Abstract
In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.
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Abbreviations
- B :
-
Strain-displacement matrix
- B i,p(ξ):
-
ith B-spline basis function of p-degree
- C p−k :
-
Continuity between knot spans
- d 1, d 2 :
-
SMDs of the two vertices of an edge
- D :
-
Stress-strain matrix
- Dis :
-
Distance from a point to a point on a triangle
- E :
-
Young’s modulus
- F :
-
Force vector
- J :
-
Jacobian matrix
- J 1, J 2 :
-
Transformation relation from the NURBS parametric space to the physical space and the integration parametric space to the NURBS parametric space, respectively
- k :
-
Multiplicity of the knots
- K e :
-
Element stiffness matrix
- m :
-
Number of polygons
- n :
-
Number of basis functions
- N :
-
Shape function vector
- N i :
-
Shape function
- N i,p(ξ):
-
ith NURBS basis function of p-degree
- p :
-
Order of the B-spline
- v 1 :
-
Vector from the vertex to the polygon plane
- v 2 :
-
Outward vector of the polygon
- V Ωe, \(V_{\hat{\Omega}_{\rm{e}}}\) and \(V_{\bar{\Omega}_{\rm{e}}}\) :
-
Volumes of the element in physical, NURBS parametric, and integration domains, respectively
- w i :
-
Positive weight
- w i,j :
-
Weight value corresponding to the tensor product Bi, p(ξ)Bj, q(η)
- x :
-
Physical value (e.g., coordinate, displacement, and force)
- x :
-
Physical value vector
- v :
-
Poisson’s ratio
- τ :
-
Traction of the loading region Ω
- ξ, η :
-
Variables for the coordinates in parameter space
- Ξ :
-
Knot vector
- φ :
-
Level set function value
- φ i :
-
LSF value of the ith vertex of the regular embedded element
- Ωe, \(\hat{\Omega}_{\rm{e}}\), and \(\bar{\Omega}_{\rm{e}}\) :
-
Physical, NURBS parametric, and integration domains of the element, respectively
- 2D:
-
Two-dimensional
- 3D:
-
Three-dimensional
- B-rep:
-
Boundary representation
- CAD:
-
Computer-aided design
- CAE:
-
Computer-aided engineering
- CSG:
-
Constructive solid geometry
- FCM:
-
Finite cell method
- FEA:
-
Finite element analysis
- FSI:
-
Fluid-structure interaction
- IGA:
-
Isogoemetric analysis
- LSF:
-
Level set function
- MC:
-
Marching cube
- MD:
-
Minimum distance
- NURBS:
-
Non-uniform rational B-spline
- SMD:
-
Sign minimum distance
- STEP:
-
Standard for the exchange of product model data
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Acknowledgements
This work has been supported by the National Key R&D Program of China (Grant No. 2020YFB1708300), the National Natural Science Foundation of China (Grant Nos. 52075184 and 51705158), and the Research Grants Council via Early Career Scheme, Hong Kong, China (RGC Ref. No. 27209817). These supports are gratefully acknowledged.
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Wang, Y., Gao, L., Qu, J. et al. Isogeometric analysis based on geometric reconstruction models. Front. Mech. Eng. 16, 782–797 (2021). https://doi.org/10.1007/s11465-021-0648-0
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DOI: https://doi.org/10.1007/s11465-021-0648-0