Research On Frequency Topology Optimization With Regular Geometrical Constraints

Wind tunnel test is an inevitable part in the development process of aircraft, so it's of vital importance to develop models which could simulate the mechanism how aerodynamic loads act on aircraft precisely. Researches indicate that only the elastic scale model could simulate aircraft's vibration in high speed tunnel accurately. Elastic scale model should be similar to original design in both geometry and corresponding modes. It can be seen as a concurrent design problem which concerns material and topology geometric characteristics. And topology optimization is an effective solution. At present, holes generating in topology optimization is mostly irregular geometric. However fuselage keel structure is generally regular grid. Therefore, in order to realize optimization design similar to real aircraft in both structure and modes, restricting hole's shape and making a study on frequency topology optimization of continuum with regular geometrical constraints plays a great value for engineering application.In this paper, firstly common topology optimization of continuum without geometrical constraints is studied. On the basis of BESO method, Bi-directional Element's Property Changing Method (BEPCM) is developed; optimization model of continuum is constructed with multiple frequencies as objects; based on element sensitivity analysis, element deletion is realized by changing a solid element into a void element with small and mutually matched elastic module and density; how matching relationship of void element's module and density influences modes is given; Sensitivity Redistribution Method is modified to restrain checkerboard; above method is applied to shell plate and verified feasible.Secondly, based on the common topology optimization of continuum, by restricting hole's shape, frequency topology optimization with regular geometrical constraints is studied. Modeling and modal analyzing is conducted by ANSYS and frequencies and modal shapes of structure are outputted; geometry description of regular square hole is presented; optimization model of continuum is constructed, with multiple frequencies as objects, volume, hole shape, minimum size and symmetry as constraints, position, size of holes and element existing state as design variables; BEPCM with regular geometrical constraints is adopted; holes insertion strategy based on objective analysis is given; accelerative search and adjustment of position and size of inserted holes is adopted; optimization program is compiled using Matlab; above method is applied to double layer flat and proved feasible.Finally, BEPCM with regular geometrical constraints is applied to topology optimization of circular fuselage elastic scale model. The model is simplified to double cylindrical shell and special strategy that the whole structure could be expanded by local modeling is adopted. With the first three frequencies at the first diameter as objects, frequency topology optimization of cylindrical shell is realized.