Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The NURBS book
Volumetric multi-texturing for functionally gradient material representation
Proceedings of the sixth ACM symposium on Solid modeling and applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Finite Elements in Analysis and Design
Material-solid modeling of human body: A heterogeneous B-spline based approach
Computer-Aided Design
Isogeometric analysis and shape optimization via boundary integral
Computer-Aided Design
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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.