Cellular models of computation in structural analysis and design

Formal methods for structural design have received considerable recent attention. The advent of high-performance digital computing has contributed to the development of new and innovative, high fidelity, numerical methods for analysis of elastic and inelastic structures. These simulation methods can be combined with formal mathematical algorithms for design optimization to develop efficient automated structural design capabilities. Design problems have grown in size and complexity, with the need to account for an increase in the number of design variables and constraints, handling uncertainties in problems parameters and constraints, and the ability to conduct a search for an optimal design in a space with discrete variables. This increase in problem complexity requires significant improvement in computer processing speeds, and recent advancements in hardware indicate a trend of using massively parallel arrays of computational processors to enhance computing speeds. To take advantage of such computational architectures, parallelizing existing numerical algorithms has been shown to yield limited returns. The problem of information coordination among many distributed processors introduces diminishing returns with an increase in the number of processors. The present research investigates new and innovative algorithms for structural analysis and design that are configured for implementation on parallel computers.; The present research examines models of cellular computation that derive from basic concepts of cellular automata (CA) approach of decentralized computation. The approach is investigated for application to problems of structural analysis and design. For the former, CA models based on physical elastic elements such as linkages of springs and point masses are developed for the analysis of both continuous and discrete structural systems. The focus of this study is in identifying appropriate local rules of interaction that comprise the essence of CA computations. The cellular computation approach is also adapted in developing new computational models for design optimization. In particular, the research develops a cellular computation framework for genetic algorithms (GA's). Genetic algorithms have received considerable recent attention in problems of design optimization. The mechanics of population-based search in GA's is highly amenable to implementation on parallel computers. The present work explores a fine-grained model of parallel GA implementation that derives from a cellular-automata-like computation. The central idea behind the approach is to treat the GA population as being distributed over a 2-D grid of cells, with each member of the population occupying a particular cell and thereby defining the state of that cell. The research explores the effectiveness of this paradigm of GA implementation vis-à-vis the traditional approach. Both computational efficiency and the ability to locate the optimal point are examined in the context of representative design problems.; The cellular genetic algorithm (CGA) has also been extended to problems involving multiple criteria. Three different methods, the weighted min-max, sum of weight and modified sum of weight methods, are examined for their effectiveness when used with the newly proposed CGA approach. Finally, the cellular genetic algorithm is explored in the context of a simultaneous analysis and design (SAND) strategy. While both FEM and CA based analysis procedures are studied in this context, the SAND approach is particular significant when combining the cellular automata model for analysis with CGA based optimal search. Such an approach allows for the use of an identical computational grid for both the analysis and design computation, and is highly amenable for implementation on parallel computational hardware.