Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems

被引:1
作者
Fromm, Jennifer E. [1 ]
Wunsch, Nils [2 ]
Maute, Kurt [2 ]
Evans, John A. [2 ]
Chen, Jiun-Shyan [3 ]
机构
[1] Univ Calif San Diego, Mech & Aerosp Engn, 9500 Gilman Dr, La Jolla, CA 92093 USA
[2] Univ Colorado, Aerosp Engn, 3775 Discovery Dr, Boulder, CO 80303 USA
[3] Univ Calif San Diego, Struct Engn, 9500 Gilman Dr, La Jolla, CA 92093 USA
基金
美国国家科学基金会;
关键词
Immersed finite element method; Lagrange extraction; XIGA; Multi-physics problems; Multi-material problems; FINITE-ELEMENT-METHOD; ISOGEOMETRIC ANALYSIS; MESH QUALITY; CRACK-GROWTH; CELL METHOD; INTEGRATION; NURBS; DISCONTINUITIES; IMPLEMENTATION; APPROXIMATIONS;
D O I
10.1007/s00466-024-02506-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a structured background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the structured background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed isogeometric method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchically refined B-splines (THB-splines) is used to both improve interface geometry representations and to resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for partial differential equations representing heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom when compared to classical boundary-fitted finite element methods.
引用
收藏
页码:301 / 325
页数:25
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