Abstract
The efficiency of sequential linear programming technique in optimizing nonlinear constrained structural optimization problems is studied in this paper considering tripod truss structure as a case study. The axial force in each of the members of the truss due to payload is estimated using vector mechanics. The problem is formulated for minimum weight considering localized buckling stress, Euler buckling stress and direct compressive stress as constraints. The structure is optimized considering mean diameter and payload height as design variables. The weight of the truss got reduced by 20.51%.The optimum values of design variables obtained are compared with the values obtained using graphical method. The optimum values of design variables obtained using both the approaches are in reasonable agreement with a mere 5.17% variation.
Highlights
The optimization of nonlinear multi variable constrained problems can be broadly addressed using four approaches
It can be seen that the optimum value of the objective function is 469.31 N at x1=0.3 meters and x2=0.0701meters
A 20.51% reduction in weight of the truss is observed from a starting value of 590N for an initial design vector of X= (0.9m, 0.08m)
Summary
The optimization of nonlinear multi variable constrained problems can be broadly addressed using four approaches. The heuristic search methods (eg: box method), methods of feasible search direction (Rosen, zoutendijk’s...etc), sequential linear and quadratic methods, using sequential unconstrained minimization techniques (Interior, exterior penalty methods and Augmented Lagrange methods). Rao (2009) presented in detail various nonlinear constrained optimization techniques, their relative advantages and limitations. The sequential linear programming has the following advantages over other methods. In case of SLP (Sequential linear programming), the nonlinear problem is solved as a series of LP (Linear programming) problems without relying on random search direction and step length. This ensures faster convergence compared to gradient (feasible direction) methods
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