Achievements of the research programme in the field of fracture mechanics and analysis of extreme structural states add to the integrity of structures made from heterogeneous materials under consideration stress-strain state in the material of the structure. This research base represents an addition to the actual research programme assuring safe and reliable application of structural components. World wide comparison of the research team is evident from the systematic and consistent research work, scientific achievements and received award "Hery Granjon" of the International Welding Institution for the best paper in the field of structural integrity assurance in 1999. Part of the research has been in the frame of a postdoctoral project, highly assessed by the EU experts. European Commission granted financial means for research at GKSS research centre. Research was successfully terminated by results and conclusions, published in national and international professional journals, which are reported by JCR. Excellence of research achievements produced further cooperation, exchange and research work in the frame of bilateral projects and the EU project "FITNET" on the problems of integrity assurance in the phase of construction and exploitation. Improvements have been made in the parametrisation of structural shape and finite element meshes, based on Bezier bodies of quadrilateral and triangular types. The developed approach and its synthesis by adequate finite elements represents in our oppinion with respect to published examples in the literature the best way to optimise the shape of structural parts, if shape parametrisation is chosen. Alternative evolution (nonparametric) methods may have some advantages in several fields, but also some disadvantages in other applications. We have improved the efficincy of our own gradient-based optimisation algorithm, which employs adaptive convex approximation with an additive convex term. In the frame of defined goals of the research programme, further development of periodic and qusiperiodic oscillations of dynamic systems by an extended method of incremental harmonic balance with use of several time scales has been made. This method development enabled evaluation of combined resonances of beams subject to various supports, being the consequence of internal resonance. Analysis of beams has been cannonised as part of nonlinear oscillations of dynamic systems with cubic nonlinearities. Method of incremental harmonic balance has been incorporated into the model which determines optimal beam shape with stepwise constant crossection from the viewpoint of its own weight, considering constraints with respect to eigen frequencies and mutual assurance of beam stability. Research of periodic and quasperiodic oscillations of nonlinear systems has been extended to the field of bending nonlinear oscillations of rotating systems with cubic bearing characteristics and electromagnetic damping. Hopf's bifurcation of transition from periodic bending oscillations to quasiperiodic oscillations of a rotating system has been investigated by the application of incremental harmonic balance method and several time scales. Research of incremental harmonic balance method has been extended by methods of the theory of bifurcations, determining branching points, types and tracing of individual branches of the bifurcation diagramme. An effective model for optimisation of joint forces and accelerations of any kinematic chain has been developed.