Abstract
A hybrid method of optimum design is developed to minimize the weight of radio telescope backup trusses. The design variables consist of the member areas and the node locations of some selected joints of the backup truss. The method of optimization treats the area and the geometry variables in two separate design phases and alternates between the two phases. The member areas are updated by a recurrence relation based on the optimality criteria approach, whereas the node locations are modified by the gradient projection method of mathematical programming. The loads on the backup truss consist of combinations of gravity and wind loads, as used in the conventional design of backup trusses. The design is subjected to constraints on the Root Mean Square path-length error (RMS error), on the maximum allowable stresses, on Euler buckling, on maximum and minimum member sizes and on the movement of the node locations. For optimizing the member areas, the RMS error is considered as a primary constraint and used to derive the recurrence relation. The remaining constraints are treated as secondary or side constraints. In the case of geometry variables, the RMS error is expressed explicitly in terms of the movable coordinates by using a first order Taylor series expansion. This constraint expression, along with the other constraints on the geometry, enclose the feasible design space. All partial derivatives in the Taylor series expansion are computed by closed form analytical expressions. A computer program is written to analyse the backup truss and obtain the optimum design. Numerical results are presented for three backup trusses, all having a different degree of complexity. The numerical results show that significant reduction in the weight of the backup truss can be achieved by changing both the member areas and the node locations. However, the percentage of weight reduction by virtue of the geometry changes alone depends on the overall framing of the backup truss. The geometry constraints are likely to become active at the optimum design. The study demonstrates that a hybrid method of optimization, such as the one described above, can be successfully applied for minimizing the weight of large radio telescope backup trusses.
Wagle, Vivek Dnyaneshwa (1984). Optimum design of radio telescope backup trusses. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -574537.