Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations

2017 ◽  
Vol 327 ◽  
pp. 411-458 ◽  
Author(s):  
Deepesh Toshniwal ◽  
Hendrik Speleers ◽  
Thomas J.R. Hughes
Keyword(s):  
Isogeometric Analysis ◽  
Cubic Spline ◽  
Geometric Design ◽  
Quadrilateral Meshes ◽  
Extraordinary Points

Data reduction for manipulator path planning

Robotica ◽  
2003 ◽  
Vol 21 (6) ◽  
pp. 605-614 ◽  
Author(s):  
Werner Korb ◽  
Inge Troch
Keyword(s):  
Path Planning ◽  
Data Reduction ◽  
Cubic Spline ◽  
Surgical Robotics ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Computer Aided ◽  
Planning Tools ◽  
Long Time

Today, in robot applications continuous paths often result from CAD or other planning tools. We present here an approach to the question that has been discussed for a long time, i.e. how to approximate a given path by a second one in such a way that the latter lies in a tube of given radius ε around the first. The approximation should be a (normally cubic) spline with a small number of breakpoints. The strategy is based on algorithms used in “computer aided geometric design” and is applied to examples from industrial and surgical robotics.

scholarly journals THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis

2016 ◽  
Vol 299 ◽  
pp. 337-365 ◽  
Author(s):  
Carlotta Giannelli ◽  
Bert Jüttler ◽  
Stefan K. Kleiss ◽  
Angelos Mantzaflaris ◽  
Bernd Simeon ◽  
...  
Keyword(s):  
Isogeometric Analysis ◽  
Geometric Design ◽  
Adaptive Refinement

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jike Han ◽  
Bo Yin ◽  
Michael Kaliske ◽  
Kenjiro Tarada
Keyword(s):  
Computational Efficiency ◽  
Isogeometric Analysis ◽  
Damage Model ◽  
Geometric Design ◽  
Experimental Results ◽  
Complex Geometries ◽  
Computational Stability ◽  
Content Type ◽  
Non Local ◽  
Crack Paths

Purpose This study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries. Design/methodology/approach For the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results. Findings The implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results. Originality/value The paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

scholarly journals Isogeometric analysis with $C^1$ functions on planar, unstructured quadrilateral meshes

2019 ◽  
Vol S5 ◽  
pp. 67-86 ◽  
Author(s):  
Mario Kapl ◽  
Giancarlo Sangalli ◽  
Thomas Takacs
Keyword(s):  
Isogeometric Analysis ◽  
Quadrilateral Meshes

Glucose Calibration Modeling in Blood with Spline Regression Approaching to Non-Invasive Tools

2018 ◽  
pp. 144-149
Author(s):  
Ria Hayatun Nur ◽  
Indahwati A ◽  
Erfiani A
Keyword(s):  
Diabetes Mellitus ◽  
Linear Regression ◽  
Good Health ◽  
Cubic Spline ◽  
The Body ◽  
Spline Regression ◽  
Linear Quadratic ◽  
Important Thing ◽  
Non Invasive

In this globalization era, health is the most important thing to be able to run various activities. Without good health, this will hinder many activities. Diabetes mellitus is one of the diseases caused by unhealty lifestyle.There are many treatments that can be done to prevent the occurrence of diabetes. The treatments are giving the insulin and also checking the glucose rate to the patients.Checking the glucose rate needs the tools which is safety to the body. This research want to develop non invasive tool which is safety and do not injure the patient. The purpose of this research is also finding the best model which derived from Linear, Quadratic, and Cubic Spline Regression. Some respondents were taking to get the glucose measuring by invasive and non invasive tools. It could be seen clearly that Spline Linear Regression was the best model than Quadratic and Cubic Spline Regression. It had 70% and 33.939 for R2 and RMSEP respectively.

Mathematical Methods in Geometric Design

1997 ◽  
Vol 1 ◽  
pp. 61-66
Author(s):  
Rimvydas Krasauskas
Keyword(s):  
Geometric Design ◽  
Mathematical Methods

  

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