Structural Optimization Of Thin Elastic Plate And Shell With Thermal Load

Plate and shell structures, which are usually subject to thermal loads, are widely used in civil and mechanical engineering field, especially in aerospace engineering field. When thermal expansion is restrained, membrane forces and bending moments generated in the plate and shell structures will lead to large deflection and seriously affect normal service. Due to the characteristic of thermal load, increasing the thickness of plate and shell structures uniformly does not necessarily lead to the reduction of thermal deformation and thermal stress effectively. Hence special experience and knowledge are required in thermal structural optimal design.Structural optimization design could provide thermal structure design with theory and method. In this paper, we assume that the material volume, thermal load and the middle surface shape of thin solid elastic plate and shell structures have been given. This objective is to reduce the structural thermal deformation by optimizing the design variables, which are described by the thickness function and subjected to the variables’ range.First, for thin plate structure, a mathematical formulation of the optimization problem with the objective of structural deformation energy and the constraint of a given material volume is present. By the optimization formula and the variational method, the optimality criterion and the iterative formula for modifying thickness distribution are derived. Then this optimization algorithm is implemented by secondary development of the commercial finite element programs. The numerical examples results show that, this method could greatly reduce the thermal deformation of thin elastic plate structure by reallocating thickness. Therefore, it is an effective optimization method for thermal structures.The difference is observed when the same method is applied to thin shell structure. For thin plate structure, optimality criterion is expressed by the sectional bending moment and twisting moment. However, for thin shell structure, optimality criterion expression is more complex since it contains both the sectional moment and the membrane force. The optimality criterion is compared with the other two heuristic criteria, each of which only contains sectional moments or membrane forces. Several numerical examples illustrate that the effectiveness of three criteria are related to the shape of middle surface and boundary conditions of the shell structure. When solving the practical problems, we should choose the suitable one from the three optimality criteria.Finally, this paper puts forward the possible research direction for the future work.