The Impact Between a Rigid Sphere and a Thin Layer

1970 ◽  
Vol 37 (1) ◽  
pp. 159-162 ◽  
Author(s):  
H. D. Conway ◽  
H. C. Lee ◽  
R. G. Bayer
Keyword(s):  
Thin Layer ◽  
Coefficient Of Restitution ◽  
Rigid Sphere ◽  
Approximate Analysis ◽  
Rigid Substrate ◽  
Perfectly Plastic ◽  
Major Loss ◽  
Elastic Perfectly Plastic ◽  
The Impact ◽  
Good Agreement

A simple model is presented for studying the impact between a rigid sphere and a thin layer of relatively soft material supported on a rigid substrate. By assuming that the major loss of energy during impact is due to the plastic deformation of the layer, an approximate analysis is made for computing the energy loss for layer materials which obey an elastic, perfectly plastic stress-strain law. An analytical expression for the coefficient of restitution is derived, and a parameter which controls the rebound characteristics is identified. Experimental results show generally good agreement with the analysis.

Analysis on the Moment-Curvature Relationship for Prestressed UHPFRC Beams without Stirrup

2011 ◽  
Vol 255-260 ◽  
pp. 236-240
Author(s):  
Sang Mook Han ◽  
Qing Yong Guo
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Steel Fibre ◽  
Fibre Reinforcement ◽  
Cracking Behavior ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Good Agreement

To simplify the analysis, an elastic perfectly plastic stress-strain law was presented for UHPFRC. The post-cracking behavior was described by the average constant post-crack tensile strength. A strain parameter μ is proposed to evaluate the performance and efficiency of steel fibre reinforcement. 8 rectangular beams were tested in this investigation. Based on the proposed constitutive model, the full history of their flexural moment-curvature relationship for UHPFRC beams was calculated and compared with experimental data on prestressed UHPFRC beams. Good agreement between calculated strengths and experimental data was obtained.

Case Study of Shakedown Evaluation of a Shell With Nozzle Based on Elastic-Plastic Analysis

2017 ◽  
Author(s):  
Jun Shen ◽  
Heng Peng ◽  
Liping Wan ◽  
Yanfang Tang ◽  
Yinghua Liu
Keyword(s):  
Temperature Change ◽  
Plastic Material ◽  
Material Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Temperature Loads ◽  
The Impact

In the past, shakedown evaluation was usually based on the elastic method that the sum of the primary and secondary stress should be limited to 3Sm or the simplified elastic-plastic analysis method. The elastic method is just an approximate analysis, and the rigorous evaluation of shakedown normally requires an elastic-plastic analysis. In this paper, using an elastic perfectly plastic material model, the shakedown analysis was performed by a series of elastic-plastic analyses. Taking a shell with a nozzle subjected to parameterized temperature loads as an example, the impact of temperature change on the shakedown load was discussed and the shakedown loads of this structure at different temperature change rates were also obtained. This study can provide helpful references for engineering design.

scholarly journals Coefficients of Restitution Based on a Fractal Surface Model

2003 ◽  
Vol 70 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Chung-Jen Lu ◽  
Ming-Chang Kuo
Keyword(s):  
Surface Topography ◽  
Material Properties ◽  
Plastic Material ◽  
Coefficient Of Restitution ◽  
Surface Model ◽  
Fractal Surface ◽  
Normal Contact ◽  
Perfectly Plastic ◽  
Fractal Models ◽  
Elastic Perfectly Plastic

Equations of rigid-body mechanics provide a means to predict the post-collision behavior without recourse to highly complex, detailed analysis of deformations during contact. Before the prediction can be completed, the coefficient of restitution, which relates the rebound velocity to the incident velocity, must be estimated properly. The coefficient of restitution depends on the surface topography in addition to the material properties and incident velocity. Recent investigations showed that surface topography can be characterized properly by fractal models. This paper proposes a normal contact model for a fractal surface in contact with a rigid smooth half-space. The fractal surface is constructed based on the Cantor set and composed of elastic-perfectly plastic material. Asymptotic continuous expressions for the load-displacement relations during loading and unloading are derived. Based on these results, we study the effects of surface roughness, material properties and incident velocity on the coefficient of restitution.

The Indentation of an Elastic-Perfectly-Plastic Half-Space by a Hard Sphere

1972 ◽  
Vol 94 (1) ◽  
pp. 251-253 ◽  
Author(s):  
C. Hardy ◽  
C.-N. Baronet ◽  
G.-V. Tordion
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Hard Sphere ◽  
Present Note ◽  
Plane Surface ◽  
Metallic Materials ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Good Agreement

The indentation of hard steel spheres into the plane surface of quasi elastic-perfectly-plastic metallic materials has been investigated experimentally. It is shown in the present note that uniform results are obtained when the experimental data corresponding to some materials are reduced to a common base. These results are in fairly good agreement with the predictions of a previous finite element analysis by the same authors.

The Impact of an Elastic Sphere on a Thin Elastic Plate Supported by a Winkler Foundation

1975 ◽  
Vol 42 (1) ◽  
pp. 133-135 ◽  
Author(s):  
H. D. Fisher
Keyword(s):  
Thin Plate ◽  
Contact Time ◽  
Viscoelastic Plate ◽  
Coefficient Of Restitution ◽  
Solution Technique ◽  
Rigid Sphere ◽  
Winkler Foundation ◽  
Thin Elastic Plate ◽  
Continuous Contact ◽  
The Impact

This paper investigates the elastic impact of a sphere on a thin plate which is in continuous contact with a foundation. The reaction pressure is considered to be proportional to the local deflection (Winkler hypothesis). A solution technique, which was originally developed to analyze the impact of a rigid sphere on a viscoelastic plate, is modified for application in the present study. The contact force, the coefficient of restitution, and the contact time are computed for a wide variation in the two dimensionless parameters which are required to describe a given problem. For the limiting cases of impact on a half space and impact on a thin plate supported by a rigid foundation, the contact time computed here is shown to correlate with the calculations of earlier investigators.

Dynamic Motion of RC Beams and One-Way Slabs Impacted by a Missile at Medium Velocity: Models for Spreadsheet Application

2010 ◽  
Author(s):  
Jean-Mathieu Rambach
Keyword(s):  
Velocity Models ◽  
Perfectly Plastic ◽  
Finite Differences Method ◽  
Order Of Magnitude ◽  
Sensitivity Studies ◽  
Rectangular Slab ◽  
Elastic Perfectly Plastic ◽  
Method Show ◽  
Spreadsheet Application ◽  
Good Agreement

This paper deals with the simulation of the motion of a one-span slender rectilinear RC beam or a thin one-way RC rectangular slab when impacted by a missile, within and beyond the elastic domain, up to a maximal displacement equal to the height of the section. The loading is variable in time and in space and the supporting conditions at each extremity are either of simply resting type or of clamping type. The equation of motion for each beam segment is expressed, through finite differences method, by relations between velocity and flexural moment that are decomposed on the basis of the first N modes of beam deformation. The plastic deformations are taken into account by constraining the flexural moment to follow elastic/perfectly plastic flexural moment–curvature law. The algorithms are well adapted to a spreadsheet application that allows easily: i) presizing such a structure against this type of loading, ii) the sensitivity studies regarding the mechanical parameters, iii) checking the order of magnitude of the results of big FEM models by using highly sophisticated codes. Simulations by this method show good agreement with experimental results and give access to some mechanical properties of the structure when damaged.

Net-Section Limit Pressure and Engineering J Estimates for Axial Part-Through Surface Cracked Pipes

2007 ◽  
Author(s):  
Yun-Jae Kim ◽  
Chang-Sik Oh ◽  
Tae-Kwang Song
Keyword(s):  
Estimation Method ◽  
Small Strain ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Axial Part ◽  
Elastic Perfectly Plastic ◽  
Axial Surface ◽  
Good Agreement ◽  
J Estimation

This paper provides net-section limit pressures and a reference stress based J estimation method for pipes with internal axial surface cracks under internal pressure. Based on systematic small strain FE limit analyses using elastic-perfectly plastic materials, closed-form approximations of net-section limit pressures are presented. Then, based on proposed net-section limit moments, a method to estimate elastic-plastic J is proposed based on the reference stress approach. Comparison with extensive FE results shows overall good agreement.

Reference Stress Solutions for Idealized Branch Junctions

2007 ◽  
Author(s):  
Yun-Jae Kim ◽  
Kuk-Hee Lee
Keyword(s):  
Three Dimensional ◽  
Limit Load ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Pipe Radius ◽  
Plastic Limit Load ◽  
The Mean ◽  
Elastic Perfectly Plastic ◽  
Good Agreement

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) FE limit analyses using elastic-perfectly plastic materials. The proposed solutions are valid to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparison with FE results shows good agreement.

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