Research And Application Of Explicit Topology Optimization Methods Based On The Spatial Descriptions

With the rapid development of science and technology,the considerable development and progress has been been made in the theories of structural optimization,which is widely used in the fields of automobile manufacturing,aerospace engineering and weapons.However,structural boundaries are usually described implicitly in traditional topology optimization methods,which often leads to poor manufacturability of the optimized results,and it is difficult to accurately control the size of important geometric features.The shortcomings of the existing methods can be overcome to some extent in the framework of moving morphable component(MMC)based on explicit descriptions,and this method has broad research prospects in different scientific fields.At present,almost all the optimized results in MMC-based topology optimization methods are solid structures with rectangular sections.However,in the field of engineering,there are different types of members(circular-shaped,hollow-shaped,T-shaped,I-shaped and U-shaped)in the design of some load-bearing frames(the skeleton of car,the satellite outrigger,the truss supports of large space telescopes,etc.)and stiffeners.It is worth noting that the appropriate types of members will make the structures have better mechanical properties under different boundary conditions and load cases.In addition,there are some complex non-design structural areas which are composed of different geometric features in the design domain.All of these put forward new requirements and challenges to the modeling ability of the MMC-based topology optimization framework.Under the MMC-based topology optimization framework,the complexity of spatial structure modeling in engineering field is fully considered,and the construction methods of various topology description functions(TDF)with different dimensions and related topology optimization methods are proposed in this paper.On this basis,the topology optimization of stiffeners is further carried out in the armored cars.The specific researchcontents are as follows:A two-dimensional(2D)method of moving morphable component(MMC)is developed based on the descriptions of area function in this paper.This method focuses on the explicit descriptions of polygonal components,and constructs the TDF of 2D components by establishing the expression of area correlation between any node in the design domain and each key point in the component.The proposed method has a very intuitive modeling effect,extends the modeling methods of the TDF of a 2D component,and can be applied to the construction of arbitrary 2D polygon component.On this basis,a two-dimensional multi-section component is constructed by the boolean operations between components,which makes the deformation ability of the component more flexible.In practical engineering,most structures are polyhedral geometric models.Inspired by the the extension of modeling methods in 2D component,a three-dimensional(3D)method of topology optimization is developed based on the descriptions of volumes.The method focuses on the explicit descriptions of polyhedral components,and the TDFs of polyhedral components are constructed by establishing the expressions of the volume correlation between any node in the design domain and the key points and faces in the component.The modeling methods of 3D polyhedral components are extended by the proposed methods,and the coordinates of key points in the components can be intuitively used for the construction of TDFs.Two kinds of flexible deformable components are also developed,which can be applied to some non-classical designs of the degenerate solution.In practical engineering applications,there are a lot of similar structures with the characteristics of rotating bodies,such as columns,shafts and bars.For this reason,a new MMC-based method is proposed based on the descriptions of rotating body in this paper.In this method,the explicit descriptions of rotating components are studied.Combined with the user-defined function of volumes and function of ends,the construction method of TDF is proposed for the rotating components,which solves the modeling problem of thestructures with the characteristic of rotating bodies under the MMC-framework.Based on the research of component-related explicit descriptions,the optimization of stiffeners is carried out for an armored car in this paper.At present,empirical and local size and shape optimization are still the main methods in the research of optimal designs of stiffeners in the armored cars.The optimized results are prone to waste of materials and excessive vehicle added mass.For this reason,the stiffeners to be optimized are mapped into a series of 3D components with explicit geometric features under the MMC-framework.The problems of the layout of the stiffeners on the roof deck of the armored car are solved by combining the descriptions of volumes and rotating bodies.On this basis,the design of the stiffeners on the roof deck of the armored car is optimized in terms of the stiffness and natural frequency of the overall structure from the statics and dynamics of the system.According to the parametric modeling function of ANSYS,the written APDL command flow can quickly realize the modeling of the top deck and stiffener on the armored vehicle,and the results of topology optimization are simulated and verified in the same working conditions.