Plastic Layout Optimization of Large-Scale Frameworks Subject to Multiple Load Cases, Member Self-Weight and with Joint Length Penalties

1. Abstract In the past few decades plastic layout optimization methods have been largely ignored in favour of those based upon elastic design principles. However, when multiple load cases are present elastic methods are generally computationally expensive and/or are prone to finding local optima. Therefore, they may not at present provide a suitable basis for practical truss layout optimization software, capable of treating real-world scale problems. In fact long computation times have impeded the development of truss layout optimization tools, both plastic and elastic. This is because, when using a fully connected ground structure, problem size quickly increases with increasing numbers of nodes in the design domain. Hence available memory can quickly become exhausted, preventing optimization even when using comparatively simple plastic problem formulations. Recently the authors presented a technique that allows large-scale plastic layout optimization to be performed on a typical desktop PC. Through the use of an iterative ‘member-adding’ algorithm, CPU times and memory requirements may be dramatically reduced, allowing problems containing up to approx. 1,000,000,000 potential members to be tackled. This paper extends the method so as to be capable of treating 3D problems with multiple load cases. Furthermore, in order to provide more realistic optimum structures, member self-weight and joint length penalties can also be included. Example problems demonstrate that the new algorithm is capable of optimizing structures with many millions of potential members, whilst still providing provably optimum solutions.