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Analytic bending solutions of rectangular cantilever thin plates

100%

Tian B. , Zhong Y. , Li R.

tom Vol. 11, no 4

1043-1052

Analytic bending solutions of rectangular cantilever thin plates subjected to arbitrary loads are derived using the double finite integral transform method. Since only the basic governing equations of the plates are used and there are no predetermined functions, the present method overcomes the deficiency of the conventional semi-inverse methods thus serves as a completely rational model in solving plate bending problems. The method can be extended to more boundary value problems of plates such as buckling and vibration.

W pracy sformułowano analityczne rozwiązania dotyczące zginania prostokątnych, wspornikowych płyt cienkich poddanych dowolnym obciążeniom przy zastosowaniu metody podwójnej, skończonej transformaty całkowej. Ponieważ zastosowano tylko podstawowe równania płyt, zaprezentowana metoda przezwycięża niedobór konwencjonalnych metod semi-odwrotnych i może służyć jako całkowicie wymierny model przy rozwiązywaniu problemów zginania płyt. Zaprezentowana metoda może być rozszerzona na dalszą klasę problemów brzegowych płyt w zakresie ich wyboczenia oraz drgań.

Hot forming and heat treatment simulation in a steel mill

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Redl C. , Tian B. , Wieser V. , Sommitsch C.

tom Vol. 7, No. 1

5-10

Numerical simulation is nowadays becoming a standard tool in industrial processes. This paper provides an insight about the usage of finite element calculations in the development and production process in the steel mill of Böhler Edelstahl GmbH, Kapfenberg, Austria. Simulation methods are used all along the value chain at the mill starting with melting and casting of the steel. Nevertheless this paper focuses on the simulation of hot forming and heat treatment as well as on the simulations done as a service for our customers. The activities of finite element simulation of hot rolling concentrate on one side on the basic principles, for example, widening, strain distributions, grain models etc. On the other side, typical chains of hot rolling have been simulated and the results verified by comparing measured parameters with calculations. As an example the widening of a cold work steel at different temperatures is presented and compared with other steel grades. Considering as example a hot work tool steel of type 1.2343 the production chain from forging over the pre heat treatment at the mill to the application as a tool for aluminium extrusion is surveyed. The forming of the casted and remelted steel block is done on a radial forging machine of the type GFM SX55. The simulation takes into account five passes and delivers strains and temperatures within the work piece. Afterwards the pre heat treatment cycle of the part consisting of heating, quenching in polymer solution and subsequent air cooling is modelled. Simulation services are provided to the customers to optimize the material selection for their specific applications. The aforementioned tool steel is used as liner or die material in the extrusion industry. By a combination of a visco-plastic material model and a damage model it is necessary to predict the lifetime of the tools in use. In order to obtain the residual stresses and phase distribution after nitrogen quenching a heat treatment simulation of the die is performed. Afterwards a simulation of the extrusion process is carried out to get the distribution of effective stress and temperature in the die. The calculated life time as well as the predicted location of the maximum damage agrees well with observations from real extrusion processes.