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From:
"Optimization of Propellant Tanks Supported by One or Two Optimized Laminated Composite Skirts", by David Bushnell, Michael S. Jacoby and Charles C. Rankin, 54th AIAA Structures Meeting, Boston, MA, April 8-12, 2013
ABSTRACT: The propellant tank is a shell of revolution completely filled with liquid hydrogen (LH2). This propellant tank is to be launched into space. During launch it is subjected to high axial and lateral accelerations. The tank is supported by one or two conical skirts each of which consists of five segments: two short segments near each end of the skirt and a central long segment that has a laminated composite wall. Each of the short segments nearest the ends of the skirt has an isotropic one-layered wall with tapered thickness. Each short segment next to each short end segment is multi-layered with the extreme layers consisting of tapered isotropic material and the remaining internal, contained layers consisting of the same laminated composite wall as the long central segment. This tank/skirt system is optimized via GENOPT/BIGBOSOR4 in the presence of two loading cases: (1) 10 g axial acceleration and 0 g lateral acceleration and (2) 0 g axial acceleration and 10 g lateral acceleration. In addition to the g-loading the tank has 25 psi internal ullage pressure, the tank wall is 200 degrees cooler than the wall of the launch vehicle from which it is supported by the conical skirt(s), and there exists axisymmetric meridionally non-uniform cooling of the skirts. In the BIGBOSOR4 modal vibration model the mass of the propellant is "lumped" into the tank wall, a conservative model. The tank/skirt system, a multi-segment branched shell of revolution, is optimized in the presence of the following constraints: (1) the minimum modal vibration frequency of the tank/skirt(s) system must be greater than a given value; (2) five stress components in each ply of the laminated composite wall of the conical skirt(s) shall not exceed five specified allowables; (3) the conical skirt(s) shall not buckle; (4) the maximum effective (von Mises) stress in the tank wall shall not exceed a specified value; (5) the tank wall shall not buckle. The objective to be minimized is in general a weighted combination of the normalized mass of the empty tank plus the normalized conductance of the support system: Objective = W x (normalized empty tank mass) + (1-W) x (normalized strut conductance), in which W is a user-selected weight between 0.0 and 1.0. Two propellant tank/skirt systems are optimized: (1) a long tank with only one supporting skirt joined to the tank at the midlength of the tank and (2) the same long tank with two supporting skirts, an aft skirt and a forward skirt. It is emphasized that the tank/skirt(s) combination is optimized as a single branched shell of revolution. The flexibility of the launch vehicle to which the tank/skirt(s) system is attached is neglected: the ends of the supporting skirt(s) attached to the launch vehicle are assumed to be attached to rigid "ground". Linear theory is used throughout. Predictions for the optimized tank/skirt designs obtained here are compared with those from the general-purpose finite element code, STAGS. The agreement between the predictions of GENOPT/BIGBOSOR4 and STAGS qualifies the use of GENOPT/BIGBOSOR4 for preliminary design in the particular cases studied here.
This slide shows the STAGS finite element model of the optimized long propellant tank with two conical skirts, aft and forward. The STAGS “410” finite element is used in the model of the propellant tank shell wall, aft skirt and forward skirt. In this STAGS model the internal orthogrid is represented by a shell wall “layer” with appropriate thickness (thickness equal to the height of the orthogrid stiffeners), material stiffnesses, and density. This is the same strategy as that used to represent the internal orthogrid in the BIGBOSOR4 models.
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