A Methodology for Optimal Design of Composite Laminates Using Polar Formalism

2016 ◽  
Vol 32 (3) ◽  
pp. 255-266
Author(s):  
M. Kazemi ◽  
G. Verchery
Keyword(s):  
Elastic Modulus ◽  
Composite Laminates ◽  
Elastic Moduli ◽  
Optimization Technique ◽  
Laminated Plates ◽  
Flexural Stiffness ◽  
Numerical Examples ◽  
Composite Laminated Plates ◽  
Plane Anisotropy ◽  
Laminated Structures

AbstractAn innovative optimization technique is presented for the design of composite laminated plates subjected to in-plane loads. A list of quasi-homogeneous laminates that can be used as angle-ply materials is proposed as a comprehensive solution for optimum lay-up. Two optimization procedures are performed: Dimensioning of the flexural stiffness and the elastic modulus, which provides the optimal orientations for the layers and offer highest in-plane resistance to composite laminated structures. The polar formalism for plane anisotropy is used to represent the flexural stiffness and elastic modulus tensors. Numerical examples are resolved for two materials with different elastic moduli.

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Stress Field ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Elasticity Solution ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Single Term ◽  
3D Elasticity ◽  
Laminated Structures

In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

Design and optimization of defense hole system for biaxial-loaded composite laminates

2015 ◽  
Vol 231 (3) ◽  
pp. 272-284 ◽  
Author(s):  
Salih N Akour ◽  
Mohammad Al-Husban
Keyword(s):  
Composite Laminates ◽  
Biaxial Loading ◽  
Optimization Technique ◽  
Laminated Plates ◽  
Design Parameters ◽  
Finite Element Models ◽  
Principal Stress Direction ◽  
Design And Optimization ◽  
Loading Ratio ◽  
Circular Cutout

Design optimization of defense hole systems placed near the main circular cutout of composite laminated plates subject to biaxial loading is performed in this study. For that purpose, a numerical framework based on finite element models validated experimentally via RGB-photoelasticity and by reproducing selected cases available in literature is developed. Redesign optimization technique is utilized to reach the optimum geometric design parameters of the defense hole system, i.e., size and location. Parametric study for fiber orientation, biaxial loading ratio, stiffness ratio and stacking sequence is conducted as well. Stress concentration near circular cutouts can be reduced by 24.5%, 25.5%, 29.1%, 31.7% and 20.6% for values of the loading ratio equal to, respectively, 0, 0.25, 0.50, 0.75 and 1. Such significant reductions are obtained by introducing four elliptical defense holes along the principal stress direction lined up with fibers.

Physical Ultrasonics of Composites

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Composite Laminates ◽  
Stiffness Matrix ◽  
Composite Plates ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Ultrasonic Waves ◽  
Laminated Plates ◽  
Structure Characteristic ◽  
Major Advance

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix", a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

scholarly journals The Effects of Creep on Elastic Modulus Measurement Using Nanoindentation

2000 ◽  
Vol 649 ◽  
Author(s):  
G. Feng ◽  
A.H.W. Ngan
Keyword(s):  
Elastic Modulus ◽  
Elastic Deformation ◽  
Elastic Moduli ◽  
Holding Time ◽  
Time Dependent ◽  
Nanoindentation Test ◽  
Modification Method ◽  
Unloading Rate ◽  
Modulus Measurement

ABSTRACTDuring the unloading segment of nanoindentation, time dependent displacement (TDD) accompanies elastic deformation. Consequently the modulus calculated by the Oliver-Pharr scheme can be overestimated. In this paper we present evidences for the influence of the measured modulus by TDD. A modification method is also presented to correct for the effects of TDD by extrapolating the TDD law in the holding process to the beginning of the unloading process. Using this method, the appropriate holding time and unloading rate can be estimated for nanoindentation test to minimise the effects of TDD. The elastic moduli of three materials computed by the modification method are compared with the results without considering the TDD effects.

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