• Steel and Composite Structures
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• v.49 no.3
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.38-42
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• 2000

In this study, the low velocity impact behavior of the composite laminates has been described by using 3 dimensional nonlinear finite elements. To describe the geometric nonlinearity due to large deformation, the dynamic contact problem is formulated using the exterior penalty finite element method on the base of Total Lagrangian formulation. The incremental decomposition is introduced, and the converged solution is attained by Newton-Raphson Method. The Newmark's constant-acceleration time integration algorithm is used. To make verification of the finite element program developed in this study, the solution of the nonlinear static problem with occurrence of large deformation is compared with ABAQUS, and the solution of the static contact problem with indentation is compared with the Hertz solution. And, the solution of low velocity impact problem for isotropic material is verificated by comparison with that of LS-DYNA3D. Finally the contact force of impact response from the nonlinear analysis are compared with those from the linear analysis.

• Steel and Composite Structures
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• v.27 no.3
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• pp.273-283
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• 2018

Nonlinear low velocity impact response of sandwich beam with laminated composite face sheets and soft core is studied based on Extended High Order Sandwich Panel Theory (EHSAPT). The face sheets follow the Third order shear deformation beam theory (TSDT) that has hitherto not reported in conventional EHSAPT. Besides, the two dimensional elasticity is used for the core. The nonlinear Von Karman type relations for strains of face sheets and the core are adopted. Contact force between the impactor and the beam is obtained using the modified Hertz law. The field equations are derived via the Ritz based applied to the total energy of the system. The solution is obtained in the time domain by implementing the well-known Runge-Kutta method. The effects of boundary conditions, core-to-face sheet thickness ratio, initial velocity of the impactor, the impactor mass and position of the impactor are studied in detail. It is found that each of these parameters have significant effect on the impact characteristics which should be considered. Finally, some low velocity impact tests have been carried out by Drop Hammer Testing Machine. The contact force histories predicted by EHSAPT are in good agreement with that obtained by experimental results.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.325-334
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• 2018

The Nonlinear dynamic response of a sandwich plate subjected to the low velocity impact is theoretically and experimentally investigated. The Hertz law between the impactor and the plate is taken into account. Using the Extended High Order Sandwich Panel Theory (EHSAPT) and the Ritz energy method, the governing equations are derived. The skins follow the Third order shear deformation theory (TSDT) that has hitherto not reported in conventional EHSAPT. Besides, the three dimensional elasticity is used for the core. The nonlinear Von Karman relations for strains of skins and the core are adopted. Time domain solution of such equations is extracted by means of the well-known fourth-order Runge-Kutta method. The effects of core-to-skin thickness ratio, initial velocity of the impactor, the impactor mass and position of the impactor are studied in detail. It is found that these parameters play significant role in the impact force and dynamic response of the sandwich plate. Finally, some low velocity impact tests have been carried out by Drop Hammer Testing Machine. The results are compared with experimental data acquired by impact testing on sandwich plates as well as the results of finite element simulation.

• Advances in nano research
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• v.5 no.2
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• pp.69-97
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• 2017

In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.2982-2994
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• 1993

Low-velocity impact responses of composite laminates are investigated using the finite element method based on various theories. In two-dimensional nonlinear analysis, a displacement field considering higher order shear deformation and large deflection of the laminate is assumed and a finite element formulation is developed using a C$^{o}$-continuous 9-node plate element. Also, three-dimensional linear analysis based on the infinitesimal strain-displacement assumptions is performed using 8-node brick elements with incompatible modes. A modified Hertzian contact law is incorporated into the finite element program to evaluate the impact force. In the time integration, the Newmark constant acceleration algorithm is used in conjuction with successive iterations within each time step. Numerical results from static analysis as well as the impact response analysis are presented including impact force histories, deflections, strains in the laminate. Impact responses according to two typical low-velocity impact conditions are compared each other.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.207-215
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• 2017

The paper presents the studies carried out on low velocity impact of Ultra high performance concrete (UHPC) panels of size $350{\times}350{\times}10mm^3$ and $350{\times}350{\times}15mm^3$. The panels are cast with 2 and 2.5% micro steel fibre and compared with UHPC without fiber. The panels are subjected to low velocity impact, by a drop-weight hemispherical impactor, at three different energy levels of 10, 15 and 20 J. The impact force obtained from the experiments are compared with numerically obtained results using finite element method, theoretically by energy balance approach and empirically by nonlinear multi-genetic programming. The predictions by these models are found to be in good coherence with the experimental results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.359-371
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• 1994

A drop weight type impact test system is designed and set up to experimentally investigate impact responses of composite laminates subjected to the low-velocity impact. Using the test system, the impact velocity and the rebound velocity of the impactor as well as the impact force history are measured. An error of the measured data due to a difference in measuring position of the sensor is corrected and, for the estimation of real contact force history, a method of correcting an error due to friction forces is developed. Experimental methods to fix the boundary edgy of laminate specimens in impact testing are investigated and the impact tests on the specimens fixed by those methods are performed. Impact force histories and dynamic strains measured from the tests are compared with numerical results from the finite element analysis using the contact law. Consequently, the nonlinear numerical results considering the large deflection effects are agreed with the experimental results better than the linear ones.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.3
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• pp.757-770
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• 1991

본 연구에서는 조속충격을 받는 복합적층판의 거동에 대해 횡전단변형과 대처 짐효과를 동시에 고려하여 선형해석한 결과와의 차이를 비교, 검토하여 저속충격무제 의 해석에 있어서 비선형해석의 중요성을 보이는데 있다.그리고 충격체의 질량과 속도가 충격하중과 판의 거동, 그리고 동적 변형도등에 미치는 영향을 파악하여 복합 적층판의 외부 물체에 의한 저속충격문제를 이해 하고자 한다.