scholarly journals Elastic shakedown limit of a steel lattice girder

2021 ◽  
pp. 12-18
Author(s):  
Aneta BRZUZY
Keyword(s):  
Energy Dissipation ◽  
Permanent Deformation ◽  
Limit State ◽  
Direct Analysis ◽  
Elastic Response ◽  
Dissipation Of Energy ◽  
Internal Forces ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Lattice Girder

This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load

1993 ◽  
Vol 60 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Limit State ◽  
Limit Load ◽  
Companion Paper ◽  
Material Structure ◽  
Perfectly Plastic ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.

Study On Energy Dissipation Mechanism of an Impact Damper System

2022 ◽  
Author(s):  
Vinayaravi R ◽  
Jayaraj Kochupillai ◽  
Kumaresan D ◽  
Asraff A. K
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Fundamental Frequency ◽  
Low Frequency ◽  
High Amplitude ◽  
Lagrangian Multiplier ◽  
Impact Damper ◽  
Contact Algorithm ◽  
Dissipation Of Energy ◽  
Excitation Time

Abstract The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behaviour of an impact damper system using a MDOF system with Augmented Lagrangian Multiplier contact algorithm. Mathematical modelling and numerical simulations are carried out using ANSYS FEA package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behaviour of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

scholarly journals Study of Mechanical Energy Dissipation by Normal and Decalcified Animals Bones

2019 ◽  
Vol 16 (1) ◽  
pp. 113-119
Author(s):  
Abdul Rauf ◽  
Syed Ismail Ahmad
Keyword(s):  
Energy Dissipation ◽  
Viscoelastic Properties ◽  
Applied Load ◽  
Mechanical Energy ◽  
Maximum Energy ◽  
Hysteresis Curve ◽  
Normal Bone ◽  
Dissipation Of Energy ◽  
Mechanical Energy Dissipation ◽  
Energy Dissipated

The energy dissipated properties of normal and decalcified femur, rib and scapula bones of animals ox and camel have been studied by uniform bending technique. A hysteresis curve has been observed between the elevation in bone and load applied. It is observed that the energy dissipated as calculated from the hysteresis loop for rib is more than that of femur and scapula of ox and camel. It has been observed that the dissipation of energy in normal bone is less than that of decalcified bone under the same condition of applied load. The highest energy dissipation was observed in case of rib bone of camel compared to that of any other bone, rib of camel and scapula of ox dissipates maximum energy than femur bones. The study suggests that this technique is simple, elegant and inexpensive besides accurate in determining viscoelastic properties of bone.

Shakedown analysis for the evaluation of strength and bearing capacity of multilayered railway structures

2018 ◽  
Vol 232 (9) ◽  
pp. 2324-2335 ◽  
Author(s):  
Kangyu Wang ◽  
Yan Zhuang ◽  
Hanlong Liu
Keyword(s):  
Bearing Capacity ◽  
Engineering Design ◽  
Permanent Deformation ◽  
Three Dimensional ◽  
Frictional Coefficient ◽  
Repeated Loading ◽  
Residual Stress Field ◽  
Shakedown Analysis ◽  
Traffic Loads ◽  
Shakedown Limit

Shakedown analysis is a robust approach for solving the strength problem of a structure under cyclic or repeated loading, e.g. railway structures subject to rolling and sliding traffic loads. Owing to the traffic loads, which are higher than the “shakedown limit”, railway structures may fail due to the excessive permanent deformation. This paper develops the analytical shakedown solutions based on Melan’s shakedown theorem, which is then applied for the evaluation of the strength and bearing capacity of multilayered railway structures. The shakedown solutions utilize the elastic stress fields obtained from the fully three-dimensional finite/infinite model, and calculate the shakedown multiplier for each layer of railway structures by means of a self-equilibrated critical residual stress field. The shakedown limits are then determined as the minimum shakedown multiplier among all layers. Parametric studies are also conducted, which indicate how the frictional coefficient, strength and stiffness of the materials, and the thickness ratio of ballast to subballast influence the shakedown limit and the stability condition of railway structures. The critical points of shakedown occur at the rail for low values of rail’s yield stress and large frictional coefficient, while they occur at the ballast layer when the frictional coefficient is relatively small. The shakedown limits are found to decrease with the increase in the strength and thickness of the ballast for a relatively small frictional coefficient. For the engineering design, there is an optimum combination of material properties and layer thickness, which provides the maximum bearing capacity of the railway structure based on this research. The results obtained from this study can provide a useful reference for the engineering design of railway structures.

A Simplified Method for Response Behavior and Reliability Analysis of Long Submerged Structures With Tension Legs in Irregular Waves

2002 ◽  
Author(s):  
Shinji Katsura ◽  
Hiroo Okada ◽  
Koji Masaoka ◽  
Takashi Tsubogo ◽  
Kiko Shimada
Keyword(s):  
Limit State ◽  
Experimental Studies ◽  
Estimation Method ◽  
Dynamic Responses ◽  
Irregular Waves ◽  
Elastic Response ◽  
Tunnel Structure ◽  
Wave Loads ◽  
Response Behavior ◽  
Wave Conditions

This paper deals with the elastic response behavior of marine tunnel structures with tension legs in regular and irregular waves. Firstly, a simplified estimation method for dynamic responses under regular wave conditions is analytically presemed using a simple beam on an elastic foundation. Then, in order to demonstrate the validity of above results, experimental studies are carried out for a marine tunnel structure model with tension legs under wave-induced loads. Next, a simplified estimation method is presented for the elastic response behavior under irregular wave conditions by using above analytical results and combining irregular sea wave spectra. Then, the limit state failure mode of the main structure is presented for estimating the reliability level for cracking failure under extreme wave loads. Finally, the applicability of the methods is investigated through numerical examples carried out for a 1,000m-class marine tunnel structure with tension legs under some irregular sea state conditions. And characteristics of the short-term responses and reliability levels for the cracking failure are numerically shown.

Shakedown Boundary and Limit Load Determination of a 90-Degree Back to Back Pipe Bend Subjected to Steady Internal Perssures and Cyclic In-Plane Bending Moments

2013 ◽  
Author(s):  
Hany F. Abdalla
Keyword(s):  
Limit Load ◽  
Bending Moments ◽  
Pipe Bend ◽  
Shakedown Analysis ◽  
Plane Bending ◽  
Piping Networks ◽  
Aero Engines ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Internal Pressures

Shakedown analysis of 90–degree back–to–back pipe bends is scarce within open literature. According the author’s knowledge, no shakedown analysis exists for such structure based on experimental data. Ninety degree back–to–back pipe bends are extensively utilized within piping networks of nuclear submarines and modern turbofan aero–engines where space limitation is considered a paramount concern. Additionally, on larger scales, 90–degree back–to–back pipe bend configurations are also found within piping networks of huge liquefied natural gas tankers. The structure analyzed is formed by bending a straight pipe to acquire the geometry of two 90–degree pipe bends set back–to–back each having a nominal pipe size (NPS) of 10 in. Schedule 40 Standard (STD). In the current research, the 90–degree back–to–back pipe bend setup analyzed is subjected to a spectrum of steady internal pressures and cyclic in–plane bending moments. A previously developed simplified technique for determining elastic shakedown limit loads is utilized to generate the elastic shakedown boundary of the 90–degree back–to–back pipe bend analyzed. In addition to determining the elastic shakedown boundary, elastic and post shakedown domains (Bree diagram), the maximum moment carrying capacities (limit moments) are also determined and imposed on the generated Bree diagram of the analyzed structure. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.

Nanoindentation Characteristics of Patterned ITO for Multi-Touch Panel

2011 ◽  
Vol 80-81 ◽  
pp. 250-254 ◽  
Author(s):  
Wen Yang Chang ◽  
Cheng Hung Hsu
Keyword(s):  
Plastic Deformation ◽  
Energy Dissipation ◽  
Elastic Energy ◽  
Glass Substrate ◽  
Elastic Response ◽  
Touch Panel ◽  
Contact Areas ◽  
High Impedance ◽  
Mems Fabrication ◽  
Pet Film

Fabrication, nanoindentation characteristics, and optical spectroscopy of patterned ITO for multi-touch panel are investigated. The fabrications were carried out in two parts. The first part fabricates the high/low impedances of ITO patterns on silicon wafer, and the second part sputters the ITO patterns on PET film using MEMS fabrication. The array strips of ITOs on the PET film are defined as contact areas and row electrodes of scanning lines. The ITO patterns on the glass substrate include the contact areas, the narrow wires for high impedance, and the column electrodes of scanning lines for low impedance. The nanoindentation characteristics of load-unload regions generated elastic energy dissipation, which is attributed to higher elastic response, frictional energy, stiffness, and compressive plastic deformation. The maximum transmittance is 74.2% at the wavelength of about 692 nm due to a thicker ITO and Al films.

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