Manufacturing tolerant topology optimization

In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in （uniformly） too thin （eroded） or too thick （dilated） structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based ＂erode＂ and ＂dilate＂ operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.

Bilateral Filter for the Optimization of Composite Structures

In the present study,we propose to integrate the bilateral filter into the Shepard-interpolation-based method for the optimization of composite structures.The bilateral filter is used to avoid defects in the structure that may arise due to the gap/overlap of adjacent fiber tows or excessive curvature of fiber tows.According to the bilateral filter,sensitivities at design points in the filter area are smoothed by both domain filtering and range filtering.Then,the filtered sensitivities are used to update the design variables.Through several numerical examples,the effectiveness of the method was verified.

Topology optimization of reactive material structures for penetrative projectiles

Recently,reactive materials have been developed for penetrative projectiles to improve impact resistance and energy capacity.However,the design of a reactive material structure,involving shape and size,is challenging because of difficulties such as high non-linearity of impact resistance,manufacturing limitations of reactive materials and high expenses of penetration experiments.In this study,a design optimization methodology for the reactive material structure is developed based on the finite element analysis.A finite element model for penetration analysis is introduced to save the expenses of the experiments.Impact resistance is assessed through the analysis,and result is calibrated by comparing with experimental results.Based on the model,topology optimization is introduced to determine shape of the structure.The design variables and constraints of the optimization are proposed considering the manufacturing limitations,and the optimal shape that can be manufactured by cold spraying is determined.Based on the optimal shape,size optimization is introduced to determine the geometric dimensions of the structure.As a result,optimal design of the reactive material structure and steel case of the penetrative projectile,which maximizes the impact resistance,is determined.Using the design process proposed in this study,reactive material structures can be designed considering not only mechanical performances but also manufacturing limitations,with reasonable time and cost.

A review of topology optimization for additive manufacturing:Status and challenges

Topology optimization was developed as an advanced structural design methodology to generate innovative lightweight and high-performance configurations that are difficult to obtain with conventional ideas.Additive manufacturing is an advanced manufacturing technique building asdesigned structures via layer-by-layer joining material,providing an alternative pattern for complex components.The integration of topology optimization and additive manufacturing can make the most of their advantages and potentials,and has wide application prospects in modern manufacturing.This article reviews the main content and applications of the research on the integration of topology optimization and additive manufacturing in recent years,including multi-scale or hierarchical structural optimization design and topology optimization considering additive manufacturing constraints.Meanwhile,some challenges of structural design approaches for additive manufacturing are discussed,such as the performance characterization and scale effects of additively manufactured lattice structures,the anisotropy and fatigue performance of additively manufactured material,and additively manufactured functionally graded material issues,etc.It is shown that in the research of topology optimization for additive manufacturing,the integration of material,structure,process and performance is important to pursue high-performance,multi-functional and lightweight production.This article provides a reference for further related research and aerospace applications.

Buckling optimization of curvilinear fiber-reinforced composite structures using a parametric level set method

Owing to their excellent performance and large design space,curvilinear fiber-reinforced composite structures have gained considerable attention in engineering fields such as aerospace and automobile.In addition to the stiffness and strength of such structures,their stability also needs to be taken into account in the design.This study proposes a level-set-based optimization framework for maximizing the buckling load of curvilinear fiber-reinforced composite structures.In the proposed method,the contours of the level set function are used to represent fiber paths.For a composite laminate with a certain number of layers,one level set function is defined by radial basis functions and expansion coefficients for each layer.Furthermore,the fiber angle at an arbitrary point is the tangent orientation of the contour through this point.In the finite element of buckling,the stiffness and geometry matrices of an element are related to the fiber angle at the element centroid.This study considers the parallelism constraint for fiber paths.With the sensitivity calculation of the objective and constraint functions,the method of moving asymptotes is utilized to iteratively update all the expansion coefficients regarded as design variables.Two numerical examples under different boundary conditions are given to validate the proposed approach.Results show that the optimized curved fiber paths tend to be parallel and equidistant regardless of whether the composite laminates contain holes or not.Meanwhile,the buckling resistance of the final design is significantly improved.

Optimal structural design for a certain near-space composite propeller of airship using adaptive region division blending model

Near-space airship is a frontier and hotspot in current military research and development,and the near-space composite propeller is the key technology for its development.In order to obtain higher aerodynamic efficiency at an altitude of 22 km,a certain near-space composite propeller is designed as a long and slender aerodynamic shape with a 10 m diameter,which brings many challenges to the composite structure design.The initial design is obtained by the composite structure variable stiffness design method using based on fixed region division blending model.However,it weighs 23.142 kg,exceeding the required 20 kg.In order to meet the structural design requirements of the propeller,a variable stiffness design method using the adaptive region division blending model is proposed in this paper.Compared with the methods using the fixed region division blending model,this method optimizes region division,stacking thickness and stacking sequence in a single level,considering the coupling effect among them.Through a more refined region division,this method can provide a more optimal design for composite tapered structures.Additionally,to improve the efficiency of optimization subjected to manufacturing constraints,a hierarchical penalty function is proposed to quickly filter out the solutions that do not meet manufacturing constraints.The above methods combined with a Genetic Algorithm(GA)using specific encoding are adopted to optimize the near-space composite propeller.The optimal design of the structure weighs 18.831 kg,with all manufacturing constraints and all structural response constraints being satisfied.Compared with the initial design,the optimal design has a more refined region division,and achieves a weight reduction of 18.6%.This demonstrates that a refined region division can significantly improve the mechanical performance of the composite tapered structure.

An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures

Additive manufacturing （AM） technologies, such as selective laser sintering （SLS） and fused deposition modeling （FDM）, have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simply- connected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method （VTM）. In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads

The purpose of this paper is to present an extended topology optimization method for the stiffeners layout design of aircraft assembled structures. Multi-fastener joint loads and manufacturing constraints are considered simultaneously. On one hand, the joint loads are calculated and constrained within a limited value to avoid the failure of fasteners. On the other hand, the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface. It is proven that the objective function is strictly continuous and differentiable with respect to the piecewise interpolation. The effects of the extended method with two different constraints are highlighted by typical numerical examples. Compared with the standard topology optimization, the final designs have clearly shown the layout of stiffeners and the joint loads have been perfectly constrained to a satisfying level.

Filters for manufacturability in design optimization of variable stiffness composites

In the design optimization of variable stiffness composites,manufacturing constraints imposed by the automated fiber placement technology must be considered.In the present paper,two filters are proposed to address this issue,and they are incorporated into the Shepard interpolation-based design optimization framework developed in our previous studies.The fiber angle arrangement of a composite is represented by a continuous function that interpolates fiber angles at scattered design points.Two filters are appointed for each design point to deal with two typical manufacturing constraints,i.e.,fiber curvature and gap/overlap.At each design point,the sensitivity is first filtered in a rectangular region around this point,and by this means the fiber curvature is controlled;then in another rectangular region around this design point,the filtered sensitivities are averaged,and the result is used to update the corresponding design variable.Several numerical examples are investigated,and the results show that the proposed method is effective.