The student should be able to design structures under constraints (e.g. maximum allowable stresses, deformations, required safety factors with respect to loss of stability, minimum and maximum dimensions) in an optimum way (generally with respect to weight). It is the goal to give an understanding of the mathematical basics, and the ability to transform the optimization problem into a mathematical formulation, to make the choice of an appropriate optimization tool and to estimate the numerical effort.
Linear and nonlinear optimization methods in structural design are introduced and explained by means of examples. Some topics: Linear programming (Simplex method) with application to optimization of trusses and nonlinear iterative shape optimization. Nonlinear Optimization: graphical solution method, simultaneous failure mode design, Lagrange multipliers, search methods without constraints (gradient methods, conjugate directions, quasi-Newton methods), method of feasibile directions, GRG (generalized reduced gradient method), SQP (sequential quadratic programming), inscribed hypersheres, penalty function methods, approximation techniques, dynamic programming, optimization by means of biological principles, optimization under the presence of tolerances.
