Abstract. In the paper, experimental results of tension member tests are used as a basis from which to develop an extended tension stiffening model for reinforced concrete, with emphasis on the specific concrete damage and the developments of residual deformations depending on the structural loading. Two characteristics are contained in the proposed model: one describes the residual deformation behaviour along the reinforcement accounting for the cracks that cannot be closed completely, while the other describes the degradation of the concrete stiffness. Within context of non-linear analysis, the model is incorporated into an analytical approach, based on the LAGRANGE principle of minimum of total potential energy. The mechanical problem is solved with the application of the mathematical optimisation, using energy principles formulated as a kinematic formulation and transforming them into non-linear optimisation problems. It was demonstrated, that this approach is eminently suitable for analysing pre-damaged or pre-loaded reinforced concrete crosssections under cyclic loading.

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In the present article an alternative approach for the coupled thermal and mechanical analysis of composite cross sections under temperature effects is introduced, which uses the mathematical optimization as a consistent methodical base. By applying the principle of the virtual source energy for the thermal and the principle of the minimum of the total potential energy for the mechanical analysis, an accurate determination of temperature fields as well as residual strain and stress distributions is possible. The coupling is enabled by the thermal strains, which are determined based on the temperature field and passed to the nonlinear mechanical analysis as tension free pre-strains. The energy functional of the heat conduction problem is derived and implemented. The resulting optimization task is strictly convex and represents an implicit formulation, which does not impose any stability criteria. The performance of the introduced method is demonstrated on a principle example and an outlook is given on possible further extensions and applications.

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<p>The potential of structural optimization in the design of structures is growing rapidly with the advancement of the computer technology. In this paper, a formulation of structural optimization problem using an energy method is presented, for which solution a nested bilevel optimization is utilized. The method is applied on two practical examples, namely a nonlinear sizing problem for a two span girder and a discrete shape optimization of a truss bridge. These demonstrate the applicability of the method.</p>