Multi-material Optimal Design Of Structures Considering Embedded Holes And Components

Topology optimization,as a powerful tool for structural conceptual design,has become a research hotspot in engineering design to achieve novel and innovative configuration design with limited materials.In the process of structural design,sometimes the researchers use a variety of materials to meet different functional requirements,and sometimes need to embed in the limited space design with one or more fixed in the shape of the hole or component.Not only it is necessary to find the optimal layout of holes or components in the design domain,but also to synchronously optimize the topology configuration of the support structure,in order to improve the global mechanical properties of structure,which brings a new challenge to the topology optimization technique.At present,most optimization methods have limitations to different extent.However,the moving morphable sandwich bars(MMSB)method,as an explicit topology optimization method,can use fewer design variables to achieve the same optimization design objectives with higher computational efficiency,and without any filtering technology in the optimization process,and the obtained topology configuration is clear.In this thesis,the topology optimization of multi-material support structure is realized based on MMSB method,and the layout optimization of embedded holes and components is achieved simultaneously.The main research contents are presented as follows:Firstly,the theoretical basis of MMSB method is introduced,and it is pointed out that this method can realize topology optimization of multi-material structures by setting the lower limit of material thickness as negative value.Based on this property,a new elastic modulus interpolation scheme is proposed for the topology optimization design of multi-material support structures,in order to synchronize the layout optimization of inlaid holes and achieve the maximum stiffness of the whole structure system.Numerical examples demonstrate the correctness of the proposed elastic modulus interpolation scheme and the effectiveness of the optimization model.For the general hole layout optimization,the change of hole position requires remeshing in the optimization process,which affects the computational efficiency to a large extent.In this thesis,the level set function is utilized to describe the holes,and the embed holes and moving sandwich bars are projected onto the fixed finite element analysis mesh by differentiable mapping,which can effectively avoid the remeshing problem in the optimization process.The formulations of sensitivity analysis are explicit,and thus the gradient-based optimization algorithm can be employed to solve the optimization problem quickly and further enhance the computational efficiency.Secondly,based on the MMSB method,a new material interpolation scheme was proposed,and an explicit optimization model is established.The geometric parameters defining the position and direction of moving bars and components are considered as the design variables of the optimization problem,and the layout optimization of embedded components and the topology optimization of multi-material support structures are fulfilled simultaneously.Although the MMSB method requires multiple density fields to represent the different materials of supporting structure,by using a fixed grid,the mapping of each moving bar only needs to calculate a minimum distance function without increasing the computational effort.The new interpolation scheme meets the requirement of material parameterization in multi-material system,and establishes the relationship between multiple density fields and elastic modulus effectively,which thus unifies the two kinds of optimization problems of embedded component layout and structural topology optimization under the same computational framework.Only a single non-overlapping constraint is involved in the optimization model,which can effectively avoid the overlap between components and overcome the drawback of low computational efficiency caused by a large number of non-overlapping constraints.