Multi-material Topology Optimization Of Continuum Structure With Embedded Components And Holes

Topology optimization can obtain novel,high-quality innovative designs without a priori assumptions of structural shape and connectivity,and has become a powerful tool for conceptual design of engineering structures.However,most of the work presented is mainly aimed at solving the optimization problem of single-phase homogeneous materials and single-component structure.In practical engineering problems,the structure is usually composed of a variety of materials,and the combined use of multiple materials not only reduces the structural weight,but also improves the performance of the structure to some extent.Besides,many structural systems typically embed one or more components of specific geometry shapes and stiffness(e.g.capacitor,engine and storage container)into a limited design space to meet certain specific functional requirements.In addition,in the design process,it is usually necessary to reserve sufficient void space to enable other components to pass through the structure smoothly,or to permit the embedding of predetermined objects,or simply for the sake of aesthetics,assembly process or equipment operation,installation,maintenance,and repair.In these applications,for multi-material structures,we need to determine the optimal distribution of each material phase to optimize the overall mechanical properties of the multi-material structure.For the latter,to improve the performance of whole structure system,we not only need to find the optimal position and direction of these embedded objects(components and holes)in the allowed design space,but also design the topological configuration of the support structure connecting these embedded objects.Moreover,structural fracture and fatigue damage caused by stress concentration or high stress value seriously affect the service life of the structure.Therefore,it is of great significance to include the stress constraint in the structural topology optimization.In the above problems,the intuition and experience of the designer or engineer is usually limited.To address these problems,in this paper,the theoretical research on four aspects of multi-material topology optimization,layout optimization of continuum structure with embedded components,layout optimization of continuum structure with embedded holes,and stress-constrained topology optimization are carried out.This can provide valuable support and guidance for designers.The main research contents and achievements of this paper can be summarized as follows:(1)A multi-material topology optimization method based on the reciprocal variable is proposed to the lightweight design of multi-material steady-state heat conduction,multi-material transient heat conduction,multi-material dynamic structure.A quadratic programming model for minimization of total weight with the prescribed constraint of various structural responses(thermal compliance,frequency,etc.)is established,and the dual sequence programming algorithm(SQP)is used to solve the problems quickly and efficiently.Numerical examples verify the advantages of quadratic programming model in computational efficiency,and reveal the advantage in weight loss of multi-material design in optimization problems of the steady-state heat conduction,transient heat conduction and vibrating structure,in comparison to single material design.(2)An explicit optimization model based on the moving morphable bars(MMB)method is developed for solving structural layout optimization problem with embedded movable components.Different from the existing works,geometric parameters used to describe the size,position and direction of the moving bars and embedded components are considered as the design variables of optimization problem,which ensures that the topological configuration of the structure can be reconstructed more easily.The moving bars representing the support structure and embedding components are then mapped into density fields on a fixed grid using a smoothed Heaviside function.This helps avoid the tedious task of re-meshing the grid,and improve the computational efficiency.Then a relationship between the multiple density fields is established based on idea of material interpolation in multi-material topology optimization.In turn,the simultaneous optimization of topological configuration of the support structure and the position,direction of embedded components can be achieved.Based on the this work,we replace embedded components with moving bars whose size and position can be changed,the proposed optimization model is further extended to the multi-material topology optimization problem.And an explicit multi-material topology optimization model based on the MMB method is established.Several numerical examples are performed to verify the effectiveness of the proposed method and optimization model.(3)A topology optimization method considering embedding movable holes and components simultaneously is proposed to realize the simultaneous optimization of the position,direction of the embedded components and holes,and the topological configuration of the support structure,for the purpose of improving the performance of the whole structural system.The material density defining the structural topology of and the geometric parameters used to describe the position and orientation of the embedded holes and components are considered as design variables of the optimization problem.To avoid remeshing the grid,we projected all embedded holes and components onto two density fields on a fixed grid using a smoothed Heaviside function.Meantime,a SIMP-like material interpolation scheme invoked at the finite element level is proposed to unite these two seemingly different representations of embedded objects(holes and components)and structural topologies into a unified computing framework.Another advantage of the proposed method is that it can be easily extended to handle single-material and multi-material structural topology optimization problems with embedded moving holes.Several numerical examples are performed to verify the effectiveness of the proposed method.(4)An improved bidirectional evolutionary structural optimization method is proposed to solve the structural topology optimization problems under volume and stress constraints.A global stress measure based on the(Kreisselmeier-Steinhauser)K-S aggregate function is introduced to reduce the computational cost caused by a large number of local stress constraints.The sensitivity of the global stress function with respect to the design variables is detailed based on the adjoint method.The stress constraint is applied by the Lagrangian multiplier method,and the appropriate Lagrangian multiplier value is determined by the dichotomy method.Two typical topology optimization examples are performed to demonstrate the validity of the present method,in which the stress-constrained designs are compared with the traditional stiffness-based designs to illustrate the merit of considering stress constraint.In addition,based on the previous work,stress constraints are integrated into the structural topology optimization problem with embedded holes.A stress-constrained topology optimization method considering embedded moving holes is proposed to realize the simultaneous optimization of the position,orientation of embedded holes and the topological configuration of supporting structure,which can effectively control the local stress level of the structure to avoid the failure and damage of the structure caused by the stress concentration effect at the critical stress areas of the structure.