AERO2463 Computational Analysis for Engineers- Problem

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Reference no: EM132384232

AERO2463 Computational Analysis for Engineers

Structural Analysis and Design of a Crewed Lunar Lander

Basic Overview and Steps

The “concept of operations” (overview) for the entire program is described below. We recommend you progressively build up the project one activity at a time, completing each function before using it in more complex steps. Activities to accomplish this are provided in Section 6.

(1) You are given a spreadsheet (excel file) < Sxxxxxxx_Syyyyyyy_Design_File.xlsx>. The main script template reads this file to get your inputs. Your main script will perform all of the following steps.

(2) Read the data from the spreadsheet (code supplied in RunAnalysis, marked “do not edit”).

(3) Starting with a truss design and chosen cross-sectional area of the truss members, complete and use RunAnalysis to perform steps 6 and 7 below.

(4) To find the optimum area, define a broad range of cross-section areas to test to find the minimum cross-sectional area and hence minimum fuel consumption, with peak stress remaining with the allowable limit. This is the “coarse search”.

(5) Determine the length of each element using ElementLengths then combine and use to determine the total mass of the truss

(6) Calculate the fuel usage for the lunar landing mission using component A – Orbital Mechanics as described below.

(7) Determine maximum stress for the truss over all two load cases using component B – Implicit Finite Element Analysis (using provided function RunFEA).

(8) Plot the stress versus axial cross-section and required fuel mass versus axial cross-section for the rough estimates of cross-sectional area at which the maximum stress is nearly equal to the allowable stress.

(9) Use polyfit to determine a polynomial fit between the maximum stress and the crosssectional area. You can fit a polynomial up to order 8, but use the lowest order that gives a reasonable fit (remember Assignment 4.1). Lower order means fewer data points are needed, so
the computationally expensive FEA need be run fewer times.

(10) Identify the cross-section areas from your coarse search that are closest to the limit of maximum allowable stress. One is the smallest area under the maximum permissible stress, and one will be the nearest largest area above the maximum permissible stress.

(11) Using the closest limits identified and the polynomial fit of the data, use the bisection method to determine the minimum allowable cross-section area (remember Assignment 1.2), and plot the progression of cross-section area vs maximum stress guesses. This is the “fine search”.

(12) Using supplied function DrawModel from within RunAnalysis, draw a representation of the truss model, e.g. Figure 5 below.

(13) Using this minimum allowable cross-section area, determine the dry mass, call RunAnalysis once more with plotting on to determine the fuel mass used and plot the stresses for each load case (using supplied function PostProcessFEA).

(14) Repeat your analysis for a total of three materials to determine which is most suitable for your truss design (by running your script once per material).

Component A - Orbital Mechanics (inside RunAnalysis function)

We will perform the orbital mechanics calculations backwards from the phase when the lander retuns to the low lunar orbital from the transfer orbit at the end of the mission.

(1) Determine the orbital velocity of the low lunar circular orbit with altitude (radius) defined in metres as the average of your student numbers divided by 10 (Orbital_Velocity)

(2) Use equations of orbital manoeuvres to determine the velocity of the ascent module at the end of the transfer orbit returning from the Moon’s surface to the low lunar orbit. Draw a plot of the orbital path, including the Moon’s surface and the path of the low lunar orbit (Manoeuvre).

(3) Calculate the fuel mass required for the ascent module to slow from the transfer orbit, back into the low lunar orbit using the rocket equation (Rocket_Eqn).

(4) Calculate the fuel mass required to produce enough velocity difference (delta-V) to reach the transfer orbit from the surface of the Moon for the ascent module using the rocket equation (Rocket_Eqn).

(5) Calculate the velocity at the end of the transfer orbit from the low lunar orbit to the Moon using orbital manoeuvre equations. Draw a plot of the orbital path, including the Moon’s surface and the path of the low lunar orbit (Manoeuvre).

Figure 6: Example of the figures you should plot from the orbital mechanics calculations

(6) Calculate the fuel mass required to slow from the velocity at the end of the descent transfer orbit to zero velocity at the surface of the Moon using the rocket equation (Rocket_Eqn).

(7) Calculate the fuel mass required to produce enough velocity change (delta-V) to enter the descent transfer orbit from the low lunar orbit using the rocket equations (Rocket_Eqn).

Component B - Implicit Finite Element Analysis (inside RunAnalysis function)

(1) Run DrawModel to draw the launch phase lander truss model with all dry and fuel masses,

(2) Run RunFEA to determine the stress in each element for the two load cases with different fuel masses determined using the orbital mechanics in component A.

(3) Determine the absolute maximum (peak) stress from the FEA and compare this to the maximum allowable stress for the selected materials.

Remember: This assignment is very open-ended. There are several choices you will have to make along the way and briefly justify in the report. Some of these choices may include:

Design of the truss structure configuration,

Material for the truss out of a metal/alloy, polymer or composite,

Cross-sectional areas of each element in the truss. Remember this is a truss analysis, so the actual cross-section shape or profile is not needed.

Allowable stress in the material, do you use yield strength or ultimate strength or failure strength, do you need to include a safety factor?

Type of engine for the lunar lander. Please choose a chemical engine that is reliable. We do not expect you to understand the limitations of some more efficient, but as yet un-proved engines.

Where are the locations of the fuel point masses?

Do you use a multi-stage lunar lander, leaving the descent module truss on the moon, or do you take it back with you?

You may make use of previous assignment’s code for optimising the design or minimising the required fuel. However, be careful when repurposing old code as there may be different required inputs and outputs, or clashes with variable names.

Development Process

Developing a large and complex project can be a difficult task. We recommend progressively developing one stage at a time, checking each behaves correctly before progressing onto the next one. The following activities are defined to assist you with this.

6.1 Activity 1 – Input data processing

(1) Use the provided spreadsheet (excel file) to develop a truss design by data input in the specified by the template.

(2) Read the data from the spreadsheet into Matlab using RunAnalysis.

(3) Use DrawModel to confirm that the truss is designed as you intended.

6.2 Activity 2 – Analysis of the truss structure for a given cross-sectional area (call RunAnalysis for a single case)

(1) Using the total length of the truss members, calculated from ElementLengths, determine the total dry mass of the descent module truss for a specific cross-sectional area.

(2) Calculate the fuel usage for the lunar landing mission using component A – Orbital Mechanics for a single cross-section area.

(3) Determine the maximum stress for the truss over both load cases using component B – Implicit Finite Element Analysis for a specific cross-section area.

6.3 Activity 3 – Analysis of the truss structure for multiple cross-sectional areas (call RunAnalysis for multiple cases)

(1) Define a coarse range of cross-sectional areas for investigating the optimal cross-section for the lunar lander truss members

(2) Call activity 2 – RunAnalysis for the various cross-sectional areas

(3) Plot the maximum stress against the cross-sectional area


(4) Plot the fuel mass against the cross-sectional area

6.4 Activity 4 – Derivation of a relationship between the peak stress and crosssectional area (using polynomial fit)

(1) Determine a polynomial fit to the coarse calculated relationship between maximum stress and cross-sectional area data from activity 3 (remember Tutorial and Assignment 4.1). Plot the polynomial fit compared to the coarse calculated values of maximum stress vs the crosssectional area

6.5 Activity 5 – Optimisation of the truss cross-sectional area (using the bisection method)

(1) Add the ability to identify the cross-section areas from your coarse search in activity 3 that are closest to the limit of maximum allowable stress. One is the smallest area under the maximum permissible stress, and one will be the nearest largest area above the maximum permissible stress.

(2) Using the closest limits identified and the polynomial fit from activity 4, use the bisection method to determine the minimum allowable cross-sectional area (remember Assignment 1.2) and plot the progression of the guesses of maximum stress vs cross-section area. This involves writing and calling the Bisection function (not supplied).

(3) Using this minimum allowable cross-section area, determine the dry mass, re-run the orbitalmechanics calculations and FEA analysis to determine the fuel mass used and plot the stresses for each load case

6.6 Activity 6 – Analysis of the truss structure for different materials

(1) Repeat the full analysis for a total of three different materials, chosen from these three categories - metals/alloys, composites, and polymers. Composite properties in the fibre direction could be chosen as the relevant properties of the materials.

Overview

You must create a main program (script file) named Run_Matlab_Project.m

The marker assessing your program should be able to run your program with their own input spreadsheet by changing the variable Filename.

The function header and comments provided below describe what each function must do.

Assessment

Your task is to implement the program design in Matlab (as outlined below) to calculate and optimise the weight (hence fuel consumption) for the lander, and ensuring the truss is safe (the maximum stress is below the allowable limit) under all of the load cases considered. You must present the results in a short report as detailed below. You will work in teams of two members for the project and submit one report and Matlab code for the team.

9.1 Report

You should prepare a short report (maximum 2000 words) including figures and appendix. The report needs to contain the following information. You should use the orbit radius assigned to you via your student numbers,

1. Three-dimensional plot showing the lunar lander geometry and dry point masses for one specific (example) material choice,

2. Description of each load case analysed for structural FEA,

3. Basic description and justification of fuel/engine type,

4. Two plots showing the transfer orbits from the low lunar orbit to the lunar surface and back again for one specific (example) material choice,

5. A table incorporating the velocities at each phase of the mission for a typical case of one specific (example) material choice,

6. Three-dimensional plots and charts showing the stress in the geometry for each load case for each material selected,

7. A plot of the relationship between the maximum stress and cross-sectional area for each material selected including the polynomial fits,

8. A plot from the bisection curve fit showing the progression of guesses of maximum stress versus cross-section area,

9. A plot of the relationship between fuel consumption and cross-sectional area for each material,

10. Three-dimensional plots and a table showing the peak stress in the lander geometry for the dynamic load case for each material choice,

11. Discussion of the materials chosen for the lunar lander truss structure including, Young’s modulus, density, and design criteria for assessing suitability,

12. A table incorporating the total lander mass at each phase of the mission for each material selected,

13. Total fuel mass required for each material choice,

14. List of references.

Attachment:- Project.rar

Reference no: EM132384232

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