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Elements of ComputerAided Design
Mathematical Programming Methods in Design
State Space Methods of Finite Dimensional Optimal Design
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adjoint algorithm basic feasible solution beam boundary conditions buckling calculations column condition of Eq considered constraint functions constraint set constraints of Eqs convergence convex cost function cross-sectional area damage conditions defined degrees of freedom denoted design sensitivity analysis design variable constraints differential displacement constraints displacement vector eigenvectors Example fail-safe Figure finite element formulation frame given in Table gradient projection method initial Kuhn-Tucker Lagrange multipliers linear linear programming linearly independent loading conditions lower bound LP format maximum minimize minimum point multipliers natural frequency necessary conditions nodal displacements nodes nonlinear programming obtained optimal design problem optimum parameters positive definite programming problem reduced relative minimum satisfied scalar Section 3.2 shown in Fig simplex method simply supported solve space steepest descent stiffness matrix straints stress constraints structural design structural systems substructure symmetric technique Theorem tion treated truss vector violated zero