Keywords: socket joints, space structures, optimum design, approximation concepts.

The most critical components of space structures are the joints where the main structural members interconnect. The connector that is used for the joints is thus the most important part of any prefabricated system and the final commercial success relies on its effectiveness and simplicity. In space structures, the connectors usually occupy 20-50% of the total amount of steel required for the structures. Thus the selection of appropriate connectors is important and would influence the economy of the space structures. There are many types of commercial joints available for space structures and the spherical joints including the ball and socket types are the most widely used in the world [1].

In this study, the optimum design of a socket type joint developed by a Japanese company, the Nippon Steel Corporation (NS) is presented [2]. The NS joints are suitable for most of the space structures such as double layer grids, domes and barrel vaults. The members of the space structures are composed of tubes and end cones with threaded borings. The end cones are welded to the ends of the tubes. Then the members with end cones are connected to the spherical hollow joints by the help of high strength bolts from inside the joints. Our main aim is to minimize the size of the joint with the main parameters as the radius (R) and the thickness (T) of the spherical joint. To achieve an optimised joint, the weight of the joint is formulated as a function of R and T. The design constraints are limits on the maximum member forces that can be applied to the joints in the most critical directions. The analysis of the joint during the optimisation process is carried out by a finite element program with shell elements. Because of the existence of the holes in the joint and the sudden increase of the stresses due to the stress concentration around the holes, it is not efficient to employ an elastic analysis. Thus, an incremental elastic-plastic analysis is used for the evaluation of the joint response against the applied loads and an appropriate factor of safety is then imposed on the results. Due to several assumptions imposed on the analysis such as selecting an appropriate yield surface, the numerical results are checked with some available experimental results. A numerical optimisation technique is employed for structural optimisation. The nature of the numerical optimisation methods is such that great number of function evaluations is required to achieve the optimal solution. In particular, each function evaluation requires an elastic-plastic finite element analysis of the joint under consideration, thus the computation work would be excessive to complete the optimisation. To reduce the computational burden of the process, the constraints that are expensive to evaluate are approximated. A second order approximation is developed in which an approximate Hessian matrix with diagonal elements is used. In addition, the elements of the Hessian matrix are estimated by the help of the first order derivatives using the information of the previous iterations. It is observed that the quality of the second order approximation is much higher than the normal first order approximation despite the fact that the Hessian matrix is not exact. With such an approximation the elastic-plastic analysis of the joint is not necessary during the optimisation process with the specified move limits. Infact, one lengthy analysis is only required for each of the move limits and the numerical results indicate that often less than ten analyses are adequate for completion of the optimisation. Thus the shape of the spherical hollow joint of the space structure is optimised with little small computational effort.

In the full length paper, the details of the jointing system, the method of analysis, the technique of optimisation, the method of function approximation and the numerical results are presented.

1

N. Subramanian, "Principles of Space Structures", Wheeler Publishing Co., New Delhi, India, 1999.

2

S.M. Seyedpoor, "Optimum Design of Hollow Sphere Joints for Space Structures", M.Sc. Dissertation, Department of Civil Engineering, University of Kerman, Kerman, Iran, 2004.

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