A systematic approach for Integrated Computer-Aided Design and Finite Element Analysis of Functionally-Graded-Material objects

doi:10.1016/j.matdes.2006.10.024

Materials & Design

Volume 28, Issue 10, 2007, Pages 2549-2565

https://doi.org/10.1016/j.matdes.2006.10.024 Get rights and content

Abstract

Computer-Aided Design (CAD) and Finite Element Analysis (FEA) of Functionally-Graded-Material (FGM) objects are generally regarded as separate domains of interest in CAD and Computer-Aided Engineering (CAE) community. Such a separation of CAD modeling and FEA of FGM objects makes it cumbersome and tedious for both designers and engineers to exchange the necessary information in the entire design process. Without appropriate CAD models, complex material distributions can hardly be represented and the FGM objects under examination remain simple in material variations (e.g. unidirectional gradations). With CAD modeling tools only, the end users are still uncertain whether or not the designed objects can really meet the functional requirements in terms of structural, thermal or other prescribed properties. This paper proposes a systematic approach to integrate these domain-dependent design tools in FGM object design. Integrated solutions to CAD modeling and property analysis of FGM objects are utilized to design complicated (bi-directional or even tri-variate) FGM objects. Complex FGM distributions are encoded into the proposed Heterogeneous Feature Tree (HFT) structure; and the material compositions of a given point of interest are interrogated from the CAD models at runtime. Integrated FEA of FGM objects are then carried out by establishing a link between the proposed CAD modeler (CAD4D) and a commercial FEA package (COMSOL Multiphysics). Four different (three unidirectional and one bidirectional) FGM objects are modeled with traditional analytic function based approaches and the proposed methods. Under the same thermal and mechanical conditions, the properties of each model are compared in terms of temperature fields, residual thermal stresses and the strain energy densities. Results show that the proposed approach can facilitate the design of complex FGM objects in a systematic way.

Introduction

Objects with Functionally Graded Material (FGM) distributions have shown superior advantages in applications where multi-fold functional requirements are demanded [1], [2], [3]. For instance, in aerospace applications, modern aerospace shuttles are subjected to super high temperatures and enormous mechanical loads; sufficient heat-resistance and stiffness properties are required. In aircraft engine design, “reduced weight and increased strength and stiffness are the major requirements for highly stressed fan blades” [4]. In biomedical applications, both the mechanical properties and the biocompatibilities of the implanted components play critical roles in clinical therapies [5], [6]. In industrial applications, the machinability of metals and the excellent heat resistance of ceramics are usually required in the same component. In all these applications, homogeneous objects can hardly meet the multi-fold functional requirements, whereas using FGM objects, different properties and advantages of various materials can be fully exploited within the single solid. Traditional problems due to material incompatibility (stress concentration, non-uniform thermal expansion, etc.) can be naturally alleviated with gradual material variations. Due to these excellent performances and unique features, FGM objects have gained great popularities in recent years. The past few decades have witnessed significant advances in FGM object design. Research efforts range from Computer-Aided Design (CAD modelling), Computer-Aided Engineering (design evaluation/validation/simulation) to optimizations and Computer-Aided Manufacturing (fabrication).

In the past, CAD modelling and FEA of FGM objects are generally regarded as separate domains of interest in CAD and CAE community. Such a separation makes it cumbersome for both designers and engineers to exchange the necessary information in the entire design process. Therefore, applications in both domains are impeded and the designable complex FGM objects are limited. This paper proposes a systematic approach to integrate these “domain-dependent” [7] design tools in FGM object design. The modelled geometry and material distribution are represented with CAD models and relevant data can be further transferred to FEA modules for design validations. Based on the proposed approach, objects with complex (bi-directional or tri-variate) FGM distributions can be intuitively modeled and properly analyzed.

Section snippets

Motivations and related work

Design of functionally graded objects with 1D dependent or unidirectional material gradations have been extensively studied in recent years. Elishakoff et al. [8] conducted a finite element analysis of an all-round clamped FGM plate based on the Ritz energy method; 3D plates with unidirectional power-law based FGM distributions are examined. Huang et al. [3] analyzed FGM objects whose materials follow a distribution characterized by the generic Bezier curves, an optimal FGM distribution is

CAD modeling of FGM objects

CAD modeling of FGM objects primarily deals with representing the geometry, topology and material distributions of FGM objects with appropriate mathematical/computer models. As there have been mature data representations for modeling the geometries and topologies, in this section, only the material distribution modeling problem will be considered. Due to the simplicities of unidirectional FGM object modeling, particular emphasis is laid on modeling non-unidirectional material gradations. For

Intergraded FEA of FGM objects

This section further presents the methodologies of using finite element method in the intergraded analysis of complex FGM objects. Thermo-mechanical analysis is conducted on the four FGM objects modeled earlier. Under the same thermal and mechanical conditions, the properties of each model are compared in terms of temperature fields, residual thermal stresses and the strain energy densities.

Results and discussion

By applying the proposed methodologies of integrating CAD modeling with finite element analysis, complex FGM objects can be intuitively designed and their properties can be properly analyzed via finite element analysis. This section presents the FEA results based on the proposed approach.

Conclusions and future work

A systematic approach for integrated CAD modeling and FEA analysis of FGM objects is proposed in this paper. The designed geometries and material compositions are represented with CAD models and further transferred to FEA modules for design validations. By integrating such domain-dependent design tools, objects with complex FGM distributions, which are hardly modeled with traditional approaches, can be intuitively modeled and analyzed; the designer’s intents can be properly captured.

Four

Acknowledgements

The authors thank the Department of Mechanical Engineering, The University of Hong Kong and the Research Grant Council for supporting this project. Grateful thanks go to the Croucher Foundation for providing the second author with a senior fellowship.

References (42)

X.C. Zhang
Modeling of the residual stresses in plasma-spraying functionally graded ZrO₂/NiCoCrAlY coatings using finite element method
Mater Design
(2006)
J. Huang
Bi-objective optimization design of functionally gradient materials
Mater Design
(2002)
C. Leyens
Materials and design concepts for high performance compressor components
Aerosp Sci Technol
(2003)
Y. Yamasaki
Action of FGMgCO₃Ap–collagen composite in promoting bone formation
Biomaterials
(2003)
J. Werner
Mechanical properties and in vitro cell compatibility of hydroxyapatite ceramics with graded pore structure
Biomaterials
(2002)
J.R. Cho et al.
Material composition optimization for heat-resisting FGMs by artificial neural network
Composites A
(2004)
J. Yang
Thermo-mechanical post-buckling of FGM cylindrical panels with temperature-dependent properties
Int J Solid Struct
(2006)
G.N. Praveen et al.
Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates
Int J Solid Struct
(1998)
J.R. Cho et al.
Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM
Comput Method Appl Mech Eng
(2002)
M. Nemat-Alla
Reduction of thermal stresses by developing two-dimensional functionally graded materials
Int J Solid Struct
(2003)

P.R. Cavalcanti et al.

Non-manifold modelling: an approach based on spatial subdivision

Comput Aided Design

(1997)

X.Y. Kou et al.

A hierarchical representation for heterogeneous object modeling

Comput Aided Design

(2005)

X.Y. Kou et al.

Modeling complex heterogeneous objects with non-manifold heterogeneous cells

Comput Aided Design

(2006)

Y.K. Siu et al.

Source-based heterogeneous solid modeling

Comput Aided Design

(2002)

X. Qian et al.

Design of heterogeneous turbine blade

Comput Aided Design

(2003)

K. Samanta et al.

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

Comput Aided Design

(2005)

D. Natekar et al.

Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis

Comput Aided Design

(2004)

W. Sun et al.

Reasoning Boolean operation based modeling for heterogeneous objects

Comput Aided Design

(2002)

H. Liu

Methods for feature-based design of heterogeneous solids

Comput Aided Design

(2004)

J. Cheng et al.

Approach of heterogeneous bio-modeling based on material features

Comput Aided Design

(2005)

B. Liang et al.

Simulation of wind-induced lateral-torsional motion of tall buildings

Comput Struct

(1997)

Cited by (37)

Level set-based heterogeneous object modeling and optimization
2019, CAD Computer Aided Design
This paper presents a level set-based heterogeneous object (HO) modeling and optimization method. This HO model employs multiple level set functions to build the geometry, utilizes zero-value level set contours as material source profiles, and realizes functionally graded material blending with a signed distance-based blending function. More importantly, this HO model supports the concurrent structure and material optimization because of the unified level set framework for both structure and material composition representation. Beyond macro HO, heterogeneous meta-material optimization will be addressed as well. This new model remedies the shortage of traditional HO models that focus more on modeling but less on optimization. About the numerical optimization, design update with the sensitivity result will be carefully discussed, since there includes infeasible terms (in domain integration format). Two strategies will be explored to address this issue: ignoring the infeasible part of the sensitivity, or transforming the sensitivity result into a purely boundary integration-based expression. A few numerical examples will be studied to prove the effectiveness of the proposed HO modeling and optimization method.
A systematic approach based on voxel modelling and APDL analysis for Functional-Graded-Material objects
2018, Procedia CIRP
With the development of additive manufacturing (AM), the Functional-Graded-Material (FGM) objects have gained great popularities and research interest in the past few decades. However, Computer-Aided Design (CAD) and Finite Element Analysis (FEA) of FGM objects are generally regarded as two separate domains. Such a separation causes that it is cumbersome for engineers to exchange the necessary information in the design process. In this paper, a systematic approach based on voxel modelling and ANSYS Parametric Design Language (APDL) analysis for FGM objects is presented. Integrated solution to modelling and property analysis of FGM objects are gained to manufacture FGM objects. Traditional CAD file is imported to the proposed software (FGMD), then designer can choose heterogeneous features in FGMD. Finally, FGMD can output an APDL file which can be used for property analysis. Several examples show the validity of the systematic approach.
Adaptive meshing for finite element analysis of heterogeneous materials
2015, CAD Computer Aided Design
Citation Excerpt :
As seen in Fig. 11(c), both boundary feature and interface feature are composed of curves and straight lines. Fig. 12 shows a case study derived from [37], in which the material heterogeneity is also represented by HFT structure. Fig. 12(a) shows the material composition of one of the primary materials (Ceramic), and Fig. 12(b) shows the topology of the tree data structure used to represent this heterogeneity.
Adaptive meshing of 2D planar regions, curved surfaces as well as 3D volumes has been extensively studied in Finite Element Analysis (FEA) in the past few decades. Despite the maturity of these adaptive meshing approaches, most of the existing schemes assume the domain or sub-domain of interest is homogeneous. In the context of FEA of heterogeneous objects, traditional adaptive mesh generation strategies become inadequate as they fail to take into account the material heterogeneities. This paper is motivated to tackle such problems and propose an adaptive mesh generation scheme for FEA of versatile heterogeneous materials. The proposed approach takes full advantages of the material heterogeneity information, and the mesh density is formulated with a specific function of the material variations. Dual triangulation of centroidal Voronoi tessellation is then constructed and necessary mesh subdivision is applied with respect to a predefined material threshold. Experiments show that the proposed approach distributes the material composition variation over mesh elements as equally as possible and thus minimizes the number of elements in terms of the given material threshold. FEA results show that the proposed method can significantly decrease the mesh complexities as well as computational resources in FEA of heterogeneous objects and compared with existing approaches, significant mesh reduction can be achieved without sacrifice in FEA qualities.
A novel CACD/CAD/CAE integrated design framework for fiber-reinforced plastic parts
2015, Advances in Engineering Software
Citation Excerpt :
The second issue remains at the poor support of CAD/CAE/CAM integration by the current HO models. There is little work addressing the CAD/CAE integration [24], and the efforts on CAD/CAM integration mainly focus on additive manufacturing. In this work, the concentration will be the modeling of fiber-reinforced plastic parts, which definitely belongs to the objects of highly-irregular material composition distribution, and is manufactured with the traditional injection molding instead of additive manufacturing.
This work presents a novel CACD/CAD/CAE integrated framework for design, modeling, and optimization of fiber-reinforced plastic parts, which can greatly enhance the current design practice by realizing partial automation and multi-stage optimization. To support this framework, a new heterogeneous feature model (HFM) has been developed to model the fiber-reinforced objects and to be transferred between engineering modules. To be specific, the CACD (computer-aided conceptual design) module employs the level-set structure and material optimization to produce the initial design with thickness control, and also the initial HFM; the CAD (computer-aided design) module allows manual editing on the HFM to reflect various design intents; then, the injection molding CAE (computer-aided engineering) simulates the manufacturing process, and the response surface method (RSM) is applied to optimize the process parameters of gate location, injection flow rate, mold temperature and melt temperature, to approach the manufactured fiber orientation distribution close to the optimized result produced by the CACD module; besides, the structural analysis CAE module generates the mechanical performance result to support the CACD module, as well as to validate the final design. By applying this framework, the final structural design including the fiber orientation distribution, will perform better in mechanical properties, and consume less matrix and fiber materials; besides, the design maturity can be approached in shorter time. To prove the effectiveness, a plastic gripper design will be comprehensively studied.
Classification and elimination of overlapped entities in DXF files
2014, Ain Shams Engineering Journal
Citation Excerpt :
In these programs, the DXF file carries data between computer aided drafting (CAD) file and G code generator. Kou and Tan [12] introduced the DXF file as information base to connect the part geometric model and the finite element analysis package. The citation of the previous researches shows that the manipulated DXF file should be based on ideal drawing.
Computer aided engineering; design, drafting and manufacturing, software packages are widely used in modern industry. The product development cycle, from idea to manufacturing, goes through different stages using different computer aided programs. These programs exchange a lot of information in different formats. One of these formats is 2D drawing in DXF standard format. The exchanged files suffer from overlapped entities and different interpretation for entity formats. This paper emphasizes on the sources of this problem and its negative effects. Moreover, it introduces software for eliminating the overlapping entities and re-classification of them. In addition, the paper explains the algorithms, which are encapsulated in the software.
An improved isogeometrical analysis approach to functionally graded plane elasticity problems
2013, Applied Mathematical Modelling
Citation Excerpt :
The material properties are assumed to be graded only through the plate thickness and static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. Refs. [25,36–39] can be consulted for a thorough review of the literature on the subject. The isogeometric analysis method, which can be considered as a logical extension of the finite element method, is more geometrically based and takes inspiration from Computer Aided Design (CAD).
The isogeometric analysis method is extended for addressing the plane elasticity problems with functionally graded materials. The proposed method which employs an improved form of the isogeometric analysis approach allows gradation of material properties through the patches and is given the name Generalized Iso-Geometrical Analysis (GIGA). The gradations of materials, which are considered as imaginary surfaces over the computational domain, are defined in a fully isoparametric formulation by using the same NURBS basis functions employed for the construction of the geometry and the approximation of the solution. The basic concept of the developed approach is concisely explained and its relation to the standard isogeometric analysis method is pointed out. It is shown that the difficulties encountered in the finite element analysis of the functionally graded materials are alleviated to a large degree by employing the mentioned method. Different numerical examples are presented and compared with available analytical solutions as well as the conventional and graded finite element methods to demonstrate the performance and accuracy of the proposed approach. The presented procedure can also be employed for solving other partial differential equations with non-constant coefficients.

View all citing articles on Scopus

View full text

A systematic approach for Integrated Computer-Aided Design and Finite Element Analysis of Functionally-Graded-Material objects

Abstract

Introduction

Section snippets

Motivations and related work

CAD modeling of FGM objects

Intergraded FEA of FGM objects

Results and discussion

Conclusions and future work

Acknowledgements

Mater Design

Mater Design

Aerosp Sci Technol

Biomaterials

Biomaterials

Composites A

Int J Solid Struct

Int J Solid Struct

Comput Method Appl Mech Eng

Int J Solid Struct

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Aided Design

Comput Struct