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This paper develops a coupling approach which integrates the meshfree method and isogeometric analysis (IGA) for static and free-vibration analyses of cracks in thin-shell structures. In this approach, the domain surrounding the cracks is represented by the meshfree method while the rest domain is meshed by IGA. The present approach is capable of preserving geometry exactness and high continuity of IGA. The local refinement is achieved by adding the nodes along the background cells in the meshfree domain. Moreover, the equivalent domain integral technique for three-dimensional problems is derived from the additional Kirchhoff-Love theory to compute the J-integral for the thin-shell model. The proposed approach is able to address the problems involving through-the-thickness cracks without using additional rotational degrees of freedom, which facilitates the enrichment strategy for crack tips. The crack tip enrichment effects and the stress distribution and displacements around the crack tips are investigated. Free vibrations of cracks in thin shells are also analyzed. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the coupling approach. [ABSTRACT FROM AUTHOR]

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles. [ABSTRACT FROM AUTHOR]

This paper presents an isogeometric formulation for frictionless contact between deformable bodies, based on the recently proposed concept of the third medium. This concept relies on continuum formulations not only for the contacting bodies but also for a fictitious intermediate medium in which the bodies can move and interact. Key to the formulation is a suitable definition of the constitutive behavior of the third medium. In this work, based on a number of numerical tests, the role of the material parameters of the third medium is systematically assessed. We also assess the rate of spatial convergence for higher-order discretizations, stemming from the regularization of the non-smooth contact problem inherent to the third medium approach. Finally, problems with self contact are considered and turn out to be an attractive application of the method. [ABSTRACT FROM AUTHOR]

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty. [ABSTRACT FROM AUTHOR]

A crucial problem of continuous adjoint shape sensitivity analysis is the numerical implementation of its lengthy formulations. In this paper, the numerical implementation of continuous adjoint shape sensitivity analysis is presented for transient heat conduction problems using isogeometric analysis, which can serve as a tutorial guide for beginners. Using the adjoint boundary and loading conditions derived from the design objective and the primary state variable fields, the numerical analysis procedure of the adjoint problem, which is solved backward in time, is demonstrated. Following that, the numerical integration algorithm of the shape sensitivity using a boundary approach is provided. Adjoint shape sensitivity is studied with detailed explanations for two transient heat conduction problems to illustrate the numerical implementation aspects of the continuous adjoint method. These two problems can be used as benchmark problems for future studies. [ABSTRACT FROM AUTHOR]

Nowadays the isogeometric analysis (IGA) represents an innovative method that merges design and numerical computations into a unified formulation. In such a context we apply the isogeometric concept based on T-splines and Non Uniform Rational B-Splines (NURBS) discretizations to study the interfacial contact and debonding problems between deformable bodies in large deformations. More in detail, we develop and test a generalized large deformation contact algorithm which accounts for both frictional contact and mixed-mode cohesive debonding in a unified setting. Some numerical examples are provided for varying resolutions of the contact and/or cohesive zone, which show the accuracy of the solutions and demonstrate the potential of the method to solve challenging 2D contact and debonding problems. The superior accuracy of T-splines with respect to NURBS interpolations for a given number of degrees of freedom (Dofs) is always proved. [ABSTRACT FROM AUTHOR]

We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. This is utilized in the shape design optimization that includes a variation of design components in its shape and orientation. By the isogeometric approach, the NURBS basis function in CAD system is directly utilized in the response analysis, which enables the seamless incorporation of higher continuity and exact geometry such as curvature and normal vector into the computational framework. The impact of exact curvature in the bending problem of Mindlin plates on the configuration design sensitivity is demonstrated through numerical examples. The obtained design sensitivity is further utilized in the shape design optimization of built-up structures. Due to the non-interpolatory property of the NURBS basis functions, a mismatch of patches in the built-up structures could occur during the isogeometric design optimization, which can be easily resolved using transformed basis functions. [ABSTRACT FROM AUTHOR]