CHAPTER 7 STRINGERS AND SHEAR PANELS
For semi-monocoque structures with stringers and shear panels, one can use a simplified model to determine the following: Axial stress on stringers Shear flows in the shear panels
7.1 Simplified Model with Stringers an
CHAPTER 4 TORSION OF THIN-WALLED STRUCTURES
Closed sections under torque Single-cell closed sections Thin-walled open sections Multi-cell closed sections
Consider a slender body such as a wing or a fuselage subjected to torsional moment or torque.
( x) :
Orbital maneuvers Changing orbits in-plane: a, e, , plane change: i, In planning a maneuver, usually the two most important quantities are total v (fuel consumption), total time of transfer (to complete the maneuvers), though other considerations may come
Attitude parameters There are several dierent parameter sets to describe attitude, among them Euler angles (313, 321, etc.) direction cosines, Euler parameters/quaternions. Much as there are 6 quantities to minimally specify the orbital state of a satelli
v at each maneuver Triangle, v1, delta v1, vt with angle alpha1 Speeds for circular orbits are determined by radii, 2 = , 2= , vi vf ri rf and the Hohmann analysis gives the transferorbit speeds,
2 vta =
2 2 ri ri + rf 2 2 2 vtb = rf ri + rf
For the two m
Solve for intersection of rotated ellipses An equation of the form a cos + b sin = c can be solved by c cos a where tan = b/a. (Variables a, b, c are just coecients, not semimajor axis etc.) The two signs correspond to the two intersection points of the e
Phasing worked example Vallado Example 68, pp. 348349 Given: ai = atg = 2 ER = 12756 km, = 20 so the interceptor leads the target. Find phasing time and v . The angular velocity is ntg = 4.382 104 rad/s Because the interceptor is not that far from the tar
Bi-elliptic details Use the Hohmann transfer computation, but apply it twice. Call rB the geocentric distance of the intermediate orbit. The semimajor axes of the two transfer ellipses: rB + rC rA + rB , at2 = . at1 = 2 2 On the two transfer ellipses, we
Recalculate example with f and g functions Once again, suppose we have a satellite which has Cartesian IJK
r0 =
r0 =
26981. 28850. km 13174. 1.2784 0.83017 km/s 0.57114
What is its state 24 hours later?
L. Healy ENAE404 Spring 2007 Lecture 12 (Mar. 6)
1
Computation of orbital elements from Cartesian
Ref.: Curtis Sec. 4.4, Vallado Section 2.5 We know about orbital elements, but how do we nd them? If were given Cartesian state vector (position vector r and velocity vector r ), we can compute them using the
ENAE404 Spring 2007 Answers to Exam #1
March 13, 2007 75 minutes L. Healy 1. [20 points] For each of the following earth-orbiting satellites, identify whether the orbit is circular, elliptical, parabolic, or hyperbolic. Give a brief justication. (a) Posit
CHAPTER 12 DAMAGE TOLERANCE
In this chapter the following topic will be covered: Safe life design Damage tolerant (Fail-Safe) design Stress intensity factors Mode I fracture, mode II fracture and mixed mode fracture Fatigue crack growth: Paris equation
Ae
CHAPTER 11 TEMPERATURE EFFECT
Structural components are often subjected to temperature changes during flight operation. high-speed aircraft, especially along the wing leading edge reentry vehicles jet engine combustion chamber and exhaust nozzle spacecraf
CHAPTER 10 FORCE METHOD
In this Chapter we will introduce the Castiglianos 2nd theorem and apply it to various structural systems of slender bodies. The Castiglianos 2nd theorem is convenient in handling statically indeterminate, flat and curved structure
CHAPTER 9 FINITE ELEMENT MODELING
The finite element method is a very powerful tool for modeling and analysis of various structures (aircraft, spacecraft, launch vehicles, engines, automobiles, bridges, buildings, machine components) with complicated geom
Pressurized Cylindrical Shells under Compression
Internal pressure stiffens cylindrical shells. For short cylindrical shells under compression, buckling stress can be expressed as
c = E
or
R t p f , t R E
Nc t p = f , ER R E where
(1)
c : buckling stress
CHAPTER 6 SHEAR FLOWS IN THIN-WALLED SECTIONS
Once resultant shear forces are given over a cross-section of a thin-walled slender structure, shear flows over the cross-section can be determined by considering the force equilibrium in the axial direction a
CHAPTER 5 BENDING OF THIN-WALLED STRUCTURES
5.1
Bending in 3-D space Kinematics of displacement Strain-displacement relationship Stress-strain relationship Centroidal bending axes and principal axes Centrodal bending (CB) axes Centroidal bending and princ
Chapter 3
Wing Box Sizing
3.1 Shear center: Decoupling of bending and torsion 3.2 Sizing of wing box 3.3 Wing divergence 3.4 Aileron reversal 3.4 Flutter
1
3.1 Shear Center: Decoupling of Bending and Torsion
Analysis of wing bending and torsion can be dec
CHAPTER 2 INTERNAL LOADS IN AEROSPACE STRUCTURES
2.1 Force and Moment Distributions Slender body under axial force Slender body under torque Slender body under lateral loads 2.2 Inertia Loads Load factor Examples
1
2.1 Force and Moment Distributions
Aircr
Special cases have usable solutions There are two approximately solvable cases of interest to satellite orbit study. The perturbative (lunisolar or planetary perturbation) approximation for earth-orbiting satellites we have seen. Restricted three body pro
Application: main problem Consider the simplest geopotential perturbation problem: J2 only. In this case the potential is: R2 U (r, ) = J2 3 (3 sin2 1) . r 2r
Disturbing function=R
The satellite latitude is not a convenient quantity. Using spherical trigo
Computation of drag force Consider a small atmospheric mass element m that hits the spacecrafts cross-sectional area A in a time interval t, m = Avrelt with the atmospheric density at the satellites location and vrel the speed of the satellite relative to
Perturbations Until now, weve dealt almost exclusively with two-body motion, a pure Keplerian orbit. It is now time to consider other forces that act on a satellite. Perturbations are small forces that are not included in the point-mass (= spherically sym
Torques and their sources Torques may be External: interaction with the outside world. May be natural or may be generated inside spacecraft, e.g., thrusters. Internal: acting totally inside the spacecraft; they must all cancel out. Nevertheless, they are
Attitude dynamics Ref.: Curtis Sec. 9.4 Attitude dynamics is the study of how spacecraft orientation changes in time with or without external torques. The principal result we will obtain are the dierential equations describing how the angular velocity cha
Examine equations for type of solution
Notice that the x and y directions are coupled together, and the z direction is not coupled to either. If you look at the z equation rst, youll see that it can be solved by a function whose second derivative is the
Assumptions of two-body motion
Only two bodies (satellite and planet), point masses (spherical distribution of mass), no other forces acting, satellite has much smaller mass than planet, so center of mass is essentially at the planets center.
L. Healy EN
Orbit propagation: the Kepler problem With an understanding of Keplers equation, we can solve the position of a satellite for a given time. This is called orbit propagation. In the two-body model, it is sometimes called the Kepler problem. With perturbati