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The objective of optimization problem is to obtain project of structure, which satisfy limit requirements of safety and serviceability conditions under various external action effects. It can only be achieved by having comprehensive information about real structure behaviour in all eventual conditions of its work and during any moment of its maintenance period. It is necessary to change assumptions of linear theory over to considerably wider and more complex nonlinear theory generalizations. It is needed to stop calculation using unstrained conditions, which tolerate small displacements, and to allow change of structure geometry influence on its stress-strain state, to swich to nonlinear relations of stresses and deformations and to allow initial plastic deformations, because some structure materials close to plastic collapse undergo very large displacements and do not satisfy normal serviceability requirements. When developing structure optimization problems mathematical models, these mentioned factors must be taken into account. An improved mathematical model and calculation algorithm with material inelastic properties are presented for cross-sectional optimization of geometrically nonlinear 3D frames. The optimal structure is considered in the state prior to plastic collapse. Used elastic response values are related to optimized parameters of standard profile cross-sections by nonlinear functional relation. Therefore, this problem has to be solved by iterative method. For beam elements the new formation procedure of tangent stiffness matrix, taking into account different alterations of structure elements caused by internal forces, is presented. Efficiency of developed algorithm is illustrated by calculation of optimal values of two-storey single-bay steel 3D frame element cross-sections, satisfying minimum volume requirements. |
