Topology Optimization Methods For Additive Manufacturing Structures With Connectivity Constraint And Structural Feature Constraints

Topology optimization has been used to improve designs through variation of their geometrical and material properties with regard to a set of prescribed objectives and constraints.It can provide some new,sometimes unanticipated,design ideas for designers without requiring a pre-established design.However,the topology results are usually too complex to be manufactured by traditional manufacturing process,engineers need to modify these designs to accommodate the manufacturing capacity.Additive manufacturing(AM)is a free-form manufacturing technique in which a component is built in a layer by layer manner.It has a demonstrated capability to produce components that are far more complex than those manufactured using traditional manufacturing techniques.The free-form nature of topology optimization,and its ability to discover novel,high performance solutions,makes it a natural design tool for integration with AM processes.Yet while AM significantly opens up the design space for engineers,manufacturing constraints and limitations remain and ultimately must be tightly integrated within the topology optimization methodology to fully leverage the capabilities and freedom provided by AM processes.Connectivity constraint and structural feature constraints are two kinds of manufacturing constraints in additive manufacturing.Of which,the connectivity constraint requires no enclosed voids in structures for removing the powder or support structure from the part once it has been built and the structural geometry feature has a greatly influence on the cost,time and difficulty in manufacturing process.In this paper,an equivalent formulation of the connectivity constraint,named as virtual temperature method,is proposed.Based upon this method,two topology optimization methods are established,in which the connectivity constraint and casting constraints are considered,respectively.For the design of stiffened plate with structural feature constraints,two methods for simultaneously optimizing the layout and size of the stiffeners are proposed.The designs of industrial structures show the validity of these two methods.The main research contents and achievements are listed as follows:(1)An equivalent formulation of structural connectivity based on virtual temperature method(VTM).The key idea of this method is to establish a structural topology related virtual temperature model in which the voids are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity.Based upon this method,the layout of the material with high heat conductivity can model the structural connectivity,and then the connectivity constraint is equivalent to a maximum temperature constraint.Compared to the method for describing the structural connectivity based on graph theory,this method can be easily computed and has the explicit formulation.The effectiveness of this method is illustrated by several examples.(2)Structural topology optimization considering connectivity constraint based on virtual temperature method.In this paper,a new topology optimization model with manufacturing process related connectivity constraint,which is formulated by virtual temperature method,is proposed.To make the constraint function applicable to gradient-based optimization,P-norm function is used as the approximate function of the maximum function and the sensitivity of the constraint function with the variables is derived.The influence of the parameters in the optimization model is discussed and an empirical criterion for determine the parameter values is given.Numerical examples show that by controlling the boundary conditions of the temperature model,topology optimization designs with different topological complexity can be obtained.(3)Structural topology optimization considering casting constraints based on virtual temperature method.In this paper,the virtual temperature method is modified to handle the casting constraints to guarantee the cast-ability of topologically designed structures.In the modified method,a new virtual thermal diffusion problem is defined and the casting constraints are set to a maximum temperature constraint.This method does not require an optimization process to start from a feasible initialization and can be applied to almost any topology optimization problems.Several numerical examples illustrate the validity and the effectiveness of the proposed method.(4)A concurrent optimization method for designing the layout and height of stiffeners.In this paper,a new Heaviside-function based topology parameterization for simultaneously optimizing the layout and height of the vertically-walled stiffeners is proposed.By using the new explicit parameterization,we can obtain a clear stiffener layout with optimized height.In order to be applicable to a non-uniform mesh,a base surface is introduced and the minimum length of a stiffener can be controlled.This method is used in the design of large-aperture mirror and artillery cradle.The new designs obtained by the proposed method show significant improvements in the mechanical performance compared to traditional designs.(5)A concurrent optimization method for designing the layout and section of stiffeners.In this paper,a new method for simultaneously optimizing the layout and section of the stiffeners is proposed.First,the section stiffness matrix of arbitrary topology is derived based on the Giavotto beam theory.Then,a concurrent optimization is conducted by optimizing the layout and the topology of the beam section.Sensitivities of the objective function with the two of variables are derived.The numerical example shows that this new method can promote structural performance greatly.