Second variation-based optimal design analysis for mechanical systems with structural performance constraints
Keywords:
Second variation analysis, structural optimization, mechanical systems design, constrained optimization, reduced hessian analysis, structural performance constraints, optimal design framework.Abstract
Optimization of design of mechanical systems in respect to their structural performance requirements is vital for obtaining lightweight, reliable and efficient engineering solutions. Nevertheless, classical first-order optimization procedures frequently lack ability to adequately account for nonlinear interdependencies, effects of uncertainties and structural responses. The present paper presents second variation-based optimal design procedure that takes into consideration second order sensitivity information for increasing accuracy and reliability of structural optimization. The methodology uses variational formulation, adjoint-based sensitivity analysis and second order optimality conditions to assess impact of variation of design parameters on structural performance. The method accounts for objective functions, such as compliance and material efficiency, while using constraints on stress, displacements, volume and structural stability. A case study on a cantilever beam is presented in order to demonstrate advantages of the approach. In particular, second variation analysis is employed to determine local optimum, curvature and stability of design. It is shown that use of second-order curvature information improves assessment of stability of designs through the analysis of reduced Hessian properties along critical design direction. The results prove that compliance-based structural optimization has strict convexity when there are no constraints, while stress constraints create certain curvature impact on structural optimization. The methodology is able to determine marginal stability cases. Developed approach provides a mathematically rigorous solution to advanced design optimization in mechanical systems, offering increased reliability, convergence and performance in the presence of complex engineering constraints. Extensions of the methodology will be done in order to apply large scale finite element implementation, nonlinear material model, multiple loads optimization and efficient solution to second-order problem.
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