An enhancement of the warping shear functions of Refined Zigzag Theory

2021 ◽  
pp. 1-15
Author(s):  
Matteo Sorrenti ◽  
Marco Di Sciuva
Keyword(s):  
Coupling Effect ◽  
Three Dimensional ◽  
Composite Plates ◽  
Laminated Plates ◽  
Point Of View ◽  
Multilayered Structures ◽  
Computational Point ◽  
Multilayered Plates ◽  
Elasticity Solutions ◽  
Zigzag Theory

Abstract The paper presents an enhancement in Refined Zigzag Theory (RZT) for the analysis of multilayered composite plates. In standard RZT, the zigzag functions cannot predict the coupling effect of in-plane displacements for anisotropic multilayered plates, such as angle-ply laminates. From a computational point of view, this undesirable effect leads to a singular stiffness matrix. In this work, the local kinematic field of RZT is enhanced with the other two zigzag functions that allow the coupling effect. In order to assess the accuracy of these new zigzag functions for RZT, results obtained from bending of angle-ply laminated plates are compared to the three-dimensional exact elasticity solutions and other plate models used in the open literature. The numerical results highlight that the enhanced zigzag functions extend the range of applicability of RZT to the study of general angle-ply multilayered structures, maintaining the same seven kinematic unknowns of standard RZT.

Two‐point ray tracing in a three‐dimensional medium consisting of homogeneous nonisotropic layers separated by plane interfaces

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 767-770 ◽  
Author(s):  
R. F. Stöckli
Keyword(s):  
Point Source ◽  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Wave Surface ◽  
Computational Point ◽  
Time Problem

The ray‐tracing problem is considered the solution to a minimum travel time problem for media where each layer may be regarded as a transversely isotropic homogeneous solid. The wave surface‐wavefront at t = 1 s, corresponding to a wave generated at the point source, associated with each layer’s anisotropy is approximated by surfaces which are not more difficult to handle, from a computational point of view, than ellipsoidal surfaces. These approximating surfaces are those used in ray‐tracing computation; a ray being a true ray approximation is thus obtained.

Three-Dimensional Solutions for Antisymmetrically Laminated Anisotropic Plates

1990 ◽  
Vol 57 (1) ◽  
pp. 182-188 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Three Dimensional ◽  
Composite Plates ◽  
Double Fourier Series ◽  
Stress And Strain ◽  
Anisotropic Plates ◽  
Stress Components ◽  
Strain Components ◽  
Elasticity Solutions ◽  
Vibration Problems ◽  
Three Dimensional Elasticity

Analytic three-dimensional elasticity solutions are presented for the stress and free vibration problems of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and antisymmetric lamination with respect to the middle plane. A mixed formulation is used with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of composite plates on the importance of the transverse stress and strain components.

Construction of Dynamic Fundamental Solutions for Piezoelectric Solids

1995 ◽  
Vol 48 (11S) ◽  
pp. S222-S229 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Integral Representations ◽  
Computational Point ◽  
Plane Wave Decomposition ◽  
Piezoelectric Solid ◽  
Piezoelectric Solids ◽  
Wave Decomposition

Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternatives to more classical approaches. The computational benefits of these new representations are displayed through a numerical example involving a transversely isotropic piezoelectric solid.

Vibration Analysis of Thin/Thick, Composites/Metallic Spinning Cylindrical Shells by Refined Beam Models

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
E. Carrera ◽  
M. Filippi
Keyword(s):  
Composite Materials ◽  
Initial Stress ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Point Of View ◽  
Displacement Fields ◽  
Previous Theory ◽  
Cross Sectional ◽  
Computational Point ◽  
Thick Composites

This paper evaluates the vibration characteristics of thin/thick rotating cylindrical shells made of metallic and composite materials. A previous theory of the authors is extended here to include the effects of geometrical stiffness due to rotation. To this end, variable kinematic one-dimensional (1D) models obtained by applying the Carrera Unified Formulation (CUF) were used. The components of the displacement fields are x, z polynomials of arbitrary order N, making it possible to go beyond the rigid cross section assumptions of the classical beam theories. A significant contribution of this formulation consists in the possibility to include the in-plane cross-sectional deformations allowing the introduction of the in-plane initial stress effects, e.g., the effect of the geometrical stiffness. Equations of motions, including both Coriolis and in-plane initial stress contributions, were solved through the finite element method. Several analyses were carried out on both thin and thick cylinders made of either metallic or composite materials with different boundary conditions. The results are compared with analytical and numerical shell formulations and three-dimensional solutions available in the literature. Various laminate lay-up have been considered in the case of composites shells. Numerical evaluations of the effect of geometric stiffness are provided, demonstrating its importance in the analyses presented. The 1D models appear very effective to investigate the dynamics of spinning shells and, contrary to shell theories, they do not require any amendments with thick shell geometry. From the computational point of view, the present refined beam models are less expensive than the shell and solid counterparts.

Assessment of Shear Deformation Theories for Multilayered Composite Plates

1989 ◽  
Vol 42 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Shear Deformation ◽  
Three Dimensional ◽  
Composite Plates ◽  
Linear Displacement ◽  
Two Dimensional ◽  
Multilayered Composite ◽  
Standard Of Comparison ◽  
Elasticity Solutions ◽  
Shear Deformation Theories ◽  
Three Dimensional Elasticity

A review is made of the different approaches used for modeling multilayered composite plates. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates

1992 ◽  
Vol 59 (4) ◽  
pp. 868-877 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Three Dimensional ◽  
Composite Plates ◽  
Double Fourier Series ◽  
Free Vibrations ◽  
Thermal Deformations ◽  
Sensitivity Derivatives ◽  
Neumann Type ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity ◽  
Thermally Stressed

Analytic three-dimensional elasticity solutions are presented for the free vibration and buckling of thermally stressed, multilayered, angle-ply composite plates. Sensitivity derivatives are also evaluated and used to study the sensitivity of the vibration and buckling responses to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. A linear, Duhamel-Neumann type constitutive model is used, and the material properties are assumed to be independent of temperature. The thermal plate response is subjected to time-varying perturbation displacements, strains, and stresses. A mixed formulation is used with the fundamental unknowns consisting of the six perturbation stress components and the three perturbation displacement components of the plate. The initial thermal deformations are accounted for. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Numerical results are presented showing the effects of variations in material characteristics and fiber orientation of different layers, as well as the effects of initial thermal deformations on the vibrational and buckling responses of the plate, as well as their sensitivity derivatives.

Three-dimensional multi-patch isogeometric analysis of composite laminates with a discontinuous Galerkin approach

2020 ◽  
pp. 147509022092573
Author(s):  
M Amin Obohat ◽  
Ehsan Tahvilian ◽  
M Erden Yildizdag ◽  
Ahmet Ergin
Keyword(s):  
Discontinuous Galerkin ◽  
Composite Laminates ◽  
Isogeometric Analysis ◽  
Numerical Models ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Point Of View ◽  
B Spline ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

In this study, a three-dimensional discontinuous Galerkin isogeometric analysis framework is presented for the analysis of composite laminates. Non-uniform rational B-splines are employed as basis functions for both geometric and computational implementations. From a practical point of view, modeling with multiple non-uniform rational B-spline patches is required in many different applications due to the complexity of computational domains. Then, a special numerical technique is necessary to couple different non-uniform rational B-spline patches to carry out the isogeometric analysis. In this study, therefore, one of the discontinuous Galerkin methods, namely, symmetric interior penalty Galerkin formulation is utilized to deal with multi-patch isogeometric analysis applications. In order to show the applicability of the proposed framework, composite laminates under sinusoidally distributed load with different stacking sequences are studied in the numerical examples. The predicted results are compared with those obtained by the three-dimensional elasticity solutions and various numerical models available in the literature.

scholarly journals Lightning Performance of Copper-Mesh Clad Composite Panels: Test and Simulation

Coatings ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 727 ◽  
Author(s):  
Hu ◽  
Yu
Keyword(s):  
Finite Element ◽  
Carbon Fiber ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Element Model ◽  
Laminated Plates ◽  
Lightning Strike ◽  
Element Analysis ◽  
Three Dimensional Finite Element ◽  
Copper Mesh

：According to simulation lightning experiments and eddy current analysis results, a three-dimensional finite element model of composite laminated plates with shield is established. By applying electric-thermal boundary and the coupling relationship between them, the lightning strike damage results under the protection of shield are realistically simulated with the commercial finite element analysis software, ABAQUS. Considering the coupling effect of heat, electricity, and force during lightning strike, the load distribution field of copper mesh and carbon fiber panel with lightning current inducted is analyzed. Comparing the thermal stress distribution of the specimen surface under various current loads, it is shown that the stress of carbon fiber panel is significantly lower than the one of the copper screen when the specimen structure suffers heavy current, since the copper network plays a role of endergonic protection. Simulation data are consistent with the test results, thus the method can be used for other similar research.

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