Optimum Design of Structures |
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Page 26
... optimum solution is always obtained when the elements of the last row are all negative . Table 2.6 Y2 y1 0.67 1 0.67 -2 -0.33 1 642 X2 y3 2 X1 -0.33 -1 -18 -Z It is interesting to compare the various stages of the simplex method with ...
... optimum solution is always obtained when the elements of the last row are all negative . Table 2.6 Y2 y1 0.67 1 0.67 -2 -0.33 1 642 X2 y3 2 X1 -0.33 -1 -18 -Z It is interesting to compare the various stages of the simplex method with ...
Page 50
... solution , shown as point E in the figure . No doubt another round of iteration produces a better solution . x1 On the other hand starting from point F , where x1 = 3 , x2 = 8 , the first cycle of iteration results in x1 = 51 and x2 = 0 ...
... solution , shown as point E in the figure . No doubt another round of iteration produces a better solution . x1 On the other hand starting from point F , where x1 = 3 , x2 = 8 , the first cycle of iteration results in x1 = 51 and x2 = 0 ...
Page 59
... solution is globally optimum . This full agreement between the actual solution and that given by piecewise linearisation is not always the case . If , for instance , during the subdivision of the variables nodes are not selected at x1 ...
... solution is globally optimum . This full agreement between the actual solution and that given by piecewise linearisation is not always the case . If , for instance , during the subdivision of the variables nodes are not selected at x1 ...
Contents
An outline of existing design methods | 11 |
Mathematical optimisation | 17 |
Design of structures by matrix force method | 82 |
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A₁ acting analysed beam becomes bending boundary calculated changes chapter column condition Consider constant constructed corresponding cost deflection constraints derived direction displacement element equal equation example express external loads factor feasible final follows forces frame given gives ground structure hand horizontal indicates inequality instance integer jointed structures kN/mm² limited linearised load manner material matrix Maximise method mm² moments necessary negative non-linear noticed objective function obtained Once original permissible pin jointed plastic positive possible reduced redundant forces reference removed replaced respectively satisfy selected shape shown in Figure shows Similarly simplex simplex method solution solved span stage statically determinate stiffness stress constraints structure Substituting Table tion unit variables vector volume weight x₁ y₁ zero