free Vibration Response
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