The inverse mapping and distortion measures for 8-node hexahedral isoparametric elements

Yuan, Kuan-Ya; Huang, Yeong-Shyang; Yang, Haibin; Pian, T. H. H.

doi:10.1007/bf00350284

Cited by 34 publications

(34 citation statements)

References 9 publications

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“…By using this coordinate system, assumed stress field, which satisfies the equilibrium equations in physical coordinates, can be achieved. Later, Yuan et al generalized this technique into 3D for hexahedral elements [21]. In this study, this 3D skew coordinate system is adopted.…”

Section: Skew Coordinate Systemmentioning

confidence: 99%

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Universal three‐dimensional connection hexahedral elements based on hybrid‐stress theory for solid structures

Sheng

et al. 2009

Numerical Meth Engineering

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SUMMARYHigh-performance hybrid-stress hexahedral solid elements are excellent choices for modeling joints, beams/columns walls and thick slabs for building structures if the exact geometrical representation is required. While it is straight-forward to model beam-column structures of uniform member size with solid hexahedral elements, joining up beams and columns of various cross-sections at a common point proves to be a challenge for structural modeling using hexahedral elements with specified dimensions. In general, the joint has to be decomposed into 27 smaller solid elements to cater for the necessary connection requirements. This will inevitably increase the computational cost and introduce element distortions when elements of different sizes have to be used at the joint. Universal connection hexahedral elements with arbitrary specified connection interfaces will be an ideal setup to connect structural members of different sizes without increasing the number of elements or introducing highly distorted elements. In this paper, the requirements and the characteristics of the hexahedral connection elements with 24 and 32 nodes will be discussed. Formulation of the connection elements by means of Hellinger-Reissner functional will be presented. The performance of connection elements equipped with different number of stress modes will be assessed with worked examples.

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Section: Skew Coordinate Systemmentioning

confidence: 99%

“…The relation between the skew coordinates (¯ ,¯ ,¯ ) proposed by Yuan et al [21] and the global coordinates (x, y, z) is:…”

Section: Skew Coordinate Systemmentioning

confidence: 99%

Universal three‐dimensional connection hexahedral elements based on hybrid‐stress theory for solid structures

Sheng

et al. 2009

Numerical Meth Engineering

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“…[19], a general solution for the inverse transformation in 2D was proposed, and a general analytical expression of the inverse isoparametric relations for the linear hexahedral element was given in Ref. [20]. However, these approaches presented in the literature appear to be too complex for the problem considered in this study.…”

Section: Methodsmentioning

confidence: 99%

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

Wittek

Miller

2014

Journal of Biomechanical Engineering

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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.

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“…The inverse isoparametric mapping [94] is applied, which maps each cell to its local configuration. By inverse mapping the signal as well, the detection of the point with the maximum signal gradient on the adjacent face becomes straightforward.…”

Section: The Adhesion Approachmentioning

confidence: 99%

Computational Evolutionary Embryogeny

Yogev

Shapiro

Antonsson

2010

IEEE Trans. Evol. Computat.

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Evolution and development (Evo-Devo), are the two main processes which produce all of the different kinds of phenotypes we see in nature. Evolutionary process is responsible for eliminating the genetic information of weak phenotypes through natural selection, and also for exploring novel genotypes through genetic operations; crossover, mutation. The development process is the process of using the set of rules (codons) written in a genome, to turn a single set (zygote) into a mature phenotype. In this thesis, evolutionary and developmental processes are used to evolve the configurations of three-dimensional structures in silico to achieve desired performances. Although natural systems utilize the combination of both evolution and development processes to produce remarkable performance and diversity, this approach has not yet been applied extensively to the design of continuous three-dimensional load-supporting structures. Beginning with a single artificial cell containing information analogous to a DNA sequence, a structure is grown according to the rules encoded in the sequence. Each artificial cell in the structure contains the same sequence of growth and development rules, and each artificial cell is an element in a finite element mesh representing the structure of the mature individual. Rule sequences are evolved over many generations through selection and survival of individuals in a population.Modularity and symmetry are visible in nearly every natural and engineered structure. Understanding of the evolution and expression of symmetry and modularity is emerging from recent biological research. Initial evidence of these attributes is present in the phenotypes that are developed from the artificial evolution, although neither characteristic is imposed nor selected for directly.The computational evolutionary development approach presented here shows promise for synthesizing novel configurations of high-performance systems. The approach may advance system design to a new paradigm, where current design strategies have difficulty producing useful solutions. In addition to a new design approach perse, this model gives us the ability to explore the development process, from the standpoint of complex systems analysis. The phenotypes in our system have been grown under a highly stochastic environment, which serves as a triggered mechanism v for gene expression. Still, evolution was able to find solutions which are robust to these stochastic elements, both at the phenotype level (the phenotype ability to function under the environment) and the growth process itself. In addition we have also explored the effects of symmetric and nonsymmetric environment over the topology of the phenotypes; we have found strong evidence that indicates a high correlation between the two. Finally we have also established a tool which enables us to understand the relationship between the environment and the degree of modularity of the phenotype.vi

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The inverse mapping and distortion measures for 8-node hexahedral isoparametric elements

Cited by 34 publications

References 9 publications

Universal three‐dimensional connection hexahedral elements based on hybrid‐stress theory for solid structures

Universal three‐dimensional connection hexahedral elements based on hybrid‐stress theory for solid structures

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

Computational Evolutionary Embryogeny

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