Nonlinear programming in structural design

The design of structural entities is formulated as a nonlinear program. In the nonlinear program the objective is the compliance (or stiffness under load) of a structure. Constraints are due to equi-librium conditions, signature of forces, failure conditions like yield and buckling, minimum length requirements and available material. Nonlinear constraints make this problem difficult to solve for realistic design problems using standard tools (Sequential Quadratic Programming: SQP) for non-linear programming. Using techniques like scaling of design variables and constraints to bring the singular values of the constraint Jacobian in a narrower range and closer to 1, introducing additional design variables to make the constraints more linear, and employing sparsity of the Jacobian of the constraints, the problem can be solved without intervention for planar (small) problems, but not readily for spatial (large) problems. Some results in the design of a special class of structures, namely tensegrities, illustrate the problems. This bad scalability and lack of robustness are disadvantages of using standard tools, like SQP, to solve large nonlinear programs, which we would like to see redressed in the current tools, or alleviated in future ones. Using constraint satisfaction programs, it may be possible to more closely follow the curved manifolds of the constraints. A multi-phase procedure, including a global optimization phase, may be a feasible approach for large scale problems, because it may avoid badly conditioned area’s in the design space