Extended Isogeometric Analysis for Strong and Weak Discontinuities

Abstract

Isogeometric analysis (IGA) is a fundamental step forward in computational mechanics that offers the possibility of integrating methods for analysis into Computer Aided Design (CAD) tools and vice versa. The benefits of such an approach are evident, since the time taken from design to analysis is greatly reduced leading to large savings in cost and time for industry. 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 R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several fracture examples in both two-dimensions and three-dimensions are given as illustration. The open source Matlab R code which accompanies the present paper can be applied to one, two and threedimensional 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. It also implements the Bézier extraction concept that allows FE analysis to be performed on T-spline geometries. An attempt was also made to include a review of recent developments of IGA.G. Beer, S.Bordas (Eds.), Isogeometric Methods for Numerical Simulation,

Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

“…In this work, topologica ment has been employed. Figure 4 shows a schematic representation of this conc According to the Figure 4, 𝐶 𝑠 denotes the crack-face control points, while notes the crack-tip-enriched control points, and 𝐶 𝑖 denotes the standard contro For the purpose of selecting enriched control points, the level set method has be We applied the procedure that has been used by [58]. Initially, the level set valu crack at the mesh's vertices are computed according to these level sets, and the f tion determines the elements intersected by the crack and the crack-tip element.…”

“…For the purpose of selecting enriched control points, the level set method has been used. We applied the procedure that has been used by [58]. Initially, the level set values of the crack at the mesh's vertices are computed according to these level sets, and the formulation determines the elements intersected by the crack and the crack-tip element.…”

Orthotropic rotation-free thin shell elements

“…Methods that directly transform the components of f int will require the additional transformation of f ext to the new local coordinate system in order to implement boundary conditions which involve shape function derivatives. All rotationfree shells require this supplementary step for their implementation of certain natural boundary conditions [25,13,2,20,4,18,24] including frictional contact [39], in-plane shear traction based conditions [21] and displacement-dependent pressure loads [30]. Some widely used formulations additionally require these shape function derivatives for curvature gradient calculations [25,20] or hourglass stabilization [2].…”

Taylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking and New Approaches for Problems with Non-smooth Solutions

“…IGA shares many common points with meshfree methods, in particular its natural ability to deal with high order approximations, which makes it suitable to handle Kirchhoff-Love plates and shells and high-order PDEs. Various approaches combining enrichment with IGA were introduced [47].…”