scholarly journals Wave theory of the laminated plates with approximate consideration of the transverse shear

2021 ◽  
Vol 5 (4) ◽  
pp. 233-241
Author(s):  
A. V. Sibiryakov
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Wave Theory ◽  
Stress Waves ◽  
Laminated Plates ◽  
Heterogeneous Structure ◽  
Shock Loads ◽  
Spalling Strength ◽  
Impulse Action ◽  
External Impulse

Composite materials are widely used in the production of aircraft for various purposes. Having several unique properties, composites, due to their heterogeneous structure, are poorly resistant to shock loads. Impulse action spreads inside the material in the form of stress waves, which are reflected on internal inhomogeneities, can overlap, and create very significant bursts of stress. This often leads to the well-known types of failure – spalling and delamination. Practice shows that these fractures occur almost immediately after the loading impulse. To verify the spalling strength, it is necessary to consider the initial unsteady phase of the response to the external impulse. There are sufficiently reliable theories to verify this strength; usually, they do not take transverse shear into account, otherwise the solution becomes unnecessarily cumbersome and poorly observable. Nevertheless, attempts are often made to refine the calculations by approximate consideration of transverse shear. This article presents the wave theory of laminated plates with approximate consideration of transverse shear. The possibility of specifying the calculation of impulse-loaded plates is considered. The inconsistency of the resulting model is proved.

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.

Dynamic Behavior of Aircraft Wings Modeled as Doubly-Tapered Composite Thin-Walled Beams

1999 ◽  
Author(s):  
Sungsoo Na ◽  
Liviu Librescu
Keyword(s):  
Composite Materials ◽  
Free Vibration ◽  
Dynamic Response ◽  
Dynamic Behavior ◽  
Transverse Shear ◽  
Dynamical Behavior ◽  
Time Dependent ◽  
Aircraft Wings ◽  
Helicopter Blades ◽  
Thin Walled

Abstract A study of the dynamical behavior of aircraft wings modeled as doubly-tapered thin-walled beams, made from advanced anisotropic composite materials, and incorporating a number of non-classical effects such as transverse shear, and warping inhibition is presented. The supplied numerical results illustrate the effects played by the taper ratio, anisotropy of constituent materials, transverse shear flexibility, and warping inhibition on free vibration and dynamic response to time-dependent external excitations. Although considered for aircraft wings, this analysis and results can be also applied to a large number of structures such as helicopter blades, robotic manipulator arms, space booms, tall cantilever chimneys, etc.

A Study of the Fiber-Matrix Interface in Composite Materials

1992 ◽  
Vol 59 (2S) ◽  
pp. S163-S165 ◽  
Author(s):  
Jin O. Kim ◽  
Haim H. Bau
Keyword(s):  
Composite Materials ◽  
Experimental Technique ◽  
Stress Waves ◽  
Matrix Interface ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
The Matrix ◽  
Fiber Matrix Interface ◽  
Dispersion And Attenuation

A novel experimental technique for studying the characteristics of the interface between the fibers and the matrix in both undamaged and damaged fiber-reinforced composite materials is described. The experimental technique involves the transmission of stress waves in one or more fibers of the composite. The characteristics of the stress waves, such as speed, dispersion, and attenuation, are measured. These measured variables can be correlated with the characteristics of the bonding between the fiber and the matrix.

Composite Laminate Stiffnesses and Their Sensitivities

1994 ◽  
Author(s):  
Bodo Geier ◽  
Rolf Zimmermann
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Composite Laminate ◽  
Shear Stiffness ◽  
Efficient Algorithms ◽  
Search Procedure ◽  
Object Function ◽  
Stiffness Matrices ◽  
Derivatives Of ◽  
Constrained Function

Abstract The great number of possible stacking orders to form laminates suggests to apply optimization, more frequently than usual, in the design of structures made of composite materials. One of the columns upon which optimization of structures is built is the mathematical search procedure for locating a minimum (or maximum) of a constrained function. Efficient algorithms will require the evaluation of derivatives of the object function as well as of the constraints. In that context the sensitivities of laminate stiffness matrices may be required. In order to meet such a requirement the derivatives with respect to both ply thicknesses and ply angles, of laminate stiffnesses, including transverse shear stiffness, will be presented in this report.

FE Design Tool for Laminated Composite Plates

2012 ◽  
Vol 248 ◽  
pp. 379-383
Author(s):  
Rasoul Khandan ◽  
Philip Sewell ◽  
Siamak Noroozi ◽  
Mohammad Reza Ramazani
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Design Tool ◽  
Computational Technique ◽  
The Finite Element Method ◽  
Laminated Composite Plates ◽  
Wide Range ◽  
Good Agreement

Considering the non-linearity, complexity and anisotropy of constitutive equations in composite materials, numerical methods are essential to evaluate the behaviour of this material. The finite element method (FEM) is a powerful computational technique for the solution of differential and integral equations that arise in various fields of engineering and applied science such as composite materials. Here, an FEM tool is designed to analyse non-linearity in the behaviour of composites caused by the effect of transverse shear and twist in laminated composite plates. The tool is established by using FEM for composites in ABAQUS combined with programming in Python to run the tests for all possible fibre orientations in laminated composite plates. It is shown that the tool has the ability to design laminated composite plates by considering the effect of transverse shear and the tool’s output provides results for all different fibre orientations. It is demonstrated that there is good agreement between numerical results obtained from this tool and experimental results. The advantages of the tool give designers the opportunity to use this tool for wide range of products.

ON ELASTIC STRESS WAVES IN AN IMPACTED PLATE

2014 ◽  
Vol 06 (04) ◽  
pp. 1450047 ◽  
Author(s):  
ZHANFANG LIU ◽  
XIAOYONG SUN ◽  
YUAN GUO
Keyword(s):  
Wave Motion ◽  
Elastic Stress ◽  
Wave Theory ◽  
Stress Waves ◽  
Ceramic Plate ◽  
Elastic Solids ◽  
Plate Impact ◽  
Impact Surface ◽  
Macro Scale ◽  
Elastic Stress Wave

Elastic stress wave theory is developed and the stress waves in the impacted plate are examined in the paper. Generalized linear elasticity is adopted where the couple stress and curvature tensor are both deviatoric tensors and they meet a linear constitutive relation. It is found that there exist volumetric, rotational, and deviatoric waves in the generalized elastic solids. However, for macro-scale elastic solids only two wave modes, namely a volumetric wave and a deviatoric wave should be taken into account. Wave motion in plate impact tests is studied that a volumetric wave and a deviatoric wave are proposed. A set of exact solutions is attained for elastic stress waves in an impact plate. Excitation of stress waves at impact surface and reflection at free surface are formulated. Propagation of stress waves in the plate is analyzed in the waveforms. The predicted stress history in a ceramic plate under impact is agreed very well with the experiment measurement.

scholarly journals Nonlinear Free Vibration for Viscoelastic Moderately Thick Laminated Composite Plates with Damage Evolution

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Y. F. Zheng ◽  
L. Q. Deng
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Superposition Principle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Damage Effect ◽  
Laminated Composite Plates ◽  
Nonlinear Free Vibration ◽  
The Galerkin Method

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with damage are established and solved by the Galerkin method, Simpson integration, Newton-Cotes, Newmark, and iterative methods. In the numerical results, the effects of transverse shear, material viscoelasticity, span-thickness ratio, aspect ratio, and damage effect on the nonlinear free vibrating frequency of the viscoelastic cross-ply moderately thick laminated plates are discussed.

scholarly journals A Test Method for Experimental Determination of Shear Moduli of Fibre Reinforced Composite Materials

1994 ◽  
Vol 3 (1) ◽  
pp. 096369359400300
Author(s):  
B. Laleh ◽  
P. Myler
Keyword(s):  
Composite Materials ◽  
Carbon Fibre ◽  
Transverse Shear ◽  
Test Method ◽  
Reinforced Composites ◽  
Simple Test ◽  
Shear Moduli ◽  
Reinforced Composite ◽  
Fibre Reinforced Composites

This paper describes a simple test method for determining the in-plane and transverse shear moduli of unidirectional carbon fibre reinforced composites. The method employs photoelastic coating techniques in conjunction with four point offset bend loading conditions.

Higher Order Global-Local Theory Coupled Bending and Extension for Laminated Composite Plates and Refined Element Methods

2006 ◽  
Author(s):  
Wanji Chen ◽  
Zhen Wu
Keyword(s):  
Transverse Shear ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Plates ◽  
Triangular Element ◽  
Local Theory ◽  
Weak Continuity ◽  
Shear Stresses ◽  
Thickness Direction ◽  
Transverse Shear Stresses

In this paper an augmented higher order global-local theories are presented to analyze the laminated plate problems coupled bending and extension. The in-plane displacement field is composed of a mth-order (9 > m > 3) polynomial of global coordinate z in the thickness direction and 1,2-3 order power series of local coordinate ζk in the thickness direction of each layer and a nth-order (5 > n >= 0) polynomial of global coordinate z in the thickness direction of transverse deflection. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this theory, a refined three-node triangular element satisfying the requirement of C1 weak-continuity is presented. Numerical results show that present theory can be used to predict accurately in-plane stresses and transverse shear stresses from direct use of the relations of stresses and strains without any postprocessing method. However, to accurately obtain transverse normal stresses, the local equilibrium equation approach in one element is employed herein. It is effective when the number of layers of laminated plates is more than five and up to fourteen, and it can solve the problems for coupling bending and extension. It is also shown that the present refined triangular element possesses higher accuracy.

scholarly journals On reflected and transmitted stress waves at an elastic-plastic boundary

1980 ◽  
Vol 15 (1) ◽  
pp. 15-20 ◽  
Author(s):  
A S Khan
Keyword(s):  
Wave Theory ◽  
Finite Amplitude ◽  
Stress Waves ◽  
Constitutive Relationship ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Transmitted Waves ◽  
The One ◽  
Dynamic Plastic Deformation

A theoretical analysis for the reflected and transmitted waves at an elastic-plastic boundary is presented. The basis of this analysis is the linear elastic wave theory in a hard load-bar and the one-dimensional, strain-rate-independent theory of finite-amplitude plastic waves in a soft specimen. The constitutive relationship during dynamic plastic deformation is an experimentally determined dynamic response function in the soft material. The analysis predicts results that agree very closely with experimental results.

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