Isogeometric analysis: an overview and computer implementation aspects

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA

ISOGEOMETRIC ANALYSIS AND PATCHWISE REPRODUCING POLYNOMIAL PARTICLE METHOD FOR PLATES

Isogeometric analysis (IGA) ([8, 16, 27]) is designed to combine two tasks, design by Computer Aided Design (CAD) and Finite Element Analysis (FEA), so that it drastically reduces the error in the representation of the computational domain and the re-meshing by the use of “exact” CAD geometry directed at the coarsest level of discretization. This is achieved by using B-splines or non-uniform rational B-splines (NURBS) for the description of geometries as well as for the representation of unknown solution fields. In order to handle the singularities arising in the PDEs, Babu?ska and Oh [7] introduced mapping techniques, called the Method of Auxiliary Mapping (MAM), into conventional p-version of Finite Element Methods (FEM). In a similar spirit to MAM, it is possible to construct a novel NURBS geometrical mapping that generates singular functions resembling the singularities. The proposed mapping technique is concerned with constructions of unconventional novel geometrical mappings by which push-forward of B-spline functions defined on the parameter space generates singular functions in a physical domain that resemble the given point singularities. In other words, the pull-back of the singularity into the parameter space by the non standard NURBS mapping becomes highly smooth. However, the mapping technique is not able to handle in the framework of IGA. Thus, we consider how to use the proposed mapping method in IGA of elliptic prob- lems and elasticity containing singularities without changing the design mapping. For this end, we embed the mapping method into the standard IGA that uses NURBS basis functions for which h - p - k-refinements are applicable for improved computational solution. In other words, the mapping method will be used to enrich NURBS basis functions around neighborhood of singularities so that they can capture singular behaviors of the solution to be approximated. Finally, Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this disserta- tion, the RPPM is employed for free vibration and buckling of the first order shear deformation model (FSDT), called the Reissner-Mindlin plate, and for analysis of boundary layer of the Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and shape functions satisfying the Kronecker delta property. Also, we demonstrate that our method is more effective than other existing methods in dealing with Reissner- Mindlin plates with various material properties and boundary conditions

A Hybrid Landmark and Contour-Matching Image Registration Model

In this manuscript, we propose a novel hybrid Landmark and Contour-Matching (LCM) image registration model to align image pairs. The proposed model uses image contour information to supplement missing edge information in between exact landmarks. We demonstrate that the model circumvent the drawbacks associated with an straightforward application of the Thin Plate Spline (TPS) registration technique.The proposed model provides higher post-registration Dice similarity between the reference and registered template images by improving the image overlap away from major landmarks and visually reduces the appearance of the ''unnatural bending'' typically present in TPS-registered images. We also show that naively increasing the number of landmarks in a TPS model does not always guarantee an accurate registration result. We indicate how the proposed model using even less number of exact landmarks along with additional approximate contour information provided suitable results, as opposed to the TPS model. Lastly, the proposed model produces physically relevant registration results with improved Dice similarity indices even when landmark localization errors are present in data.Overall, the proposed Landmark and Contour-Matching (LCM) model increases the flexibility of the TPS approach especially when only a few landmarks can be defined, when defining too many landmarks leads to high oscillations in the registration transformations, or when the identification of exact landmarks is susceptible to human error

Mid-sagittal plane and mid-sagittal surface optimization in brain MRI using a local symmetry measure

This paper describes methods for automatic localization of the mid-sagittal plane (MSP) and mid-sagittal sur-face (MSS). The data used is a subset of the Leukoaraiosis And DISability (LADIS) study consisting of three-dimensional magnetic resonance brain data from 62 elderly subjects (age 66 to 84 years). Traditionally, the mid-sagittal plane is localized by global measures. However, this approach fails when the partitioning plane between the brain hemispheres does not coincide with the symmetry plane of the head. We instead propose to use a sparse set of profiles in the plane normal direction and maximize the local symmetry around these using a general-purpose optimizer. The plane is parameterized by azimuth and elevation angles along with the distance to the origin in the normal direction. This approach leads to solutions confirmed as the optimal MSP in 98 percent of the subjects. Despite the name, the mid-sagittal plane is not always planar, but a curved surface resulting in poor partitioning of the brain hemispheres. To account for this, this paper also investigates an opti-mization strategy which fits a thin-plate spline surface to the brain data using a robust least median of squares estimator. Albeit computationally more expensive, mid-sagittal surface fitting demonstrated convincingly better partitioning of curved brains into cerebral hemispheres. 1