CHAPTER 4 4 NUMERICAL ANALYSIS

Transcription

1 41 CHAPTER 4 4 NUMERICAL ANALYSIS Simulation is a powerful tool that engineers use to predict the result of a phenomenon or to simulate the working situation in which a part or machine will perform in a real world. In the present work after completion of experimental testing, simulation is also conducted. Results show a good agreement between experimental result and simulation result. In this part a brief explanation will be given on FEA analysis as well as the software used to simulate our work. Steps taken for modeling and solving are also described in this part; 4.1 MSC/Dytran Finite element analysis software used in this project - MSC/Dytran version 4.0 MSC/Dytran - is a three dimensional analysis explicit software for analyzing dynamic, non linear behavior of solid components, structures, and fluids which simulate a wide range of material and geometric nonlinearity.

2 42 It is particularly suitable for analyzing short, transient dynamic events that include large deformations, a high degree of material nonlinearity (foam, rubber, and large deformations in metal), large geometric nonlinearity (buckling, crippling, and cracking), extreme boundary nonlinearity (a structure folding over onto itself) and interaction between fluids and structures. Typical applications of MSC/Dytran include: Airbag inflation Sheet metal forming analysis Bird strike on aerospace structure Structural response to explosion and blast loading High velocity penetration Ship collision MSC/Dytran uses a combination of Lagrangian and Eularian solver technology to analyze short-duration transient events that require finer time step to ensure a more accurate solution. Solid, shell, beam, membrane, spring and rigid elements can be used within Lagrangian solver to model the structure while three-dimensional elements can be used to create Eulerian meshes. A wide range of material models are available to model the nonlinear response and failure. These include linear elasticity, yield

3 43 criteria, equations of state, failure and spall models, explosive burn models and composite materials to name a few. Contact surfaces allow structural components to interact with each other or with rigid geometric structures. This interaction may include frictionless contact, sliding with frictional effects and separation. Single surface contact can be used to model buckling of structures where material may fold onto itself. 4.2 Simulation of experimental work The test set-up simulated using FEM methodologies to study the behavior of Tubes under buckling loads more in detail. The Finite Element Model [FEM] developed as similar as the test setup, to capture the appropriate behavior of tubes under compression. The key factors for this analysis are: Simulation of Contacts Constant velocity application for specific time Study the various locations for peak responses Simulation of Contacts:

4 44 Buckling happens when samples are under compression load. This means tube makes foldings as the upper head of the testing machine comes downward. These folding sit on each other, press one another and transmit the compression force to lower part of the tube. The important part of this analysis is to simulate the proper contact regions. There would be many contact pairs comes into picture during the simulation of compression test. The contact between the compression plate and tube should be intact throughout the analysis. The self contact within tube due to the buckling nature also simulated as shown in figure 4.2. Constant velocity application for specific time: During experimental test samples are subjected to the vertical compression load at constant rate of 10mm/min. It is simulated by moving the top plate at constant velocity toward bottom of the tube. Study the various locations for peak responses: During analysis, reference point should be selected such that it can predict the appropriate response from that this particular location. The location selected at the bottom of the tube since any other location at top or in between of the top and bottom may fail because of buckling.

5 45 Practically there are many limitations during capturing the responses from the test: number of sensors Placing sensor at appropriate/critical location Recording proper response throughout the testing In order to capture all the mentioned factors there is a need for appropriate analytical software; to conduct numerical analysis, Hypermesh v.11.0 is used for finite element modeling [pre-processor], MSC-Dytran is used to solve the explicit analysis in order to perform structural analysis as well as the MSC-Patran for post-processing to review the analysis output. 4.3 FE Modeling: As per the test set-up the tube is mounted on the base with fixing the bottom end in all DOF. The compression arm in the test set-up is simulated with a sheet [modeled with shell elements] as shown in Fig 4.1.

6 46 Figure 4.1 FE model of tube compression The contacts simulated between the top-plate and tube to transfer the compression load to tube. Also there is a self contact definition required for the tube alone, as tube surface will comes into a contact with the same surface. Dytran has a capability of self-contact which will helps in simulating the self-contact during the buckling under crushing load. Tube is modeled with shell elements with the thickness equal to the thickness of tube. The compression plate modeled with shell elements made of very high stiffened material.

7 47 There are various models simulated under the compressive loads shown in Fig.1.24 as listed below: Tube without holes Tube with a pair of holes of diameter 4.3mm Tube with three pairs of holes diameter 4.3mm Tube with six pairs of holes diameter 4.3mm Tube with a pair of holes of diameter 7.5mm Tube with three pairs of holes diameter 7.5mm Tube with six pairs of holes diameter 7.5mm There are totally 14 models analyzed under the similar compression loads. Seven models made for Aluminum and seven models are made for Steel

8 48 Figure 4.2 FE Models of different samples Load Application: The applied compression load simulated with constant velocity applied on plate.

9 49 The load is applied in the form of velocity in order to apply downward displacement at constant rate of upper-head of the testing machine. In below diagram of Velocity versus Time and Displacement versus time are shown: Figure 4.3 Graph of velocity vs. time (constant velocity) Figure 4.4 Graph of displacement vs. time (rate =10mm/min)

10 50 Tools Used: Hypermesh is used to model the tubes and plate setup. In Hypermesh, Finite Element models for 14 Set of tubes developed and then exported into Dytran profile. The FE model exported from Hypermesh then imported into MSC/Patran and applied all the transient loads required to analyze under compression loads. The FE model of Tube and Plate with appropriate load data will be exported finally into Dytran profile. The exported FE model was analyzed using MSC/Dytran. Results from the analysis of the crushing force response extracted into *.ARC file format, which is compatible to post-process in MSC/Patran. The crushing force versus crushing time data profile was extracted for the base of each tube where tube is fixed in all degrees of freedom (DOF). The crushing force response extracted in the form of report with details of force at each time step. In below the environment of softwares which is used during pre-processing, solving and post-processing is shown.

11 51 Figure 4.5 Hypermesh v.11.0 used for modeling

12 52 Figure 4.6 MSC/Dytran used for processing the simulation

13 53 Figure 4.7 MSC/Patran used for applying load and post processing The extracted crushing forces versus displacement are further processed to study the behavior of tubes. Analytical results will be discussed in detail in the next chapter.