Design and manufacture of optimum product structures
W. S. Hemp established an optimality criterion for designing minimum weight structures that employ materials with different strength in compression and tension following A. G. M. Michell's work. W. Prager extended the optimality criterion for designs with materials with different densities. The first part of this dissertation brings together a full set of analytical tools to generate structural layouts which satisfy these dual-material optimality conditions.
Chapter 3 is concerned with methods to suppress local and global instability of least-weight structures. Perforated webs placed between structural members, structural member shape optimization and light-weight foam inserts are methods investigated in the research to address the instability problems. Simply supported least-weight arch beams were designed and mechanically tested. The experimental results were compared with FEA. Experimental results and FEA predictions were found to be in good agreement with the theoretical predictions, except for the perforated web design in which experimental and FEA results were close agreement, but were found to perform in a sub-optimal manner. In addition to the beam designs and experiments, a minimum-weight cantilever design was used to measure the effectiveness of foam inserts. Both experimental and FEA results showed that either shape optimization or foam inserts can be used for effective suppression of instability.
In Chapter 4 matrix operator methods proposed by S. Srithongchai to generate optimal layouts with straight boundaries were extended to include curved boundaries. A Matlab program originally written by Srithongchai was generalized to generate layouts for cantilevers with curved boundaries by using this method.
In Chapter 5 the design of an arch structure with a continuous profiled-thickness web, as described by Kozlowski and Mroz is analyzed. The analysis showed that a continuous design cannot produce an efficient least-weight structure.
In Chapter 6 optimal layouts with two and three-bar trusses were investigated for two alternate loading cases. A Matlab program was written to determine the minimum-weight from alternative structures. As suggested by Nagtegaal and Prager, the addition of a third member was found to reduce the total weight. However, a case study given in Chapter 6 suggests that it may be possible to find 3-bar structures of lower weight.