Optimum design of structures

Abstract

[Master of Philosophy thesis] The work presented in this Thesis aims at producing a computer method that uses mathematical programming to obtain optimum design of different types of structures. The optimisation of elastic structures usually turn out to be that of nonlinear programming, thus the formulation of such problems is done in the form of sequentially approximating linear programming. ‘The two-phase simplex method is then employed to obtain the solutions. The matrix displacement method is used in formulating the design problems. The method for optimum design is general and can be applied to minimise the weight or the total cost of the structure. ‘The total cost is assessed realistically, and this includes the material amd the construction costs of the members, plus the cost of constructing the foundations. The reduction of the weight does not include any variation in the configuration of the structure. But, on the other hand, minimising the total cost is achieved by altering the topology of the structure, depending on economical and structural requirements. This method of optimisation is applied for the design of three distinct types of large structures. The first type includes plane rigidly jointed multi-storey steel sway frames. The method is applied to obtain minimum weight or minimum cost topological design that satisfies the stiffness, the sway deflection and the practical constraints. The stress constraints are not included in this case. The second type is described as complete structures consisting of arbitrary parallel systems of reinforced concrete shear walls and floor slabs, with additional restraining frames made fram steel or reinforced concrete. The structures are assumed to be subjected to the effect of static wind loads only. The optimisation method is employed to obtain a topological design of minimum cost that satisfies the stiffness, the differential sway deflection and the practical constraints. The third type is represented by reinforced concrete horizontal grillages made fram straight orthogonal rectangular beams, with or without supporting columns. The optimisation method is applied to obtain a minimum weight or a minimum cost topological design that satisfies stiffness, stress and deflection constraints. The stress constraints include that of bending moment and that of combined shear and torsion.