scholarly journals Rigid-Plastic Approximations for Predicting Plastic Deformation of Cylindrical Shells Subject to Dynamic Loading

1996 ◽  
Vol 3 (3) ◽  
pp. 169-181 ◽  
Author(s):  
Michelle S. Hoo Fatt ◽  
Tomasz Wierzbicki ◽  
Minos Moussouros ◽  
John Koenig
Keyword(s):  
Plastic Deformation ◽  
Tensile Force ◽  
Bending Moment ◽  
Expansion Method ◽  
Rigid Plastic ◽  
Closed Form Solutions ◽  
Eigenfunction Expansion Method ◽  
Longitudinal Bending ◽  
Final Deformation ◽  
String State

A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.

scholarly journals Plastic Deformation and Rupture of Ring-Stiffened Cylinders under Localized Pressure Pulse Loading

1994 ◽  
Vol 1 (3) ◽  
pp. 289-301 ◽  
Author(s):  
Michelle S. Hoo Fatt
Keyword(s):  
Plastic Deformation ◽  
Cylindrical Shell ◽  
Pressure Pulse ◽  
Fracture Initiation ◽  
Pulse Loading ◽  
Rigid Plastic ◽  
Stiffened Shell ◽  
Closed Form Solutions ◽  
Stiffened Cylindrical Shell ◽  
Lumped Masses

An analytical solution for the dynamic plastic deformation of a ring-stiffened cylindrical shell subject to high intensity pressure pulse loading is presented. By using an analogy between a cylindrical shell that undergoes large plastic deformation and a rigid-plastic string resting on a rigid-plastic foundation, one derives closed-form solutions for the transient and final deflection profiles and fracture initiation of the shell. Discrete masses' and springs are used to describe the ring stiffeners in the stiffened shell. The problem of finding the transient deflection profile of the central bay is reduced to solving an inhomogeneous wave equation with inhomogeneous boundary conditions using the method of eigenfunction expansion. The overall deflection profile consists of both global (stiffener) and local (bay) components. This division of the shell deflection profile reveals a complex interplay between the motions of the stiffener and the bay. Furthermore, a parametric study on a ring-stiffened shell damaged by a succession of underwater explosions shows that the string-on-foundation model with ring stiffeners described by lumped masses and springs is a promising method of analyzing the structure.

Application of an Eigenfunction Expansion Method in Plasticity

1974 ◽  
Vol 41 (2) ◽  
pp. 448-452 ◽  
Author(s):  
T. Wierzbicki
Keyword(s):  
Plastic Material ◽  
Expansion Method ◽  
Plastic Behavior ◽  
Sensitive Material ◽  
Rigid Plastic ◽  
Simple Method ◽  
Elastic Mode ◽  
Perfectly Plastic ◽  
Eigenfunction Expansion Method ◽  
Expansion Technique

Possibilities of extending the eigenvalue expansion method to dynamic problems for plastic continua and structures are examined. A model of a pseudo strain rate sensitive material is introduced as an approximation to the concept of rigid-perfectly plastic material. A simple method is then developed which parallels the familiar elastic mode expansion technique but yet retains the main features of rigid-plastic behavior. The accuracy of the method is discussed and comparison with previous theories is made. An illustrative example is presented.

scholarly journals Analysis of Strain-Hardening Viscoplastic Wide Sheets Subject to Bending under Tension

Metals ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 118
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina
Keyword(s):  
Strain Hardening ◽  
Thickness Distribution ◽  
Tensile Force ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Equivalent Strain ◽  
Accurate Solution ◽  
Viscoplastic Material ◽  
Rigid Plastic ◽  
Bending Under Tension

The present paper provides an accurate solution for finite plane strain bending under tension of a rigid/plastic sheet using a general material model of a strain-hardening viscoplastic material. In particular, no restriction is imposed on the dependence of the yield stress on the equivalent strain and the equivalent strain rate. A special numerical procedure is necessary to solve a non-standard ordinary differential equation resulting from the analytic treatment of the boundary value problem. A numerical example illustrates the general solution assuming that the tensile force vanishes. This numerical solution demonstrates a significant effect of the parameter that controls the loading speed on the bending moment and the through-thickness distribution of stresses.

scholarly journals Near-Fault Seismic Response Analysis of Bridges Considering Girder Impact and Pier Size

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 704
Author(s):  
Wenjun An ◽  
Guquan Song ◽  
Shutong Chen
Keyword(s):  
Seismic Response ◽  
Bending Moment ◽  
Expansion Method ◽  
Response Analysis ◽  
Seismic Action ◽  
Transient Wave ◽  
Cross Sectional ◽  
Displacement Response ◽  
Near Fault ◽  
Continuous Girder Bridge

Given the influence of near-fault vertical seismic action, we established a girder-spring-damping-rod model of a double-span continuous girder bridge and used the transient wave function expansion method and indirect modal function method to calculate the seismic response of the bridge. We deduced the theoretical solution for the vertical and longitudinal contact force and displacement response of the bridge structure under the action of the near-fault vertical seismic excitation, and we analyzed the influence of the vertical separation of the bridge on the bending failure of the pier. Our results show that under the action of a near-fault vertical earthquake, pier-girder separation will significantly alter the bridge’s longitudinal displacement response, and that neglecting this separation may lead to the underestimation of the pier’s bending damage. Calculations of the bending moment at the bottom of the pier under different pier heights and cross-sectional diameters showed that the separation of the pier and the girder increases the bending moment at the pier’s base. Therefore, the reasonable design of the pier size and tensile support bearing in near-fault areas may help to reduce longitudinal damage to bridges.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

Study on Dynamic Stability of Single Floating Pier Under Waves

2021 ◽  
Author(s):  
Yikuan He ◽  
Bing Han ◽  
Wenyu Ji
Keyword(s):  
Dynamic Stability ◽  
Expansion Method ◽  
Diffraction Effect ◽  
Exterior Region ◽  
Factors Affecting ◽  
Eigenfunction Expansion Method ◽  
Floating Bridge ◽  
Response Equation ◽  
Floating Pier ◽  
Wave Excitation Force

Abstract Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

Effective Estimation of Water Waves Scattering by Double-Row Pile Breakwaters

2012 ◽  
Author(s):  
Omid Nejadkazem ◽  
Ahmad Reza Mostafa Gharabaghi
Keyword(s):  
Water Waves ◽  
Wave Length ◽  
Expansion Method ◽  
Optimum Number ◽  
Intermediate Water ◽  
Double Row ◽  
Eigenfunction Expansion Method ◽  
Efficient Performance ◽  
Efficient Calculation ◽  
Efficient Prediction

This paper describes various hydraulic characteristic of double-row pile breakwaters (DPB). Applying an eigenfunction expansion method, a numerical method have been developed that can compute wave transmission, reflection, and other hydraulic characteristics. To verify the validity of developed prediction, laboratory experiments of Isaascson et al. (1999) have been utilized. Then for an efficient calculation, optimum number of necessary evanescent waves for an effective and efficient prediction is discussed for various hydraulic quantities of interest. In a nutshell, for an effective and efficient performance of the DPB, intermediate water wave and porosity range of [0.2 0.3] are recommended. Relative distance between two barriers must be set depending on significant wave length of design.

Study of the Titanium Alloy Deformation Behavior in Equal Channel Angular Extrusion

2007 ◽  
Vol 345-346 ◽  
pp. 177-180 ◽  
Author(s):  
Dyi Cheng Chen ◽  
Yi Ju Li ◽  
Gow Yi Tzou
Keyword(s):  
Plastic Deformation ◽  
Titanium Alloy ◽  
Deformation Behavior ◽  
Equal Channel Angular Extrusion ◽  
Effective Strain ◽  
Processing Conditions ◽  
Rigid Plastic ◽  
Die Geometry ◽  
Extrusion Processing ◽  
Plastic Deformation Behavior

The shear plastic deformation behavior of a material during equal channel angular (ECA) extrusion is governed primarily by the die geometry, the material properties, and the processing conditions. Using commercial DEFORMTM 2D rigid-plastic finite element code, this study investigates the plastic deformation behavior of Ti-6Al-4V titanium alloy during 1- and 2-turn ECA extrusion processing in dies containing right-angle turns. The simulations investigate the distributions of the billet mesh, effective stress and effective strain under various processing conditions. The respective influences of the channel curvatures in the inner and outer regions of the channel corner are systematically examined. The numerical results provide valuable insights into the shear plastic deformation behavior of Ti-6Al-4V titanium alloy during ECA extrusion.

Effect of Bend Angle on Gross Plastic Deformation of Pipe Bends: A Finite Element Based Study

2015 ◽  
Author(s):  
Anindya Bhattacharya ◽  
Sachin Bapat ◽  
Hardik Patel ◽  
Shailan Patel
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Failure Mechanisms ◽  
Bending Moment ◽  
Bend Angle ◽  
Piping System ◽  
Plastic Collapse ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bend Angles

Bends are an integral part of a piping system. Because of the ability to ovalize and warp they offer more flexibility when compared to straight pipes. Piping Code ASME B31.3 [1] provides flexibility factors and stress intensification factors for the pipe bends. Like any other piping component, one of the failure mechanisms of a pipe bend is gross plastic deformation. In this paper, plastic collapse load of pipe bends have been analyzed for various bend parameters (bend parameter = tRbrm2) under internal pressure and in-plane bending moment for various bend angles using both small and large deformation theories. FE code ABAQUS version 6.9EF-1 has been used for the analyses.

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