with your host… Dr. Hyland

489, Lecture 8 - Questions Addressed  What phenomena drive structural design requirements?  What are some simple types of structures and how do they respond to forces?  What geometric and material properties are most important to the performance of structures?  Some data on potential materials.  Some ways we can use structural concepts in LBSS. Suggested reading: L&W, Chapter 11

Assuming that the cargo transport vehicle(s) are not launched from the Earth’s surface, structural design requirements are driven by: o Steady-state Thruster accelerations o Propulsion system engine vibrations o Transient loads during pointing maneuvers, attitude control burns or docking events o Pyrotechnic shock from separation events, deployments o Thermal environments Basic requirements are that cargo are not subjected to excessive steady state accelerations or transient shocks and that relative displacements among cargo elements be kept small.

The Simplest Structure of All: The Ideal Axial Member or Strut PP L LL Area A Resists only axial forces – either tension or compression  = Stress = P/A  = strain =  L/L Hook’s Law:  = E  E = Modulus of elasticity Materials are also characterized by: F tu = Allowable tensile ultimate stress F cy = Allowable compressive yield stress  = Coefficient of thermal expansion

Representative Stress-Strain Curves Strain,  Stress,  A B C A, C A B C Ductile (aluminum alloy, Kevlar) Perfectly brittle (glass) Relatively brittle (cast iron, Graphite-Epoxy) A = Proportional Limit B = Yield Stress C = Ultimate Stress

 Numerous types of truss structures can be built from axial members alone:  Good design practice for precision space structures recommends the use of Statically Determinate designs.  For 3-D structures, no more than three, non- coplanar strut meet at a joint  For a 2-D structure, no more than two struts meet at a joint  Under these conditions, the forces in all members can be determined solely from static force equilibrium at each joint. Analysis is more accurate since the force distributions are independent of material properties.

Example: A cantilevered frame attached to an accelerating support M   #1 #2 L M F=M  –F –F 1 –F 2 F1F1 F1F1 F2F2 F2F2 x x y Equilibrium along x: F 1 sin  + F 2 = 0 Equilibrium along y: – F 1 cos  + M  = 0 F 1 = M  /cos , F 2 = –M  tan 

Simple model for sizing the structural framework for a cargo-carrying vehicle x   L L Vehicle bus, engine and propellant

But you can do many other things with axial members: Consider the Rotovator Surface of planet VoVo  = 2V o /L

To design the rotovator, we need to find the variable cross section that will keep axial stresses below the ultimate yield stress of the material s A(s) =  r 2 (s) L/2  = 2V o /L Volumetric mass density = 

The Cable as an Apogee Raising Device Cargo in LEO Rotovator in elliptical orbit L1L1 V max 2V max -V LEO o Cargo vehicle in LEO. Rotovator in elliptical orbit with r min = r LEO + L/2 o One end of rotovator hooks up with cargo. Rotovator makes one half turn and releases cargo at speed 2V max –V LEO o Cargo travels on a much more eccentric ellipse – out to near L 1 o Then cargo proceeds via a low-thrust trajectory to lunar orbit

More complex structures: Beams Beams resist both axial loads and lateral forces and torques M S W(s) x M(s) M(s+  s) ss S Beam x- section S 2t 2b

More complex structures: Beams   m E,  L   m L Everything is scaled by L, b and the speed, V b !

Property Material Tensile Modulus (10 9 N/m 2 ) Breaking Tenacity (10 9 N/m 2 ) Density (10 3 kg/m 3 ) Modulus speed (km/s) Tenacious speed (km/s) Kevlar 29 (w/resin) Kevlar 49 (w/resin) S-Glass E-Glass Steel Wire Polyester HS Polyethylene High Tenacity Carbon Carbon nanotubes  13,000  130  1.3  100  10 Material Properties o L&W list properties only for metals o However, most precision space structures are made of carbon or graphite composites with titanium joints and end fittings o We should be looking for materials with high tenacious speed: tenacious speed = (Tensile modulus/ density) 1/2

RmRm meridian mm RhRh hh Doubly-Curved Shells as Pressure vessels

Air bag Another Thin-Walled Structure: Air Bags  Assume the air bag is a thin membrane (no bending resistance) that is stiff to stretching  The bag starts with an intrenal – external pressure difference of P 0

Another Thin-Walled Structure: Air Bags Air bag deformed shape P = pressure in the deformed shape

Another Thin-Walled Structure: Air Bags Air bag

Hope you enjoyed the show! And may your shields never fail….