Optimiranje mehanskih sistemov (Slovene)

The main objective of the proposed project is further development of the procedures for systematic design of optimally shaped frame structures. Specifically, the following topics will be considered. Introduction of eigen-frequency constraints in to the design problem. For this purpose an adequate description of the inertial forces for the chosen beam element will be derived. After that the corresponding mass matrix as well as its design derivatives will be derived. These expressions will then be employed to calculate the eigen-frequencies of the structure (in either undeformed or extremely deformed configuration) and to include the eigen-frequencies into the constraints describing the design problem. Removal of the singularity problem of the stiffness matrix. For the chosen beam element it turned out that its tangent stiffness matrix exhibits singularity at a constant rotation field of magnitude k*2*Pi, k=1,2,3,... . In practical problems, such rotational fields are encountered rather seldom. In spite of that, it would be better to remove this problem for the sake of robustness of the optimization process. This might be possible by employing adequate mappings of rotational fields and integrating this procedure into the response as well as into the sensitivity analysis. Improvement of the shape representation concept. The shape representation concept employed at the time is based on tensor product Bezier surfaces. For the sake of generality and ease of use it would be necessary to investigate the possibility of employing Bezier surfaces of the triangular type as well as other alternatives which would lead to the reduction of the set of design elements and design variables. The (elastoplastic) material nonlinearity will be also included at shapeoptimum design of plane frames. The periodic and almost periodic nonlinear response and optimal shape of dynamical loaded beams from the minimum weight viewpoint will be determined with the fulfilment of the natural frequency constraints and stability region constraints. Determination of the stability of the periodic and almost periodic solutions of nonlinear mechanical systems Research of the fracture mechanics behaviour of the strength of the heterogeneous specimens is devoted to the determination of the stress and strain distribution in the case of the initiation of the stable and unstable fracture.