Optimum Design of Structures |
Contents
An outline of existing design methods | 11 |
Mathematical optimisation | 17 |
Design of structures by matrix force method | 82 |
Copyright | |
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A₁ A₂ artificial variables beam becomes bending moment boundary calculated column Consider deflection constraints design of structures design problem displacement dynamic programming element example external loads feasible region feasible solution final design geometric programming given by equation gives gradient method graphically ground structure horizontal deflection inequality integer programming intpt jointed plane frame kN/mm² last row linear programming problem local optimum Maximise subject member forces minimum weight mm² mm³ modulus non-linear objective function non-linear programming problem obtained optimisation optimum design optimum solution P₁ piecewise linearisation pin jointed structure pivot plastic hinge portal frame r₁ redundant forces redundant members removed rigidly jointed selected shown in Figure Similarly simplex method slack variables solving span statically determinate structure stiffness equations stress constraints surplus variable tion tonnes topology unit loads vertical deflection x₁ zero Zmax