Novel Topology Optimization Techniques Adapted to Strengthening of Civil Structures Suffering from the Effects of Material Degradation

Over years, cultural heritage monuments and historical buildings, as well as old civil structures, have been exposed to slow aging processes, material damage and degradation due to climate and environmental changes or problems resulting from poor maintenance. The task of repairing and strengthening of historical structures can be extremely challenging, because of architectural value of buildings, from one side, and selection of appropriate engineering techniques, from the other. The estimation of technical condition of the old structures, from the engineering point of view, is usually difficult or even impossible to carry out in a precise way. Because of a limited knowledge about stiffness of the considered structure, the designing of strengthening elements for historical structures becomes a motivation for developing new concepts and engineering techniques. In what follows some of the well-known, conventional reinforcing methods, like implementation of wood and steel frames or tie rods, have been gradually replaced by innovative approaches, which allow the resulting structures to become lighter, stronger and also attractive from the aesthetic point of view. This paper presents the novel design technique for retrofit strengthening of existing civil structures suffering from the effects of material degradation. The unknown stiffness distribution within weakened structure is modelled by randomly distributed material data, including cracks and reinforcements of original structure. The idea is to adopt topology optimization techniques to find the optimal layout of strengthening elements for loaded, initially and randomly weakened structure. Classical approach to topology optimization is to find within considered design domain the distribution of the material, which is optimal in some sense. The material data for design-active and design-passive regions of the structure are defined first. Then, optimization process, understood as minimization of the structure compliance, is performed and material is removed from the parts of the structure where it is not necessary to the parts, where it is essential. Finally, the considered structure takes on a new shape, while the amount of the material is reduced to assumed volume fraction. The new idea discussed in this paper is to implement into optimization process a random information about the stiffness of the original structure by modelling design-passive regions with randomly distributed values of material data. As a result, the new layout of strengthened structure for which the assumed volume fraction is preserved can be obtained. This approach allows to reduce a mass of strengthening elements, but what is essential, the complete information about the material degradation level of the original structure is not necessary to perform the optimization process.