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The increasing demands placed upon design engineers to evolve optimal solutions to prescribed problem specifications necessitates more definitive analysis of system response to modifications.Traditional solution techniques including discretised methods are required to be repeatedly evaluated in multiple re-analysis solution environments in the search for optimal behavioural response. Modern developments in sequential linear programming techniques in both unconstrained and constrained environments have enabled the methods of optimisation to be applied in a structural context.Such advances are now being limited by the present state of solution to criterion and constraint functions. The state of the art in structural optimisation is reviewed and the application of current methods in the presence of discontinuities examined.The extension of such methods to the discretised problem is advocated.The search for an effective and economical re-solution vehicle is described with reference to the classical formulation of sensi tivi ties defined in a discretised context. The development of a solution technique based on sensitivity is described and limitations examined.The extension of sensitivities into the clearly defined non-linear state with large design variable changes is discussed and the development of a residual correction technique to linearise the sensitivities documented.Utilising residual correction the sensitivity method is extended into the concept of adjoint structures and predictive solution models for design variable changes. Quantitative and qualitative techniques for design performance assessment are evolved and an interactive program developed to graphically display the effect of design variable changes on design parameter response. A new design philosophy based upon design system syntheais is advocated and demonstrated wi th reference to particular design problems.Exploratory work is discussed with reference to the general application and the interfacing of the developed software system with alternate systems.

The following work describes the measurement of longitudinal residual stresses in hot finished structural steel hollow sections. All samples were supplied by the Tubes Division of British Steel Corporation (B.S.C.)and include circular and rectangular profiles manufactured by all of the methods employed by B.S.C. A total of sixty-eight profiles were examined. The technique used to determine the longitudinal stress state was the slicing method with strain release measured by mechanical extensometers. A new experimental method has been developed for the rectangular sections, where access to the inside corner area was restricted. The effect of these measured residual stress values, or idealisations based on them, on the behaviour of axially loaded pin ended columns is then examined by the development of inelastic column buckling computer programs. Various iterative solution routines are compared and a new accelerated relaxation procedure is developed. The relative effects of material and geometric imperfections on column behaviour are examined and the results obtained compared with existing and proposed column buckling design methods. One of the analysis programs is extended to cater for the application of primary bending moments at the ends of the columns and results obtained compared with existing design equations for beam-columns and modifications are suggested. The column buckling behaviour of hot finished hollow steel sections is also compared to geometrically similar profiles manufactured by cold forming or by welding. The phenomenon of local buckling of sections with relatively thin walls is also theoretically examined by utilising a non-linear finite element program. The effects of various parameters on local buckling are examined, including corner geometry, stiffening effect of stockier adjacent faces, initial geometric imperfections and residual stresses. Existing design rules for local buckling are described and comparisons made.

The development of mixed and hybrid models provides viable alternatives in finite element structural analysis which overcome the shortcomings of conventional displacement and force methods. In this thesis, a mixed triangular finite element model in two-dimensional stress analysis is studied. The mixed finite element model has several features which are distinct from those of conventional methods: (i) the use only of mid-side nodes; (ii) a global coordinate system is not required; (iii) nodal variables include both forces and displacements; (iv) the element matrix consists of a mixture of stiffness, flexibility, equilibrium and compatibility coefficients; (v) the ability to deal with incompressible materials; (vi) internal equilibrium and compatibility are satisfied; (vii) the entire stress field of the assembled structure is in equilibrium; (viii) formulation of element equations is not based on an extremum principle. The derivation of element matrix equations for small-strain, small-displacement linear-elastic analysis is discussed and a scheme for assmebling the final set of algebraic equations is presented. Accurate and balanced results for both stress and displacement are obtained for a number of problems in plane elasticity including thermal strain and body-force problems. The ability of the mixed element to deal with incompressible materials makes it useful for the computation of collapse loads in elastic-perfectly plastic analysis, for example in undrained soil mechanics problems. Ideal plastic behaviour is approximated by the use of an extremely soft incompressible material. This approximation enables an incremental plastic stress-strain matrix to be written down, relating a plastic strain-increment to an imposed stress-increment in the ideal plastic range. The performance of the mixed element in elastic-perfectly plastic analysis is studied and numerical results are compared with those obtained by analytical techniques and the displacement finite element method. The use only of mid-side nodes in the mixed model has the advantage that a global coordinate system is not required in the analysis. This makes it relatively simple to follow the behaviour of structures in large-deflection problems. Examples are studied to investigate how the mixed element works in small-strain, large-deflection problems.