An analytical model to predict the impact response of one-dimensional structures

2016 ◽  
Vol 22 (12) ◽  
pp. 2253-2268 ◽  
Author(s):  
Mohammad Tahaye Abadi
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Impact Loading ◽  
Impact Force ◽  
Displacement Function ◽  
Impact Response ◽  
Elastic Rod ◽  
Base Function ◽  
One Dimensional ◽  
The Impact

An analytical solution method is presented for the transient axial response of one-dimensional structures subjected to impact loading. The transient structural response is expressed as a series of the impact loading function and its progressive shifting values depending on both material position and time scale. The governing differential equation on the impact force is derived considering the general solution and constitutive equation of the contact interface. The analytical solution of differential equation yields a recursive function describing the impact force and displacement function of the total geometry. Depending on the contact surface roughness and the material properties, an impact function is introduced as a base function for impact response. The procedure is implemented to determine the shock waves generated at the collision of the elastic rod on the rigid surface and two elastic rods. The analytical solution also derives the steady-state response of the structure after the impact loading.

scholarly journals SOLUTION OF THE EQUATION OF IMPACT THE ELASTIC BODY, ONE OF WHICH CONE

2019 ◽  
pp. 43-49
Author(s):  
Vasyl Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Impact Force ◽  
Raw Materials ◽  
Theory Of Elasticity ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Static Contact ◽  
The Impact ◽  
Good Agreement

The impact interaction of elastic bodies with a small initial velocity is considered, when one of them is limited in the contact zone with another conical surface of revolution. Using the well-known solution of the static contact problem of the theory of elasticity, which found I. Shtaermann, and the assumptions of G. Hertz, which he made when creating his own theory of quasistatic impact of solids, compiled a nonlinear differential equation of impact force as a function of time. His closed analytical solution, which describes the process of dynamic interaction of bodies in time, is expressed through the periodic Ateb-sine. To simplify the use of the obtained analytical solution in the calculations, a separate table of the specified special function has been compiled and its approximation with elementary functions has been proposed, the relative error of which is less than one percent. In order to confirm the reliability of the constructed solutions, the integration of the equation of impact force on the computer was carried out in parallel. A good agreement is established between the results obtained by the constructed analytical solution and the numerical integration of the nonlinear Cauchy problem on a computer for a second-order differential equation. Compact formulas for the maxima of the impact force and the magnitude of the compression of bodies, as well as the formula for the duration of the impact process are derived. It is noted that the obtained results can be used in determining the dynamic loads acting on the rubber-lined rolls of the vibration classifier when pieces of solid raw materials fall on them. Examples of calculations are given and a comparative analysis of the results is carried out.

Finite Element Analysis of a Single-Layer Reticulated Dome and the Suspendome under Impact Loading

2012 ◽  
Vol 594-597 ◽  
pp. 844-848
Author(s):  
Liang Zheng
Keyword(s):  
Finite Element ◽  
Impact Loading ◽  
Impact Force ◽  
Numerical Models ◽  
Time History ◽  
Single Layer ◽  
Impact Response ◽  
Element Analysis ◽  
Peak Displacement ◽  
The Impact

This paper treats the impact force and the displacement of the lamella single-layer reticulated dome and the suspendome under axial impact loading using non-linear finite element techniques. The influence of loading parameters and the cable force of the suspendome on the impact response is investigated using validated numerical models. Results are quantified in terms of important impact response parameters and indicate that the peak displacement of the lamella single-layer reticulated dome and the suspendome can be clearly divided into four stages with time , and time history curve of the impact force can be divided into three stages.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

Dynamic Responses of Buried Pipelines Under Impact Loading Caused by Landslide

2012 ◽  
Vol 204-208 ◽  
pp. 3476-3479 ◽  
Author(s):  
Xiu Xing Zhu ◽  
Shi Feng Xue ◽  
Xing Hua Tong ◽  
Chuan Qi Liu
Keyword(s):  
Impact Loading ◽  
Impact Force ◽  
Large Diameter ◽  
Influence Factors ◽  
Dynamic Responses ◽  
Thin Wall ◽  
Buried Pipelines ◽  
Steel Pipes ◽  
Mountainous Regions ◽  
The Impact

Cases of pipeline damage caused by landslide are common in coastal or mountainous regions, where the design of buried pipelines should be improved in order to reduce the risk of damage or failure. Dynamic responses of large diameter thin wall steel pipes under impact loading were analyzed using a nonlinear contact model of pipe-soil coupling in this paper. Several influence factors were studied, such as the impact velocity of rockfall, buried depth of pipeline, ratio of diameter to thickness and style of soil. The results show that an ellipsoid induces much more impact force than a sphere which has the same volume, and the larger one in volume have greater impact force for two spheres. Dangerous compressive areas of pipeline occupy 1/6 of the whole area, so the pipelines subject to landslide occur local failure. Based on results, some useful suggestions for the design of pipelines in landslide region are given

Dynamic Response and Shear Demand of Reinforced Concrete Beams Subjected to Impact Loading

2019 ◽  
Vol 19 (08) ◽  
pp. 1950091 ◽  
Author(s):  
Wuchao Zhao ◽  
Jiang Qian
Keyword(s):  
Dynamic Response ◽  
Impact Loading ◽  
Parametric Study ◽  
Shear Failure ◽  
Impact Force ◽  
Rc Beams ◽  
Local Response ◽  
Shear Demand ◽  
The Impact ◽  
Peak Impact Force

Reinforced concrete (RC) beams under the impact loading are typically prone to suffer shear failure in the local response phase. In order to enhance the understanding of the mechanical behavior of the RC beams, their dynamic response and shear demand are numerically investigated in this paper. A 3D finite-element model is developed and validated against the experimental data available in the literature. Taking advantage of the above calibrated numerical model, an intensive parametric study is performed to identify the effect of different factors including the impact velocity, impact mass and beam span-to-depth ratio on the impact response of the RC beams. It is found that, due to the inertial effect, a linear relationship exists between the maximum reverse support force and the peak impact force, while negative bending moments also appear in the shear span. In addition, the local response of the RC beams can be divided into a first impact stage and a separation stage. A shear plug is likely to be formed near the impact point at the first impact stage and a shear failure may be triggered near the support by large support forces. Based on the simulation results, simplified methods are proposed for predicting the shear demand for the two failure modes, whereas physical models are also established to illustrate the resistance mechanism of the RC beams at the peak impact force. By comparing with the results of the parametric study, it is concluded that the shear demand of the RC beams under the impact loading can be predicted by the proposed empirical formulas with reasonable accuracy.

Vibration Analysis of Different Micro-Beams with Laser Ablation

2013 ◽  
Vol 462-463 ◽  
pp. 428-431
Author(s):  
Liang Cai Xiong ◽  
Quan Sheng Zhou ◽  
Peng Chen
Keyword(s):  
Laser Ablation ◽  
Dynamic Response ◽  
Vibration Analysis ◽  
Laser Excitation ◽  
Impact Force ◽  
Laser Doppler Vibrometer ◽  
Impact Response ◽  
Vibration Velocity ◽  
Laser Shock ◽  
The Impact

The dynamic response of different micro-beams after laser excitation experiments have been investigated in this paper. The impact force that induces the vibration of micro-beams is the interaction of focused pulse laser and tested beams. The impact response of micro-beams after being excited is measured by Laser Doppler Vibrometer. Different beams such as cantilever beam, L-shaped beam are employed in our experiments. Comparisons of the vibration velocity and its frequencies of different beams have also been performed. Experimental results show that the mechanical effects of laser shock do really exist and can be utilized.

scholarly journals Experimental study of the impact response of geocells as components of rockfall protection embankments

2009 ◽  
Vol 9 (2) ◽  
pp. 459-467 ◽  
Author(s):  
S. Lambert ◽  
P. Gotteland ◽  
F. Nicot
Keyword(s):  
Experimental Study ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Composite Structures ◽  
Impact Force ◽  
Impact Response ◽  
Rigid Base ◽  
Transmitted Force ◽  
The Impact ◽  
Rockfall Protection

Abstract. Rockfall protection embankments are ground levees designed to stop falling boulders. This paper investigates the behaviour of geocells to be used as components of these structures. Geocells, or cellular confinement systems, are composite structures associating a manufactured envelope with a granular geomaterial. Single cubic geocells were subjected to the impact resulting from dropping a spherical boulder. The geocells were filled with fine or coarse materials and different boundary conditions were applied on the lateral faces. The response is analysed in terms of the impact force and the force transmitted by the geocell to its rigid base. The influence on the geocell response of both the fill material and the cell boundary conditions is analysed. The aim was to identify the conditions resulting in greatest reduction of the transmitted force and also to provide data for the validation of a specific numerical model.

scholarly journals Experimental Investigation of Impact Response of RC Slabs with a Sandy Soil Cushion Layer

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Jianli Wu ◽  
Guotao Ma ◽  
Zhenhua Zhou ◽  
Xuefeng Mei ◽  
Xiewen Hu
Keyword(s):  
Layer Thickness ◽  
Sandy Soil ◽  
Failure Modes ◽  
Impact Force ◽  
Concrete Slab ◽  
Failure Process ◽  
Impact Response ◽  
Rc Slabs ◽  
Cushion Layer ◽  
The Impact

The impact response of reinforced-concrete (RC) slabs covered with a sandy soil cushion layer was investigated using an outdoor rockfall impact test platform. Impact tests were carried out by releasing rockfalls with different weights from different heights to impact a combined structure. Test data included the acceleration duration curve of the rockfall, strain of the concrete slab at multiple measuring points, and midpoint displacement duration curve of the slab. The test results showed an exponential relationship between the impact force acting on the cushion layer surface and cushion layer thickness. An empirical formula was used to calculate the maximum penetration, and the result was in good agreement with the test value. In addition, the attenuation rate of the impact force acting on the cushion layer increased exponentially with the increase in the cushion layer thickness, and the peak impact force could be attenuated by approximately 70% at a thickness of 0.6 m. Finally, the failure process and failure modes of the RC slabs were investigated.

Impact Response Spectrum for Design of Ship-Bridge Collisions

2014 ◽  
Vol 587-589 ◽  
pp. 1547-1553 ◽  
Author(s):  
Jun Jie Wang ◽  
Zhi Ran Yu
Keyword(s):  
Impact Force ◽  
Response Spectrum ◽  
Degree Of Freedom ◽  
Impact Response ◽  
Amplification Effect ◽  
Spectrum Method ◽  
Time Histories ◽  
Dynamic Amplification ◽  
Force Time ◽  
The Impact

Due to the complexity involved and limited study on the topic, the equivalent static method, adopted in the current codes for structural design of bridges under ship collisions, does not take into account the dynamic amplification effect correctly. An accurate assessment of impact force based on refined numerical simulation is time consuming and is normally too complex for ordinary design procedure. Herein, with reference to the earthquake response spectrum method, an impact response spectrum method, which considers the dynamic amplification effect and is efficient for design, is proposed. Through refined numerical simulations of ship-rigid wall collisions, 81 impact force time histories associated with 9 typical ships under 9 velocities are obtained. The dynamic magnification factor (DMF) of single-degree-of-freedom (SDOF) systems with different periods and damping ratios experiencing the 81 impact force time histories are then studied. The relationship of DMF and period under different damping ratios, i.e. the DMF spectrum, is yielded by statistical analysis, based on which the impact response spectrum is obtained. Finally, the design combination method for multi-degree-of-freedom based on the impact response spectrum of SDOF is discussed for a continuous beam bridge.

Effect of Flexibility in Transverse Impact Problems

1997 ◽  
Author(s):  
Ahmet S. Yigit ◽  
Andreas P. Christoforou
Keyword(s):  
Multibody Systems ◽  
Computational Models ◽  
Functional Relationship ◽  
Impact Force ◽  
Impact Response ◽  
Flexible Body ◽  
Transverse Impact ◽  
Impact Problems ◽  
Maximum Impact Force ◽  
The Impact

Abstract The nature of impact response of a flexible body is studied. The key parameters which govern the nature of impact response are identified. The effects of these parameters on the impact response are examined through numerical simulations. It is shown that the normalized impact force and the type of impact response can be predicted through the functional relationship between the normalized maximum impact force and two nondimensional parameters termed as “loss factor” and “relative stiffness”. It is expected that the results of this study will be of great value in choosing adequate impact and computational models for the dynamic analysis of multibody systems subject to transverse impacts.

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