The application of dynamic relaxation to the design of modular space structures

This thesis is concerned with the development and assessment of computer techniques for the formfinding and sizing of large modular building space structures suitable for urban development. The contents of the Chapters are summarised as follows: 1: An introduction to conceptual and computer aided design of large building space structures. 2: A review of topological computer design methods. 3: A comparison of a dynamic relaxation method, for the formfinding of modularly constrained structures subject to a dominant design loading case, with linear programming and fully stressed design methods. This comparison shows that the dynamic relaxation method is efficient and particularly suitable for interactive use. 4: A parametric study of the effects of the iteration parameters on the stability and rate of convergence is presented. No general rules appear to be possible regarding the effects of these parameters on stability. It is noted, however, that the number of structure modifications before the solution becomes apparent is independent of the parameters. The dynamic relaxation formfinding procedure is generalised to cater for different stress constraints in tension and compression members and, for the problem considered, derives a lighter form than the fully stressed design technique. The optimum form of the D.R. solution is verified by the linear programming technique. 5: An intuitive dynamic relaxation method for the sizing of structures of fixed topology subject to multiple loading cases ,and stress constraints is presented. The method also caters for maximum member area sizes and deflection constraints by the use of parallel elastic and elasto-plastic analyses. Solutions derived using this method are compared with solutions derived using the non-linear program algorithm. They are shown to be of similar weight and to require similar solution times. 6: Two dynamic relaxation methods are presented for the formfinding and sizing of multiply loaded space structures. The first or parallel method is suitable for deriving and sizing forms of optimum or near optimum weight by deleting members which are small in area size and reducing in size. The second or series method is particularly suitable for interactive use and consists of testing the efficiency of each member with respect to each loading case. The final topology is then sized considering all loading cases simultaneously. These methods are both applied to a bridging ground structure subject to multiple loads and compared with solutions derived using linear, nonlinear programming and topological design methods. The parallel dynamic relaxation method is then extended to cater for cable members allowing for on-off non-linearities and prestress effects. The bridging structure is subsequently redesigned using internal cable members and adjusting the prestress level to ensure that the bridge deck does not deflect vertically under the action of the primary loading case. 7: A summary of conclusions

Special Issue: Eigenvalues of continuous systems

Editorial. The purpose of the special session was to bring together researchers who have successfully developed established techniques for formulating or solving different types of eigenvalue problems and those who are in the process of searching for new strategies to tackle emerging or longstanding problems, to exchange ideas on furthering the knowledge base of solving eigenvalue problems, in mechanics

A variational approach to non-local energy minimization of random elastic lattices

The purpose of this paper is to establish variational principles for the mechanical behavior of two-phase random elastic lattices. By restricting the attention to the systems characterized by second-order statistics, the variational bounds on the stored energy of the Hashin-Shtrikman-Willis type are established using basic tools of structural statics and linear algebra. Accuracy of the improved bounds is verified against elementary estimates as well as detailed Monte-Carlo simulations. Finally, selected numerical results related to the accuracy of the bounds are presented