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Course of Spacecraft Structures Written test, July 21 st, 2017 Exercise 1 The structure in the figure is composed of two beams of lengthl. The axial, bending and torsional stiffnesses are denoted withEA, EJ and GJ, respectively. The structure is elastically supported by two translational springs of stiffnessk. By applying a force-based approach, determine the vertical displace- ments in correspondence of the two springs. Data EA = 1.5e6 N EJ = 3.0e6 N mm 2 GJ = 3.0e6 N mm 2 k = 100 N/mm l = 1000 mm P = 1000 kN Exercise 2 Consider the wing structure in the figure. The total length is equal to 4l, while the ribs are characterized by a pitch equal tol. The wing section is modeled using a semi-monocoque scheme and is characterized by two closed cells. The equivalent stringer area is equal to2A on the upper cover, andA on the lower cover. A uniform pressure distribution of magnitudep is assumed. In addition, a concentrated load equal to P is introduced in correspondence of one rib, as illustrated in the figure. Plot the internal actions on the highlighted rib by modeling the rib itself as a beam. Data A = 100 mm2 a = 200 mm b = 300 mm l = 600 mm p = 1e-2 N/mm2 P = 3000 N Question 1 Discuss the isoparametric formulation with regard to a 4-node membrane finite element. Illustrate how the stiffness matrix is calculated and how the stress recovery can be performed. 1