Feature-based design and material blending for free-form heterogeneous object modeling

In this paper, a new feature-based method is proposed to represent and design heterogeneous objects. Material governing features are defined to control material composition inside the objects. Interrelations between the material governing features and material attributes are established in the design process and retained in the object model. Free-form B-spline functions are used to represent complex shapes of geometry and material features. A new material feature blending method is used to determine continuous material variation. To obtain the best material features, an optimization problem is constructed based on the object's functional requirements. Variant models are easily generated by changing the geometric and material features using the constraints between them. Implementation and examples are also presented in this paper.     

Multi-directional blending for heterogeneous objects

This paper presents a novel multi-directional blending method for heterogeneous object design. Contrary to earlier studies, this paper introduces material blending through multiple features with different heterogeneous material composition. Feature-based method is used to represent and design heterogeneous objects with multi-directional material composition. The Voronoi diagram of multiple curves is constructed to generate bisector of the geometric domain. Then, metamorphosis from the bounding curve to multiple internal curves is performed using dynamic programming based optimization approach in two steps. First, optimum curve matching between internal curves and enclosing Voronoi cells is obtained. Then, an optimum ruling line alignment and insertion technique between the Voronoi diagram and the bounding curve is developed. Metamorphosis through complex concavities is also achieved. Finally, multi-directional material composition is mapped based on a set of relations.     

Design of heterogeneous turbine blade

Constantly rising operating pressure and temperature in turbine drivers push the material capabilities of turbine blades to the limit. The recent development of heterogeneous objects by layered manufacturing offers new potentials for the turbine blades. In heterogeneous turbine blades, multiple materials can be synthesized to provide better properties than any single material. A critical task of such synthesis in turbine blade design is an effective design method that allows a designer to design geometry and material composition simultaneously.This paper presents a new approach for turbine blade design, which ties B-spline representation of a turbine blade to a physics (diffusion) process. In this approach, designers can control both geometry and material composition. Meanwhile, material properties are directly conceivable to the designers during the design process. The designer's role is enhanced from merely interpreting the optimization result to explicitly controlling both material composition and geometry according to the acquired experience (material property constraints).The mathematical formulation of the approach includes three steps: using B-spline to represent the turbine blade, using diffusion equation to generate material composition variation, using finite element method to solve the constrained diffusion equation. The implementation and examples are presented to validate the effectiveness of this approach for heterogeneous turbine blade design.     

A B-spline-based approach to heterogeneous objects design and analysis

The recent advancement of solid freeform fabrication, design techniques and fundamental understanding of material properties in functionally graded materials has made it possible to design and fabricate multifunctional heterogeneous objects. In this paper, we present an integrated design and analysis approach for heterogeneous object realization, which employs a unified design and analysis model based on B-spline representation and allows for direct interaction between the design and analysis model without laborious meshing operation. In the design module, a new approach for intuitively modelling of multi-material objects, termed heterogeneous lofting, is presented. In the analysis module, a novel graded B-spline finite element solution procedure is described, which gives orders of magnitude of better convergence rate in comparison with current methods, as demonstrated in several case studies. Further advantages of this approach include simplified mesh construction, exact geometry/material composition representation and easy extraction of an isomaterial surface for manufacturing process planning.     

A level-set based variational method for design and optimization of heterogeneous objects

A heterogeneous object is referred to as a solid object made of different constituent materials. The object is of a finite collection of regions of a set of prescribed material classes of continuously varying material properties. These properties have a discontinuous change across the interface of the material regions. In this paper, we propose a level-set based variational approach for the design of this class of heterogeneous objects. Central to the approach is a variational framework for a well-posed formulation of the design problem. In particular, we adapt the Mumford-Shah model which specifies that any point of the object belongs to either of two types: inside a material region of a well-defined gradient or on the boundary edges and surfaces of discontinuities. Furthermore, the set of discontinuities is represented implicitly, using a multi-phase level set model. This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations. Promising features of the proposed method include strong regularity in the problem formulation and inherent capabilities of geometric and material modeling, yielding a common framework for optimization of the heterogeneous objects that incorporates dimension, shape, topology, and material properties. The proposed method is illustrated with several 2D examples of optimal design of multi-material structures and materials.     

Bayesian computer-aided experimental design of heterogeneous scaffolds for tissue engineering

This paper presents a Bayesian methodology for computer-aided experimental design of heterogeneous scaffolds for tissue engineering applications. These heterogeneous scaffolds have spatial distributions of growth factors designed to induce and direct the growth of new tissue as the scaffolds degrade. While early scaffold designs have been essentially homogenous, new solid freeform fabrication (SFF) processes enable the fabrication of more complex, biologically inspired heterogeneous designs with controlled spatial distributions of growth factors and scaffold microstructures. SFF processes dramatically expand the number of design possibilities and significantly increase the experimental burden placed on tissue engineers in terms of time and cost. Therefore, we use a multi-stage Bayesian surrogate modeling methodology (MBSM) to build surrogate models that describe the relationship between the design parameters and the therapeutic response. This methodology is well suited for the early stages of the design process because we do not have accurate models of tissue growth, yet the success of our design depends on understanding the effect of the spatial distribution of growth factors on tissue growth. The MBSM process can guide experimental design more efficiently than traditional factorial methods. Using a simulated computer model of bone tissue regeneration, we demonstrate the advantages of Bayesian versus factorial methods for designing heterogeneous fibrin scaffolds with spatial distributions of growth factors enabled by a new SFF process.     

‘Source-based’ heterogeneous solid modeling

This paper proposes a new scheme for modeling heterogeneous objects. Concepts of ‘grading source’ and material parameters are introduced so that the material composition and material varying information can be represented. In order to model the grading sources and ‘source-included’ objects, extended operations (e.g. insertion, merge, immersion) in addition to the CSG type Boolean operations are defined. The sliced file format of a heterogeneous object for rapid prototyping fabrication is also briefly discussed.     

Reasoning Boolean operation based modeling for heterogeneous objects

A reasoning Boolean operation based CAD modeling approach applied to construct heterogeneous material objects is presented. This reasoning Boolean operation consists of a merging operation and an extracting operation, and it is executed according to the material-dominant information defined in the designed heterogeneous object database. In addition to the material-dominant Boolean union, subtraction, and intersection, a new Boolean complex_union operation is defined and introduced to the set of the reasoning Boolean operation. The Boolean complex_union ‘assembles’ the results of the material-dominant Boolean intersection and subtraction to form a new modeling assembly for the heterogeneous object. Due to the CAD-based nature, the thus formed heterogeneous model can be readily implemented with advanced CAD/CAE/CAM software for integrated design, analysis, and simulation. An example of such an application, its hierarchy of the model database, and the major steps of the model construction are described.     

Modeling complex heterogeneous objects with non-manifold heterogeneous cells

This paper presents a new approach to model complex heterogeneous objects with simultaneous geometry intricacies as well as complex material distributions. Different from most of the existing approaches, which utilize manifold B-Rep and the assembly representations, the proposed scheme takes advantage of the non-manifoldcellular representations to model the geometries of the heterogeneous objects. With the aid of the cell adjacency information and attribute based reasoning, complex, smooth and versatile material distributions can be defined upon the intricate geometries. Compared with other similar approaches, the proposed scheme (1) generates heterogeneous object models with higher data consistencies and lower redundancies; (2) naturally avoids unnecessary/repetitive computations and thus improves computation efficiencies; (3) represents versatile material variations/distributions using different heterogeneous feature tree (HFT) structures. The detailed representation, associated algorithms and a prototype software package are presented. Example heterogeneous objects modeled with the proposed approach are provided.     

A model of domain-polymorph component for heterogeneous system design

Heterogeneous systems mix different technical domains such as signal processing, analog and digital electronics, software, telecommunication protocols, etc. Heterogeneous systems are composed of subsystems that are designed using different models of computation (MoC). These MoCs are the laws that govern the interactions of the components of a subsystem. The design of heterogeneous systems includes the design of each part of the system according to its specific MoC, and the connection of the parts in order to build the model representing the system. Indeed, this model allows the MoCs that govern different parts of system to coexist and interact.To be able to use a component which is specified according to a given MoC, under other, different MoCs, we can use either a hierarchical or a non-hierarchical approach, or we can build domain-specific components (DSC). However, these solutions present several disadvantages. This paper presents a new model of component, called domain-polymorph component (DPC). Such a component is atomic and is able to execute its core behavior, specified under a given MoC, under different host MoCs. This approach is not a competitor to the approaches above but is complementary.     

A hierarchical representation for heterogeneous object modeling

A hierarchical representation for heterogeneous object modeling is presented in this paper. To model a heterogeneous object, Boundary representation is used for geometry representation, and a novel Heterogeneous Feature Tree (HFT) structure is proposed to represent the material distributions. HFT structure hierarchically organizes the material variation dependency relationships and is intuitive in modeling different types of material gradations. Based on the HFT structure, a recursive material evaluation algorithm is proposed to dynamically evaluate the material compositions at a specific location. Such a hierarchical representation guarantees complex material gradations and the user's design intent can be intuitively represented. Example heterogeneous objects modeled with this scheme are provided and potential applications are discussed.     

Constructive sculpting of heterogeneous volumetric objects using trivariate B-splines

This paper deals with modeling heterogeneous volumetric objects as point sets with attributes using trivariate B-splines. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of variable attributes assigned at each point. An attribute is a mathematical model of an object property of an arbitrary nature (material, photometric, physical, statistical, etc.). In our approach, the function representation (FRep) is used as the basic model for both object geometry and attributes represented independently using real-valued scalar functions of point coordinates. While FRep directly defines object geometry, for an attribute it specifies a space partition used to define the attribute function. We propose a volume sculpting scheme with multiresolution capability based on trivariate B-spline functions to define both object geometry and its attributes. A new trivariate B-spline primitive is proposed that can be used as a leaf in an FRep constructive tree. An interactive volume modeler based on trivariate B-splines and other simple primitives is described, with a real-time repolygonization of the surface during modeling. We illustrate that the space partition obtained in the modeling process can be applied to define attributes for the objects with an arbitrary geometry model such as BRep or homogeneous volume models.     

Feature-based crystal construction in computer-aided nano-design

Providing nanoengineers and scientists efficient and easy-to-use tools to create geometry conformations that have minimum energies is highly desirable in materials design. Recently we developed a periodic surface model to assist the construction of nanostructures parametrically for computer-aided nano-design. In this paper, we present a feature-based approach for crystal construction. The proposed approach creates models of basic features with the aid of periodic surfaces followed by operations between basic features. The goal is to introduce a rapid construction method for complex crystal structures.     

Modeling the material grading and structures of heterogeneous objects for layered manufacturing

The emphasis of this work is to discuss a scheme for modeling the material grading and structures of heterogeneous objects. To model the material grading of a heterogeneous object, a termed ‘grading source’ is defined. The grading sources are reference features, which specify the type and position of grading, and a material grading function for controlling the material variation within the geometric boundary of the objects. Within the proposed modeling scheme, a concept on representing objects, which are both heterogeneous in material and structure (e.g. composite laminates), will also be elaborated. For downstream layered manufacturing purposes, a contour sub-division algorithm on each layer arising from slicing a heterogeneous object is proposed. Within each slice, the material grading is decomposed into sub-contours according to the different grading variation. A parameter called ‘grading step-width’ is defined to control the number of sub-contours and resolution of the grading. With such discretization, it is, therefore, possible to build a heterogeneous object on layered manufacturing machines of different fabricating precision specification.     

Computer-aided design of porous artifacts

Heterogeneous structures represent an important new frontier for 21st century engineering. Human tissues, composites, ‘smart’ and multi-material objects are all physically manifest in the world as three-dimensional (3D) objects with varying surface, internal and volumetric properties and geometries. For instance, a tissue engineered structure, such as bone scaffold for guided tissue regeneration, can be described as a heterogeneous structure consisting of 3D extra-cellular matrices (made from biodegradable material) and seeded donor cells and/or growth factors.The design and fabrication of such heterogeneous structures requires new techniques for solid models to represent 3D heterogeneous objects with complex material properties. This paper presents a representation of model density and porosity based on stochastic geometry. While density has been previously studied in the solid modeling literature, porosity is a relatively new problem. Modeling porosity of bio-materials is critical for developing replacement bone tissues. The paper uses this representation to develop an approach to modeling of porous, heterogeneous materials and provides experimental data to validate the approach. The authors believe that their approach introduces ideas from the stochastic geometry literature to a new set of engineering problems. It is hoped that this paper stimulates researchers to find new opportunities that extend these ideas to be more broadly applicable for other computational geometry, graphics and computer-aided design problems.     

Flow-based fabrication: An integrated computational workflow for design and digital additive manufacturing of multifunctional heterogeneously structured objects

Structural hierarchy and material organization in design are traditionally achieved by combining discrete homogeneous parts into functional assemblies where the shape or surface is the determining factor in achieving function. In contrast, biological structures express higher levels of functionality on a finer scale through volumetric cellular constructs that are heterogeneous and complex. Despite recent advancements in additive manufacturing of functionally graded materials, the limitations associated with computational design and digital fabrication of heterogeneous materials and structures frame and limit further progress. Conventional computer-aided design tools typically contain geometric and topologic data of virtual constructs, but lack robust means to integrate material composition properties within virtual models. We present a seamless computational workflow for the design and direct digital fabrication of multi-material and multi-scale structured objects. The workflow encodes for and integrates domain-specific meta-data relating to local, regional and global feature resolution of heterogeneous material organizations. We focus on water-based materials and demonstrate our approach by additively manufacturing diverse constructs associating shape-informing variable flow rates and material properties to mesh-free geometric primitives. The proposed workflow enables virtual-to-physical control of constructs where structural, mechanical and optical gradients are achieved through a seamless design-to-fabrication tool with localized control. An enabling technology combining a robotic arm and a multi-syringe multi nozzle deposition system is presented. Proposed methodology is implemented and full-scale demonstrations are included.     

基于梯度有限元的异质材料实体优化设计

针对具有空间分布梯度的异质材料实体的优化设计,建立了两相材料梯度 有限元的概念,利用拉格朗日单元的形函数对体积分数进行插值,在节点邻域内引入设计变 量自适应下界进行梯度控制,利用移动渐近线算法求解优化设计数学模型以使结构满足特定 的功能和目标,以金属夹钳为算例验证了该方法的可行性和鲁棒性。     

Hybrid feature modeling for sport shoe sole design

Feature-based method has been successfully applied in several fields of manufacturing. However, most of the applications use the solid modeling method that cannot meet the requirements of a product design that needs a free-form surface or a complicated surface. A sports shoe is one of the products that need a complex surface to design its sole. In addition, sport shoes are rapidly changed with their styles based on customer and market demands. Thus, the design must be flexible enough to meet those demands particularly when a short lead time design is concerned. Previously, shoe designs have been created by using a commercial standard CAD/CAM system. Surface modeling is normally selected. However, it is time consuming and not competitive. This paper presents a new method of a sport shoe sole design using the hybrid features of surface and solid modeling. Primitive features are prepared in the library, which is written in C of Cimatron API. The user can select and modify before joining them together to create a new shoe sole model. This system has the ability to extend sizes or grading in 3D automatically. The system was tested satisfactorily. Design time is saved 35.388% by average with a single piece design, whereas 88.42% can be saved when 12 sizes grading is performed.     

Tolerances in computer-aided geometric design

In the design of discrete part shapes, the specification of tolerance constraints can have major consequences for product quality and cost. Traditional methods for tolerance analysis and synthesis are timeconsuming, and have limited applicability. This paper presents the results of research into the use of solid modeling technology for the automated solution of tolerancing problems. A linear programming method is presented for the solution of tolerance analysis problems on a worst-case basis. A Monte Carlo method is presented for both worst-case and statistical tolerance analysis. Both methods automatically derive all necessary geometric relationships from a solid model of the assembly. Example problems are solved using the experimental GEOTOL geometric design system.     

Trust-based consensus reaching process for product design decision-making with heterogeneous information

Pursuing a consensual result is vital for selecting optimum product design schemes as it helps eliminate preference conflicts in product design decision-making (PDDM). As a dynamic and iterative activity, the consensus reaching process (CRP) of PDDM always involves heterogeneous, vague, and inconsistent information, which makes it challenging to adjust decision-makers’ judgement to achieve an acceptable consensus level. To address this issue, triangular fuzzy numbers were introduced to depict decision-makers’ heterogeneous judgement. The indicator weights were determined by integrating the fixed weight obtained from the interval analytic hierarchy process (IAHP) and the variable weight acquired using the maximizing deviation method. Decision-makers’ weights were identified through a combination of the uncertainty degree measured by fuzzy entropy and the consistency degree solved by a distance minimizing model of the PDDM matrix. A dynamic CRP for PDDM was proposed by adjusting decision-makers’ judgement based on their trust relationships and updating the PDDM matrix in an evolutionary manner. A case study is conducted to verify the feasibility and effectiveness of the proposed method.