• Title/Summary/Keyword: Higher order zig-zag theory

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A Finite Element Analysis based on Higher-Order Zig-Zag Shell Theory for Laminated Composites Cylinderical Shell with Multiple Delaminations (다중 층간분리부가 있는 복합재 원통쉘의 지그재그 고차이론에 기초한 유한요소 진동해석)

  • Cho Maenghyo;Oh Jinho;Kim Heung-Soo
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2004.10a
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    • pp.69-72
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    • 2004
  • A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

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Dynamic analysis for delaminated composites based on finite element (다중 층간분리부가 내재된 복합재 평판의 유한요소 진동해석)

  • 오진호;조맹효;김준식
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2003.04a
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    • pp.143-146
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    • 2003
  • A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

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Development and Assessment of Higher Order Zig-zag Theory for smart composite plates under mechanical, thermal, and electric loads (열-전기-기계 하중을 받는 스마트 복합재 평판의 고차 지그재그 유한요소의 개발 및 성능 평가)

  • 오진호;조맹효
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2001.10a
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    • pp.191-194
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    • 2001
  • A partially coupled thermo-piezoelectric-mechanical triangular finite element model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied mechanical load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness. Nonconforming shape functions by Specht are employed in the transverse displacement variables. Numerical examples demonstrate the accuracy and efficiency of the proposed triangular plate element.

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Vibration Analysis of Pretwisted Composite Plates with Embedded Viscoelastic Core using Zig-Zag Triangular Finite Element (지그재그 삼각형 유한요소를 이용한 점탄성물질이 심어진 비틀린 복합재료판의 진동해석)

  • Lee,Deok-Gyu;Jo,Maeng-Hyo
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.31 no.1
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    • pp.18-24
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    • 2003
  • A three node triangular element with drilling rotations incorporating improved higher-order zig-zag theory(HZZT) is developed to analyze the vibration of pretwisted composite plates with embedded damping layer. Shear force matching conditions are enforced along the interfaces between the embedded damping patch and the border patch by matching the shear forces of the embedded damping patch to the shear forces of the adjacent border patch. The natural frequencies and modal loss factors are calculated for cantilevered pretwisted composite blade with damping core with the present triangular element, and compared to experiments and MSC/NASTRAN using a layered combination of plate and solid elements.

Cylindrical bending of laminated cylindrical shells using a modified zig-zag theory

  • Icardi, Ugo
    • Structural Engineering and Mechanics
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    • v.6 no.5
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    • pp.497-516
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    • 1998
  • A relatively simple two-dimensional multilayered shell model is presented for predicting both global quantities and stress distributions across the thickness of multilayered thick shells, that is based on a third-order zig-zag approach. As for any zig-zag model, the layerwise kinematics is accounted for, with the stress continuity conditions at interfaces met a priori. Moreover, the shell model satisfies the zero transverse shear stress conditions at the upper and lower free surfaces of the shell, irrespective of the lay-up. By changing the parameters in the displacement model, some higher order shell models are obtained as particular cases. Although it potentially has a wide range of validity, application is limited to cylindrical shell panels in cylindrical bending, a lot of solutions of two-dimensional models based on rather different simplyfying assumptions and the exact three-dimensional elasticity solution being available for comparisons for this benchmark problem. The numerical investigation performed by the present shell model and by the shell models derived from it illustrates the effects of transverse shear modeling and the range of applicability of the simplyfying assumptions introduced. The implications of retaining only selected terms depending on the radius-to-thickness ratio are focused by comparing the present solutions to the exact one and to other two-dimensional solutions in literature based on rather different simplyfying assumptions.

지그재그이론을 이용한 유한요소개발 및 응용

  • Lee, Deog-Gyu
    • Aerospace Engineering and Technology
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    • v.3 no.1
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    • pp.257-266
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    • 2004
  • A three node triangular element with drilling rotations incorporating improved higher-order zig-zag theory(HZZT) is developed to accurately assess the stress distribution through thickness of the laminated plate and analyze the vibration of pretwisted composite plates with embedded damping layer. Shear force matching conditions are enforced along the interfaces between the embedded damping patch and the border patch. The natural frequencies and model loss factors are calculated for cantilevered pretwisted composite blade with damping core with the present triangular element, and compared to experiments and MSC/NASTRAN using a layered combination of plate and solid elements.

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Refined Decoupled Stress Analysis for Thermo-piezoelectric Composite Plate (열-전기-기계 하중에서의 복합재 평판의 응력해석)

  • 오진호;조맹효
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2000.11a
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    • pp.46-49
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    • 2000
  • A decoupled thermo-~lezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.

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Superharmonic vibrations of sandwich beams with viscoelastic core layer with the multiple scale method

  • Benaoum, Abdelhak;Youzera, Hadj;Abualnour, Moussa;Houari, Mohammed Sid Ahmed;Meftah, Sid Ahmed;Tounsi, Abdelouahed
    • Structural Engineering and Mechanics
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    • v.80 no.6
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    • pp.727-736
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    • 2021
  • In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

On the Modification of a Classical Higher-order Shear Deformation Theory to Improve the Stress Prediction of Laminated Composite Plates (적층평판의 응력해석 향상을 위한 고전적 고차전단변형이론의 개선)

  • Kim, Jun-Sik;Han, Jang-Woo;Cho, Maeng-Hyo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.3
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    • pp.249-257
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    • 2011
  • In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

Nonlinear damping and forced vibration analysis of laminated composite plates with composite viscoelastic core layer

  • Youzera, Hadj;Ali, Abbache;Meftah, Sid Ahmed;Tounsi, Abdelouahed;Hussain, Muzamal
    • Steel and Composite Structures
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    • v.44 no.1
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    • pp.91-104
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    • 2022
  • The purpose of the present work is to study the parametric nonlinear vibration behavior of three layered symmetric laminated plate. In the analytical formulation; both normal and shear deformations are considered in the core layer by means of the refined higher-order zig-zag theory. Harmonic balance method in conjunction with Galerkin procedure is adopted for simply supported laminate plate, to obtain its natural and damping properties. For these aims, a set of complex amplitude equations governed by complex parameters are written accounting for the geometric nonlinearity and viscoelastic damping factor. The frequency response curves are presented and discussed by varying the material and geometric properties of the core layer.