Integrating Optimal Truss Design Methodologies Into Mechanical Engineering Technology

The author has previously shown that single criterion optimization methodologies can be effectively integrated into lower-division mechanical engineering technology courses using single beam elements and a variety of load cases. In that paper, multiple methodologies of varying beam cross-section to minimize weight of the beam or to approach a constant stress state in the beam were described and their use investigated. This paper describes the application of these single criterion optimization methodologies to multiple-part assemblies, specifically engineering trusses. Although the optimization methodologies are similar, they are all far more complex in multiple-part assemblies than in single beam element optimization problem. The truss optimization theory, analysis, and testing that were utilized in the classroom and laboratory will be discussed in this paper. The correlation between optimization results from both spreadsheet solver and finite element analysis (FEA) solutions is presented. Also, the subsequent correlation between the analysis results and the experimental verification from photoelastic studies of prototype trusses is presented.

A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members

A shape annealing approach to truss topology design is presented that considers the tradeoff between the mass of the structure and the grouping of members, where all members of a group are given the same size. The problem of optimal grouping involves finding a structural design with an optimal number of groups and the optimal sizes for each group. In this paper cross-sectional area is considered as the measure of group size. Designs incorporating multiple members with the same cross-sectional area are advantageous when considering the cost of purchasing and fabricating materials. The shape annealing method is used as an approach to solve this problem by incorporating a method for dynamic grouping of members based on cross-sectional area that creates a tradeoff between mass and the number of groups through a weighted objective function that includes a group penalty function. This method is demonstrated on transmission tower and general truss problems.

A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members

A shape annealing approach to truss topology design considering the tradeoff between the mass of a structure and multiple members of the same size, called a class of members, is presented. The problem of optimal grouping involves finding a structural design with an optimal number of classes and the optimal sizes of those classes; cross-sectional area is considered as the measure of size in this paper. Multiple members of a uniform cross-sectional area is advantageous when considering the cost of purchasing and fabricating materials to build a structure. The shape annealing method (Reddy and Cagan 1994) is used as an approach to solve this problem by incorporating a method for dynamic grouping of members into classes and adding a constraint for the number of allowable classes. This method is demonstrated on arch and truss problems. As well, results from an imposed symmetry constraint for the truss problem will be shown.