Level Set-based Topology Optimization Method Considering Manufacturing Constraints

Topology optimization can obtain novel structural configurations by designing the material distribution.Driven by the revolution of science and technology and the increasing requirement of high-performance but Lightweight structures,topology optimization has achieved a rapid development in recent decades.It has become an importance structural design technology and been widely used in many academic and engineering areas.Topology optimization results usually have relatively complex shapes and topologies,on the other hand,every manufacturing process requires the geometry of structures satisfying certain manufacturable conditions.Thus,topology optimization results are mainly used in early design stages of products and some modifications in sizes and shapes are need before the results satisfy the specified manufacturing constraint.This is one of the main factors that limit the further development and application of topology optimization.Therefore,it is necessary to consider the manufacturing constraint in topology optimization,in which way the optimization result can be directly fabricated by the specified manufacturing process while having extraordinary performances.However,introducing manufacturing constraints usually turn the topology optimization problem into one with multiple constraints and even with multiple kinds of design variables.Representing the complicated manufacturing constraints in topology optimization models and developing more efficient topology optimization methods are the main difficulties in this problem.Based on the above background,this thesis mainly studies the level set-based topology optimization method considering certain manufacturing constraints.The research works of this thesis are stated as follows:(1)The velocity field level set method is proposed.The key idea of this method is constructing the normal velocity field by basis functions and velocity design variables defined on a given set of points.Compared with the traditional level set method,this method maps the variational boundary shape optimization problem into a finite-dimensional design space and allows using of a general mathematical optimizer to find the optimal normal velocity field.Thus,it offers a more efficient and straightforward way to solve topology optimization problems with multiple constraints and multiple kinds of design variables in the level set framework.Moreover,the level set function is still updated by the Hamilton-Jacobi equation using the normal velocity field.Therefore,the current method inherits merits of the implicit representation and capabilities of extracting the geometrical features in the traditional level set method.The velocity field level set method is then applied to the concurrent two-scale topological design.A topology optimization framework based on the velocity field model and the density model is proposed to design the microstructural topology of multiple unit cells and their corresponding spacial distribution in the macroscale concurrently.(2)Structural topology optimization with the minimum distance constraint of multiple embedded components is studied.In many complex engineering structures,like the spacecraft,it is often necessary to embed components with specified shapes for fulfilling certain functionality and manufacturing requirements.To avoid possible interferences,the components usually need to satisfy the specified minimum distance constraint.This thesis proposes an integrated design of both the structural topology and the component layout based on the velocity field level set method.Using the signed distance property of the level set function,the minimum distance constraint of embedded components is equivalent to a volume constraint with a simple and unified form.The proposed constraint avoids difficulties in direct calculation of the distance between components with complex shapes and is effective for any number of arbitrary shaped components.(3)Level set-based topology optimization design with geometry related manufacturing constraints is studied.This thesis proposes to represent the geometry related manufacturing constraint,including the casting constraint and the overhang constraint,by the form of integral-type geometry constraint,which can be directly added into the topology optimization model as an additional constraint.Thus,the obtained optimization results not only have excellent performances but also satisfy the manufacturable conditions of the specified manufacturing process naturally.Moreover,the proposed manufacturing constraint form has unified and relatively simple expressions,which facilitates the sensitivity analysis and the numerical implementation in topology optimization.(4)A level set-based topology optimization method of shell-infill structures is proposed.The shell-infill structure has been widely used in many engineering areas,and the recent development of advanced manufacturing technologies further enlarges its design space.This thesis studies the topological design of the shell-infill structure with uniform shell thickness and uses only one level set function to describe the distribution of two solid materials.The level set model can represent the shell thickness accurately and obtain optimization results with clear and smooth material interfaces.