Constraint paths in non-linear structural optimization

• Equilibrium paths are used to investigate the constraints in optimization.
• Highly non-linear quasi-static equilibrium problems are addressed.
• Criticality conditions allow evaluation of parametric dependence in instability.
• Two-dimensional equilibrium surfaces are used to visualize parametric effects.
• A plane 3-parametric pressurized membrane is investigated.

Optimization of significantly non-linear structures is a demanding task. The paper discusses how boundaries of the feasible region can be followed as generalized equilibrium paths in parametric space, reflecting engineering demands on stiffness, strains and stability. Solutions on the constraint paths are then evaluated with respect to any chosen objective function. For few design parameters, this approach is efficient and robust. This is demonstrated for a pre-stressed pressurized membrane of three parameters, showing several constraint paths for the problem, and indicating how these are used in optimization. The view is often closer to engineering design analyses than the mathematical optimization settings, which often has problems in handling stability constraints.