with your host… Dr. Hyland

426, 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?  What structural types are especially relevant to the design challenge? Suggested reading: L&W, Chapter 11

Likely structural design requirements: o Steady-state Thruster accelerations o Launch loads 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 Main challenges: maintaining structural integrity during launch and boost burns Pressure and centrifugal loads

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 struts 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 piggy-back vehicle x   L Carrier Vehicle and primary payload

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 !

Internal Loads Constrain the Main Structural Form For economy in structural mass large shells holding gas at some pressure must act as membranes in pure tension. There is a direct relationship between the internal loading and the shape of the surface curve of such a membrane configuration. When the major internal loads are pressure and artificial gravity the possible membrane shapes must be doubly symmetric, closed shells of revolution Possibilities: Sphere: rotate 1 about r or z Cylinder: rotate 2 about z “Pancake”: rotate 2 about r Torus: Rotate 3 about r Dumbell: Rotate 3 about z A Cassini oval is the set of points in the plane such that the product of the distances to two fixed points is constant.

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

Toroidal Shell Under Internal Pressure x y z   R (= 1/  ) s r

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 – Here’s some non-metalic materials o 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 strength-to-weight

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