Structural analysis of launch vehicles

Structural analysis of launch vehicles

“S ” U Rapienza Niversity of Omes A Echool of Erospace Ngineeringd ’ Tegree S Hesis Ini Angegneria Erospaziales A L Vtructural Nalysis of Aunch Ehiclest Sutor Tudentp . P G E Brof Aolo Asbarri Manuele Asilea Y 2022/2023cademic Ear 1Structural Analysis of Launch Vehicles 2Structural Analysis of Launch Vehicles

T cable of ontentsi

• Introduction ......................................................................................................................................... 12
• 1 S E ................................................................................................................ 13 Tructural Lasticity
• 1.1 L E .................................................................................................................... 14 Inear Lasticity
• 1.2 O N M ................................................................................................. 16 Overview of Ormal Odes
• 1.2.1 N .................................................................................... 17 Ormal Modes in Linear Systems
• 1.2.2 N , N ........................................................................... 19 Ormal Mode Types Analysis Masses
• 1.3 F M N M A .................................................... 21 Inite Element Ethod Applied to Ormal Ode Nalysis
• 1.4 T E N M A L V ..................................... 23 Heory of Lasticity in Ormal Ode Nalysis of a Aunch Ehicle
• 1.5 M B L ................................................................................... 24 Echanical Ehaviour of a Auncher
• 1.6 D F L ........................................................................................... 26 Ynamics of a Lexible Auncher
• 2 Rak, F E CAD model M ....................................................................................... 28 Light Nvelope and Odel
• 2.1 CAD M D ......................................................................................................... 29 Odel Escription
• 2.1.1 P ..................................................................................................................... 30 Ropellant
• 2.1.2 S ...................................................................................................................... 32 Tructure
• 2.1.3 M ............................................................................................................... 36 Ass Variation
• 2.1.4 S L .......................................................................................................... 36 Imilar Aunchers
• 2.1.5 L -E O , S E ............................................................................ 38 Ow Arth Rbit Pace Nvironment
• 2.1.6 S L .................................................................................................... 39 Peed of the Auncher
• 2.1.7 S ............................................................................................................................. 40 Hock
• 2.2 T ........................................................................................................... 41 Hermal Environment
• 2.3 A , ........................................................................ 42 Pplied Loads and Analyses Summary Tables
• 3 Rak, F A R ................................................................................. 44 Inite Element Nalyses and Esults
• 3.1 T F E U A .............................................................. 45 Ypologies of Inite Lement Sed for the Nalysis
• 3.1.1 S E , CQUAD4 ................................................................................................. 45 Hell Lement
• 3.1.2 S E , CTRIA3 ................................................................................................... 46 Hell Lement
• 3.1.3 S E , CHEXA .................................................................................................... 48 Olid Lement
• 3.1.4 C M E , CMASS1 .......................................................................... 49 Oncentrated Ass Lement
• 3.2 C A .............................................................................................................. 49 Onducted Nalyses
• 3.3 FEA model M D ........................................................................................................ 50 Odel Escriptions
• 3.3.1 FE M D , G N .......................................................................... 50 Odel Escriptions General Otes
• 3.3.2 S E H D D – I ........................................................... 53 Hell Lements Aving Ifferent Ensity Nput
• 3.3.3 S E S T - ........................................................ 54 Olid Lements in the Ections of the Anks Input
• 3.3.4 T M S E H D D - I ................................ 56 Ube Odel with Hell Lements Aving Ifferent Ensity Nput 3Structural Analysis of Launch Vehicles
• 3.3.5 T M S E S T - I ............................. 56 Ube Odel with Olid Lements in the Ections of the Anks Nput
• 3.4 N M FEA A – O ................................................................................. 58 Ormal Ode Nalysis Utputs
• 3.4.1 S E H D D – O ........................................................ 58 Hell Lements Aving Ifferent Ensity Utput
• 3.4.2 S E S T – O .................................................... 60 Olid Lements in the Ections of the Anks Utput
• 3.4.3 T M S E H D D – O ............................ 61 Ube Odel with Hell Lements Aving Ifferent Ensity Utput
• 3.4.4 T M S E S T – O ......................... 63 Ube Odel with Olid Lements in the Ections of the Anks Utput
• 3.5 T FEA A – I .............................................................................................. 65 Hermal Nalysis Nputs
• 3.5.1 FE M C M ............................................................................ 65 Odel with Oncentrated Asses
• 3.5.2 FE M , A L ................................................................................................ 66 Odel Pplied Oads
• 3.6 T FE A – O ............................................................................................ 68 Hermal Nalyses Utputs
• 3.6.1 FE M H D E – O ........................................................ 68 Odel with Igher Ensity Lements Utputs
• 3.6.2 FE M S E T S – O ............................................. 70 Odel with Olid Lements in Ank Ections Utputs
• 3.6.3 FE M C M T S – O .................................. 72 Odel with Oncentrated Asses in Ank Ections Utputs
• 3.7 Q -S FEA A – I ....................................................................................... 74 Uasi Tatic Nalysis Nputs
• 3.7.1 Q -S FE M , S 1, A L .................................................................. 74 Uasi Tatic Odel Et Pplied Oads
• 3.7.2 Q -S FE M , S 2, A L .................................................................. 75 Uasi Tatic Odel Et Pplied Oads
• 3.8 Q -S A , L S 1 – O ........................................................................ 77 Uasi Tatic Nalyses Oad Et Utputs
• 3.8.1 FE M H D E , L S 1 – O ...................................... 77 Odel with Igher Ensity Lements Oad Et Utputs
• 3.8.2 FE M S E T S , L S 1 – O ........................... 79 Odel with Olid Lements in Ank Ections Oad Et Utputs
• 3.8.3 FE M C M T S , L S 1 – O ................ 80 Odel with Oncentrated Asses in Ank Ections Oad Et Utputs
• 3.9 Q -S A , L S 2 – O ........................................................................ 81 Uasi Tatic Nalyses Oad Et Utputs
• 3.9.1 FE M H D E , L S 2 – O ...................................... 81 Odel with Igher Ensity Lements Oad Et Utputs
• 3.9.2 FE M S E T S , L S 2 – O ........................... 84 Odel with Olid Lements in Ank Ections Oad Et Utputs
• 3.9.3 FE M C M T S , L S 2 – O ................ 86 Odel with Oncentrated Asses in Ank Ections Oad Et Utputs
• 4 T -S L , F E CAD M .......................................................... 89 Hree Tage Auncher Light Nvelope and Odel
• 4.1 CAD M D ......................................................................................................... 90 Odel Escription
• 4.1.1 P ..................................................................................................................... 91 Ropellant
• 4.1.2 S ...................................................................................................................... 92 Tructure
• 4.1.3 M ............................................................................................................... 94 Ass Variation
• 4.1.4 S L .......................................................................................................... 95 Imilar Aunchers
• 4.2 A , ........................................................................ 97 Pplied Loads and Analyses Summary Tables
• 5 T S L , F A R ..................................................... 98 Hree Tage Auncher Inite Element Nalyses and Esults
• 5.1 FEA M D ........................................................................................................ 99 Odel Escriptions
• 5.1.1 FE M D , G N .......................................................................... 99 Odel Escriptions General Otes
• 5.1.2 S E H D D – I ......................................................... 101 Hell Lements Aving Ifferent Ensity Nput 4Structural Analysis of Launch Vehicles
• 5.1.3 S E S T - ...................................................... 101 Olid Lements in the Ections of the Anks Input
• 5.1.4 T M S E H D D - I .............................. 103 Ube Odel with Hell Lements Aving Ifferent Ensity Nput
• 5.1.5 T M S E S T - O ....................... 104 Ube Odel with Olid Lements in the Ections of the Anks Utput
• 5.2 FEA A – O ....................................................................................................... 105 Nalysis Utputs
• 5.2.1 S E H D D – O ...................................................... 105 Hell Lements Aving Ifferent Ensity Utput
• 5.2.2 S E S T – O .................................................. 108 Olid Lements in the Ections of the Anks Utput
• 5.2.3 T M S E H D D – O .......................... 109 Ube Odel with Hell Lements Aving Ifferent Ensity Utput
• 5.2.4 T M S E S T – O ....................... 111 Ube Odel with Olid Lements in the Ections of the Anks Utput
• 5.3 T FEA A – I ............................................................................................ 113 Hermal Nalysis Nputs
• 5.3.1 FE M C M .......................................................................... 113 Odel with Oncentrated Asses
• 5.3.2 FE M , A L .............................................................................................. 114 Odel Pplied Oads
• 5.4 T FE A – O .......................................................................................... 116 Hermal Nalyses Utputs
• 5.4.1 FE M H D E – O ...................................................... 116 Odel with Igher Ensity Lements Utputs
• 5.4.2 FE M S E T S – O ........................................... 118 Odel with Olid Lements in Ank Ections Utputs
• 5.4.3 FE M C M T S – O ................................ 120 Odel with Oncentrated Asses in Ank Ections Utputs
• 5.5 Q -S FEA A – I ..................................................................................... 122 Uasi Tatic Nalysis Nputs
• 5.5.1 Q -S FE M , S 1, A L ................................................................ 123 Uasi Tatic Odel Et Pplied Oads
• 5.5.2 Q -S FE M , S 2, A L ................................................................ 124 Uasi Tatic Odel Et Pplied Oads
• 5.6 Q -S A , L S 1 – O ...................................................................... 125 Uasi Tatic Nalyses Oad Et Utputs
• 5.6.1 FE M H D E , L S 1 – O .................................... 125 Odel with Igher Ensity Lements Oad Et Utputs
• 5.6.2 FE M S E T S , L S 1 – O ......................... 127 Odel with Olid Lements in Ank Ections Oad Et Utputs
• 5.6.3 FE M C M T S , L S 1 – O .............. 129 Odel with Oncentrated Asses in Ank Ections Oad Et Utputs
• 5.7 Q -S A , L S 2 – O ...................................................................... 130 Uasi Tatic Nalyses Oad Et Utputs
• 5.7.1 FE M H D E , L S 2 – O .................................... 130 Odel with Igher Ensity Lements Oad Et Utputs
• 5.7.2 FE M S E T S , L S 2 – O ......................... 133 Odel with Olid Lements in Ank Ections Oad Et Utputs
• 5.7.3 FE M C M T S , L S 2 – O .............. 135 Odel with Oncentrated Asses in Ank Ections Oad Et Utputs
• 6 L M V C ............................................................................. 138 Umped Ass Alidation and Onclusions
• 6.1 E , E M A ..................................................................... 139 Igenvalues Igenvectors in Odal Nalysis
• 6.1.1 2-S L (RAK), L ......................................................... 140 Tage Auncher Umped Masses Analysis
• 6.1.2 3-S L , L .................................................................. 142 Tage Auncher Umped Masses Analysis
• 6.2 2-S L (RAK), S ..................................................................................... 142 Tage Auncher Ummary
• 6.2.1 N A ................................................................................................. 143 Ormal Mode Nalysis
• 6.2.2 T A , S ......................................................................................... 143 Hermal Nalysis Ummary
• 6.2.3 “Q -S ” A , S ............................................................................... 144 Uasi Tatic Nalysis Ummary
• 6.3 3-S L , S T .................................................................................... 144 Tage Auncher Ummary Ables 5Structural Analysis of Launch Vehicles
• 6.3.1 N A ................................................................................................. 145 Ormal Mode Nalysis
• 6.3.2 T A ......................................................................................................... 145 Hermal Nalysis
• 6.3.3 “Q -S ” A ................................................................................................ 146 Uasi Tatic Nalysis
• 6.4 C ........................................................................................................................ 147 Onclusions
• R ....................................................................................................................................... 148 Eferences 6Structural Analysis of Launch Vehicles

T fable of igures

• Figure 1 – Resonance, standing wave effect, Ref. [29] ......................................................................... 18
• Figure 2 – Any motion can be decomposed in a sum of mode motions, Ref [28] ................................ 18
• Figure 3 – Graphical representation of the equation, Ref [28] ............................................................. 21
• Figure 4 – Idealised launch vehicle coordinate system ........................................................................ 23
• Figure 5 – Forces and moments acting on typical primary beam element .......................................... 23
• Figure 6 - RAK total Assembly ............................................................................................................... 29
• Figure 7 - Example of one of the HTPBs (R-45HTLO) ............................................................................. 30
• Figure 8 - The star shaped solid grain ................................................................................................... 31
• Figure 9 - Design of the nose cone ........................................................................................................ 31
• Figure 10 - Design of the canard wings ................................................................................................. 32
• Figure 11 - Design of the tail wings ....................................................................................................... 32
• Figure 12 – RAK, First stage .................................................................................................................. 33
• Figure 13 – RAK, Second stage .............................................................................................................. 33
• Figure 14 – Canard Box and Ogive ........................................................................................................ 34
• Figure 15 – RAK, global view. ................................................................................................................ 35
• Figure 16 - RAK overall dimensions ....................................................................................................... 35
• Figure 17 - Mass variation due to propulsion of the first and second stages ....................................... 36
• Figure 18 - Typical longitudinal static acceleration for SSO mission, Ref [14] ...................................... 39
• Figure 19 - Envelope shock response spectra (SRS) for stages/fairing separations and clamp-bandrelease at the spacecraft base (Q=10) .................................................................................................. 41
• Figure 20 – Load envelope in case of Quasi-Static transverse load set, Ref. [33] ................................ 43
• Figure 21 – Load distribution in case of Quasi-Static (transverse) loads, Ref. [33] .............................. 43
• Figure 22 - CQUAD4 Element Geometry and Coordinate Systems, Ref [15] ........................................ 46
• Figure 23 - CTRIA3 Element Geometry and Coordinate Systems, Ref [15]........................................... 47
• Figure 24 - CHEXA Element Geometry and Coordinate Systems, Ref [18] ........................................... 48
• Figure 25 - Shell elements FE model – global view ............................................................................... 50
• Figure 26 - Shell elements FE model – First stage – stabilizing wings section and EXA6 detail of thewing ........................................................