a method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the gauss points, has been already introduced. this paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by...

dynamic analysis of two-dimensional elasticity problems using the isogeometric analysis method and its comparison with the finite element method is the subject of this research. for this purpose, formulation of the governing differential equation is obtained by using the b-spline basis functions. some numerical examples employing consistent and lumped mass matrices are presented in order to com...

Isogeometric analysis has been proposed as a methodology for bridging the gap between computer aided design (CAD) and finite element analysis (FEA). Although both the traditional and isogeometric pipelines rely upon the same conceptualization to solid model steps, they drastically differ in how they bring the solid model both to and through the analysis process. The isogeometric analysis proces...

Gk (geometrically continuous surface) constructions were developed to create surfaces that are smooth also at irregular points where, in a quad-mesh, three or more than four elements come together. Isogeometric elements were developed to unify the representation of geometry and of engineering analysis. We show how matched Gk constructions for geometry and analysis automatically yield Ck isogeom...

Isogeometric analysis is a quickly emerging alternative to the standard, polynomialbased finite element analysis. It is only the question of time, when it will be implemented into major software packages and will be intensively used by engineering community to the analysis of complex realistic problems. Computational demands of such analyses, that may likely exceed the capacity of a single comp...

Isogeometric analysis (IGA) aims to bridge the geometric divide between CAD systems and FEA software tools. It is founded on the idea of using the same basis functions to represent the CAD geometry and to approximate the physical quantities appearing in analysis. It promises to revolutionize the design and analysis processes for automobile, aerospace and marine industry by eliminating the need ...

This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeomet...

We present an introduction to Isogeometric Analysis, a new methodology for solving partial differential equations (PDEs) based on a synthesis of Computer Aided Design (CAD) and Finite Element Analysis (FEA) technologies. A prime motivation for the development of Isogeometric Analysis is to simplify the process of building detailed analysis models for complex engineering systems from CAD represe...

We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element-wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T-splines are used for the description of the geometry as well...