A local multivariate Lagrange interpolation method for constructing shape functions

Numer Methods Biomed Eng

2010

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SUMMARYIn this paper, a r -adaptation algorithm is presented. The algorithm is based on weighted Laplacian smoothing. In the proposed algorithm, the gradients of strain energy density are used as weight functions; Laplacian smoothing is iterated until the maximum deviation or standard deviation in mesh intensity is smaller than a prescribed value. Numerical results show that the algorithm is sensitive and robust. The algorithm can be extended to other finite element formulations by replacing strain energy density with its corresponding counterpart.

Section: Laplacian Smoothing Weighted By Gradients Of Strain Energy Dmentioning

confidence: 98%

r‐Adaptation algorithm guided by gradients of strain energy density

Numer Methods Biomed Eng

2010

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“…After the selection of a set of nearest nodes, several methods are available for constructing shape functions, e.g. the moving least-square method [14], the point interpolation method [15], the local multivariate Lagrange interpolation method [16], etc. The newly developed local multivariate Lagrange interpolation method [16] does not require solving local problems, and the constructed shape functions satisfy the Kronecker delta condition.…”

Section: Mechanism In Nn-fem For Dealing With Element Distortionmentioning

confidence: 99%

An effective way for dealing with element distortion by nearest‐nodes FEM

Numer Methods Biomed Eng

2010

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SUMMARYIn this paper, the performance of recently developed nearest-nodes finite element method (NN-FEM) ( Numerical results demonstrated that the accuracy of NN-FEM is nearly unaffected by element distortion. The reason is that in NN-FEM, a set of nearest nodes of a quadrature point is always selected for the construction of shape functions. In this way, the quality of shape functions is solely determined by the locations of the selected nearest nodes, and not affected by element shapes.

“…In this study, bone density is considered as a continuous function within a voxel. The function is constructed using an interpolation method, for example, the local multivariate Lagrange interpolation method [18], and density data from neighboring voxels.…”

Section: Variation Of Bone Density Within Voxelmentioning

confidence: 99%

Constructing anisotropic finite element model of bone from computed tomography (CT)

Kazembakhshi

Bio-Medical Materials and Engineering

2014

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Image-based finite element (FE) modeling of human bones has been increasingly applied as a useful tool in biomedical engineering. However, most existing image-based FE models assume isotropic mechanical properties for bones, although bones are typically anisotropic material. In this study, we attempted to construct anisotropic FE models from medical computed tomography (CT) scans by modifying the existing empirical relations of bone elasticity-density. The hypothesis adopted in the study is that bone anisotropy is generated by the variations of bone density and the proposed anisotropic relations should degenerate to the isotropic ones if bone density variation is taken zero. The effect of considering bone anisotropy in FE models was investigated by numerical studies. The obtained numerical results showed that the relative error in the finite element solutions produced respectively by the isotropic and anisotropic FE models can be as large as 50%. We concluded from this preliminary study that the consideration of anisotropy in bone FE models has a significant effect on the accuracy of bone behavior predicted by the FE models. However, well-designed bone tests have to be conducted to validate the anisotropic bone elasticity-density relation proposed in this study.