A study of alternative formulations for optimization of structural and mechanical systems subjected to statics and dynamic loads

The concept of simultaneous analysis and design (SAND) is revisited with two objectives in mind: (i) to propose and evaluate alternative formulations for various structural and mechanical system optimization problems, and (ii) to study implementation aspects of the formulations. SAND formulates the optimization problem in a mixed space of design variables and behavior variables, to imbed the state equations in one single optimization framework. Therefore explicit analysis and design sensitivity analysis of the system are not needed.

Several alternative formulations for structural design optimization based on the SAND concept are defined using displacements, and forces or stresses as optimization variables. As sample application areas, optimal design of trusses and frames are considered. Existing analysis software is integrated with an optimizer to solve example problems. Only the pre- and post-processing capabilities of the analysis software are needed to evaluate the problem functions. In addition, at least one of the alternative formulations does not even require assembly of the global stiffness matrix for the structure.

Alternative formulations for transient dynamic response optimization and digital human motion simulation are also presented, analyzed and evaluated. Similar to the SAND approach used for optimization of structures subjected to static loads, the equations of motion are not integrated explicitly; they can be imposed as equality constraints in these formulations.

For the alternative formulations, the optimization problem is quite large in terms of the numbers of variables and constraints. However, the problem functions are quite sparse, which is exploited in the optimization process. Performance of various formulations is evaluated with extensive numerical experiments and their advantages and disadvantages are discussed. It is concluded that the alternative SAND-type formulations are more efficient compared to the conventional approach where gradients of implicit functions must be evaluated. In addition, they offer flexibility and ease of numerical implementation because linear systems of equations are not solved for analysis or design sensitivity analysis.

The alternative formulations represent a fundamental shift in the way analysis and design optimization are currently treated. This shift in paradigm needs to be further nurtured and developed for optimization of more complex multidisciplinary systems.