Notice of RetractionOn solving the min-max problem of the stress of the structural elements in the structural topology optimization
In this paper, we deal with the min-max problem of the stress of the structural elements in the structural topology optimization. A generalized KS function is presented which transforms the local stress to global strain energy of structure through Von Mises Criterion. The ICM method is employed for solving the topology optimization problem. Some classic numerical examples are presented which provide quality solutions and the minimum stress design to obtain the final design.
Topology Optimization of Continuum Structure With Globalization of Stress Constraints
There are three difficulties in the topology optimization problem of continuum structure:1) The problem under multiple load case is not easy to be approached than that under single load case, because the former becomes a multiple objective problem on the basis of compliance objective function. 2) The problem with local constraints, such as elemental stress limit, is not easy to be solved than that with global constraints, such as displacement or frequency limits, because sensitivity analysis of the former has too expensive computation. 3) The problem with a phenomenon of ill-conditioned load, which is similar to ill-conditioned stiffness matrix in the structural analysis, is not easy to get reasonable final topological structure, because the former is difficult to consider different influences between the loads with small forces and the loads with big forces, and some of topology paths of transferring small forces may disappear during the process of iteration. To overcome the above difficulties, some measures are adopted as follows:1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises criteria in theory of elastic failure, all element' s stress constraints are transformed into a structural energy constraint, namely, a global constraint substitutes for lots of local constraints. 3) The phenomenon of the ill-conditioned load is divided into three cases: (a) Ill-condition exists between load cases, but not within each load case; (b) Ill-condition exists within some load case; (c) Ill-condition exists not only between load cases, but also within some load case. (4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the three cases of ill-conditioned load mentioned above are solved in term of different complementary approaches one by one. Numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of ill-conditioned load can be solved well by the weighting method which takes structural energy as weighting coefficient.
Microstructure of the solder-casting zone in bridges of dental gold alloys.
The composition and structure were studied in the cast and in the solder of bridges which had failed clinically. Both materials were gold alloys but with different contents of Pt, Ag and Zn. The metallographic investigation revealed defects mostly in the solder, situated in the subsurface layer. SEM studied of the fracture surface revealed large porosites and a structure of dense parallel lines--striations--, indicating that the material had failed from fatigue. The materials in the fractured bridges were identified by micro-probe measurements. It was stated that cast material and solder material used together, were of different composition.