The Research On Structural Topology Optimization Based Moving Morphable Components (MMC) Method

For structural topology optimization, it is an inevitable trend to describe structural topology in an explicit and geometrical way, which is one of the challenging issues in the existing structural topology optimization frame. In this paper, a new computational framework for structural topology optimization based on the concept of moving morphable components (MMC) is proposed and two construction methods are used to describe the component. The first one uses Lagrangian framework to describe the component, whose central line is the line segment. The component geometry is described by the coordinates of two end points and linearly varying thickness explicitly. For the second one, the continuous functions f(x') and d(x') are introduced to describe the central line and thickness of the component in the local coordinate system, respectively. The combination of different continuous functions can describe the components of various shapes.In the first method, the coordinates of four corner points can be expressed by coordinates of the end points, the outward normal vector and thickness. Then the coordinates of any points on the component boundary can be calculated through the parameterized expression. Due to using explicit geometry parameters to describe the component, the sensitivity of a typical objective or constraint functional with respect to variables can be calculated based on boundary integral. For the finite element analysis, the extended finite element method (X-FEM) is used to calculate the approximate displacement fields, and uniform four node bilinear square elements are used to discretize the design domain. Besides, the boundary element method and the meshless method can also be introduced. Some representative examples, such as the short beam, MBB beam and compliant mechanism, are presented to illustrate the effectiveness of the proposed method. The optimal structures which don't have zigzag boundary and checkerboard pattern are similar to the results obtained by traditional topology optimization methods.In order to broaden the applicable scope of MMC method, the second method which uses the continuous functions f(x') and d(x') to describe the central line and thickness of the component is proposed, and four different combinations between f(x') and d(x') are presented. In this paper, the quadratic function f(*')= a(x')2 and constant function d(x')= d are introduced to describe the central line and thickness of the component, which is the basic building block of the initial structure of the topology optimization problem. In order to illustrate the effectiveness of moving morphable components method based on the second construction method, it is first used to solve the short beam and MBB beam problems, whose optimal topologies are same as the results obtained by traditional topology optimization methods. Then, for the bridge example, the structure which is only consist of straight components serves as the initial design, and the optimal structure obtained by the proposed method includes the curve structure, which illustrates that the second topology description method has very flexible geometry modeling capability. Last but not least, using traditional topology optimization methods to solve the topology optimization problem whose design objective is to maximize the structural compliance will inevitably leads to degenerated solutions such as disconnected structures. While the proposed method which uses continuous functions to describe the components can avoid above-mentioned problems essentially, it can make sure the structure designable and manufacturable.The moving morphable components method provides a new idea to do topology optimization in an explicit and geometrical way, which has a significant influence in extending the application of topology optimization method in designing the complicated structure.