A HIERARCHICALLY SUPERIMPOSING LOCAL REFINEMENT METHOD FOR ISOGEOMETRIC ANALYSIS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350074 ◽  
Author(s):  
ZOO-HWAN HAH ◽  
HYUN-JUNG KIM ◽  
SUNG-KIE YOUN
Keyword(s):  
Tensor Product ◽  
Isogeometric Analysis ◽  
Spline Space ◽  
Local Refinement ◽  
Compatibility Conditions ◽  
Spline Surfaces ◽  
Refinement Method ◽  
Refinement Strategy ◽  
Different Levels ◽  
Made In

In isogeometric analysis, the tensor-product form of Nonuniform Rational B-spline (NURBS) represents spline surfaces. Due to the nature of the tensor-product, the local refinement in isogeometric analysis has many issues to be resolved. Attempts have been made in this regard, such as T-splines and hierarchical approaches. In this work, a local refinement method for isogeometric analysis based on a superimposing concept is proposed. Local refinements are performed by superimposing hierarchically-created finer overlay meshes onto the regions of high error rather than a change of analysis basis (from NURBS to some other spline space). To employ the superimposing concept as a local refinement strategy in isogeometric analysis, a hierarchical framework to construct overlay meshes is developed, and compatibility conditions across the interfacial boundaries of different levels of meshes is discussed. Through numerical examples, the effectiveness and validity of the proposed method are demonstrated.

scholarly journals Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis

2017 ◽  
Vol 316 ◽  
pp. 966-1004 ◽  
Author(s):  
René R. Hiemstra ◽  
Francesco Calabrò ◽  
Dominik Schillinger ◽  
Thomas J.R. Hughes
Keyword(s):  
Tensor Product ◽  
Isogeometric Analysis ◽  
Quadrature Rules

scholarly journals A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis

2018 ◽  
Vol 39 (4) ◽  
pp. 1627-1651 ◽  
Author(s):  
Pablo Antolin ◽  
Annalisa Buffa ◽  
Mathieu Fabre
Keyword(s):  
Isogeometric Analysis ◽  
A Priori ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Spline Space ◽  
Three Dimensions ◽  
B Spline ◽  
A Priori Error Estimate ◽  
The Stability ◽  
Unilateral Contact Problems

Abstract In this paper we consider a unilateral contact problem without friction between a rigid body and a deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem. For the displacement, we use the pushforward of a nonuniform rational B-spline space of degree $p$ and for the Lagrange multiplier, the pushforward of a B-spline space of degree $p-2$. These choices of space ensure the proof of an inf–sup condition and so on, the stability of the method. We distinguish between contact and noncontact sets to avoid the classical geometrical hypothesis of the contact set. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two and three dimensions and in small and large deformation frameworks demonstrate the accuracy of the proposed method.

scholarly journals Considerations on the Necessity of Modernization of Engineer Forces from NATO Members Countries

2017 ◽  
Vol 23 (1) ◽  
pp. 344-347
Author(s):  
Mircea Vladu ◽  
Ioan-Dan Popa
Keyword(s):  
Armed Forces ◽  
Historical Evolution ◽  
Social Activities ◽  
Member States ◽  
Joint Forces ◽  
The Common ◽  
Different Levels ◽  
Over Time ◽  
Made In ◽  
Structural Perspective

Abstract The engineer branch has been established at a certain stage of historical evolution of the armed forces to provide engineer support to the combat forces, as well as to support civil societies to achieve, develop and maintain the necessary infrastructure elements in order to conduct of economic and social activities. Having in mind all these elements and taking into account the structural perspective and the endowment, the evolution of engineer forces should have been made in accordance with the evolution of the common combat joint forces, keeping the same rhythm of development. Unfortunately, the engineer forces within the armies of the NATO member states did not evolve under the aforementioned aspects, even if some commitments have been made at the various summits held over time at different levels. As a result of these realities, in this paper we present some considerations about what should be the way ahead in the evolution of the engineer forces until the horizon of 2050.

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