Calculation of Internal Force on Arbitrary Cross Section Based on Direct Force Method with Finite Element

Direct force method based on finite element for the calculation of the internal force of cross section has the advantages of high accuracy and stability. However, the method can only be applied to the sections with element boundary surface, which limits the application scope of the method. Given the advantages of direct force method based on finite element in calculating the internal force of cross section, a new approach for calculating internal force of cross sections in any location is proposed in this study. In this approach, the inverse isoparametric mapping and the direct force method based on finite element are combined together to solve the internal force of cross section at any location in a finite element model.

Efficient Inverse Isoparametric Mapping Algorithm for Whole-Body Computed Tomography Registration Using Deformations Predicted by Nonlinear Finite Element Modeling

Biomechanical modeling methods can be used to predict deformations for medical image registration and particularly, they are very effective for whole-body computed tomography (CT) image registration because differences between the source and target images caused by complex articulated motions and soft tissues deformations are very large. The biomechanics-based image registration method needs to deform the source images using the deformation field predicted by finite element models (FEMs). In practice, the global and local coordinate systems are used in finite element analysis. This involves the transformation of coordinates from the global coordinate system to the local coordinate system when calculating the global coordinates of image voxels for warping images. In this paper, we present an efficient numerical inverse isoparametric mapping algorithm to calculate the local coordinates of arbitrary points within the eight-noded hexahedral finite element. Verification of the algorithm for a nonparallelepiped hexahedral element confirms its accuracy, fast convergence, and efficiency. The algorithm's application in warping of the whole-body CT using the deformation field predicted by means of a biomechanical FEM confirms its reliability in the context of whole-body CT registration.

SMOOTHED FINITE ELEMENT METHODS FOR THERMO-MECHANICAL IMPACT PROBLEMS

We present a Smoothed Finite Element Methods (SFEM) for thermo-mechanical impact problems. The smoothing is applied to the strains and the standard finite element approach is used for the temperature field. The SFEM allows for highly accurate results and large deformations. No isoparametric mapping is needed; the shape functions are computed in the physical domain. Moreover, no derivatives of the shape functions must be computed. We implemented a visco-plastic constitutive model and validate the method by comparing numerical results to experimental data.