Topology Optimization Of Composite Structures Via Moving Morphable Components (MMC) Method

With the intensification of competition for resources,engineering designers brings forward an impending demand for the comprehensive performance requirements and lightweight design of structures.Therefore multi-functional structures composed of a variety of materials with different properties and fiber reinforced composite structures have received ever increasing attention.Recently many domestic and overseas researchers have carried out optimization design on these structures,however most are based on implicit topology optimization methods,and there exist a series of problems,like too many design variables,gray elements and so on.The present paper mainly depends on an explicit topology optimization method-moving morphable components(MMC)method.A new multiple materials topology optimization approach is proposed,and a constraint which can control the intersection area between components is advanced.Besides,the integrated optimization design model for fiber reinforced composite structures is established.The main contents and research results are as follows:(1)The research on topology optimization with multiple materials based on MMC framework.Traditionally,this kind of optimization problem is solved within the implicit solution framework,and for each type of material,a corresponding density field/level set function defined on the entire design domain must be introduced to describe its distribution.This treatment,however,will inevitably lead to a large number of design variables especially when three-dimensional(3D)problems are considered.In the present approach,a set of components with different material properties are introduced to describe different phases,and this kind of optimization problem can be solved with much less number of design variables and degrees of freedom.Besides,no complex interpolation scheme is used here.Numerical examples provided demonstrate the effectiveness and advantages of the proposed method.(2)The research on the method about controlling the intersection area between components.For some coating structures or components containing microstructures,it is required that components are independent of each other.In this thesis,a sandwich component model is designed whose inner and outer layer use different materials.In the calculation,a constraint which let the intersection area between the inner of each component and other components equal to zero is introduced to ensure the material property of inner layer unchanged.The constraint can be made corresponding change according to the problems.It has been successfully applied in the topology optimization for fiber reinforced composite structures.(3)The winding parameter optimization of fiber reinforced composite structures.The MMC-based framework and fiber winding molding technology are combined for the first time in this paper,and two-dimensional continuum composite structures are designed for minimize the compliance.In the optimization process,the fiber winding angles and the parameters describing components are introduced as independent variables,and the stiffness of the structure is derived in detail with the classical laminated plate theory.Besides,the case that a component cut by multiple components is avoid through controlling the intersection area between components,so that we can ensure that the fiber winding angle changes continuously and completely.In this work,the problems that the angle is not clear in the gray elements or changes discontinuously between adjacent elements are nonexistent,and no post-processing steps are need to find the boundaries of the structure.As a result,this method is more significant for guiding engineering application.A large number of numerical examples are also work out to validate the feasibility of this method.