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Abstract This paper investigates the static bending and buckling behaviors of functionally graded microplates under mechanical and thermal loads by using isogeometric analysis (IGA) and modified strain gradient theory (MSGT). The material properties are assumed to be temperature-dependent and three different temperature rise patterns including uniform, linear and non-linear are considered. The material properties vary through the plate thickness based on the rule of mixture scheme. A refined hyperbolic shear deformation theory with four independent unknowns is used for analysis, which doesn't need a shear correction factor. For analysis the IGA using B-Spline or Non-Uniform Rational B-Spline (NURBS) functions can easily meet the C2 continuity requirement. Various parameters are dealt with including power index, material length scale parameter, temperature rise patterns and material combination. The MSGT results are also compared with those obtained by modified couple stress and classical theories. The obtained results indicate that the two studied types of functionally graded microplates show different behaviors under thermal load and the type of functionally graded material is an important parameter for thermal analysis. [ABSTRACT FROM AUTHOR]

Abstract Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. Typically, quadrilateral patches are adopted in both frameworks. We consider the particular class of multi-patch parametrizations that are analysis-suitable G 1 (AS- G 1), which is a specific geometric continuity definition which allows to construct, on the multi-patch domain, C 1 isogeometric spaces with optimal approximation properties (cf. Collin et al., 2016). It was demonstrated in Kapl et al. (2018) that AS- G 1 multi-patch parametrizations are suitable for modeling complex planar multi-patch domains. We construct a local basis, and an associated dual basis, for a specific C 1 isogeometric spline space A over a given AS- G 1 multi-patch parametrization. The space A is C 1 across interfaces and C 2 at all vertices, and is therefore a subspace of the entire C 1 isogeometric space V 1. At the same time, A allows optimal approximation of traces and normal derivatives along the interfaces and reproduces all derivatives up to second order at the vertices. In contrast to V 1 , the dimension of A does not depend on the domain parametrization. This paper also contains numerical experiments which exhibit the optimal approximation order in L 2 and L ∞ of the isogeometric space A and demonstrate the applicability of our approach for isogeometric analysis. Highlights • We define a C1-smooth isogeometric subspace over multi-patch domains. • The isogeometric subspace is C1 across edges and C2 at vertices. • We present a basis construction for the isogeometric subspace. • The isogeometric subspace displays optimal approximation properties. [ABSTRACT FROM AUTHOR]

Highlights • We derive the model of concurrency for refined isogeometric analysis. • We associate basic undividable tasks with macro-elements separated by C0 hyperplanes. • We define the communication channels between tasks. • We aggregate the tasks to map into architecture of distributed memory parallel machine. • We analyse the computational and communicational costs of the resulting algorithm. Abstract We perform the analysis of the concurrency of the parallel refined isogeometric analysis (rIGA) computations. Namely, we consider three-dimensional mesh partitioned into several macro-elements, with tensor product B-spline basis functions, and C° separators introduced between the macro-elements. We partition the computational problem into a sequence of tasks, and we define the dependency relation between the tasks. Next, we use the trace theory approach to identify the sets of tasks that can be executed in concurrent, one set after the other. We also estimate the computational cost of the tasks. To generalize our model for the distributed memory case, we use the Partitioning Communication Agglomeration and Mapping (PCAM) model with tasks and communication channels mapped into the architecture of the parallel distributed memory machine. We perform numerical experiments on the representative three-dimensional meshes partitioned into macro-elements with quadratic and cubic B-splines, and we compare the numerical results with theoretical estimates. [ABSTRACT FROM AUTHOR]

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]

Trimmed CAD models are the most popular geometry representation in engineering design, but their direct application to an isogeometric analysis can lead to ill‐conditioned system matrices. An approach is presented that effectively resolves this issue by combining so‐called extended B‐splines with a local refinement procedure. [ABSTRACT FROM AUTHOR]

Membranes constitute an important category of thin‐walled and in particular tensile structures [1], for which in contrast to shells their structural rigidity is obtained by means of prestress rather than relying on bending stiffness. In particular, the structures considered in this study act in pure membrane state and have no bending stiffness. A big challenge of such structures is finding the shape of static equilibrium. This is not a trivial task since not every shape under any prestress distribution or loading condition renders a static equilibrium configuration. This is even more prominent when prestressed cables are attached to the structure. To overcome this problem for general tensile structures, various types of form‐finding methods were developed [2, 3]. In this study, the Updated Reference Strategy (URS) [4, 5] is presented in combination with multipatch isogeometric analysis [6] as discretization method. The enforcement of the continuity constraints along the common patch interfaces [7] is realized using a Nitsche‐type method [8] while the results are evaluated and compared with the Penalty‐based approach [9]. [ABSTRACT FROM AUTHOR]

We introduce the concept of isogeometric boundary element methods, by first reviewing the required trace spaces and then constructing a conforming spline discretisation. We highlight how to use this approach to solve Dirichlet problems induced by the Helmholtz‐ and electric wave equation, and conclude by presenting numerical examples. [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]

Highlights • Bézier extraction based XIGA approach is successfully implemented for the analysis of 3-D crack problems. • SIFs for 3-D cracks are evaluated by interaction integral approach using virtual cuboidal domain. • Auxiliary fields used in the interaction integral are obtained approximately in terms of level set functions. • Higher-order continuity of NURBS basis functions produces smooth variation of level set functions. • Results obtained by Bézier extraction based XIGA are found in good agreement with XFEM and analytical solutions. Abstract In this work, Bézier extraction based extended isogeometric analysis (XIGA) has been performed for three-dimensional (3-D) crack simulations in linear elastic materials. The Bézier extraction represent the original NURBS basis functions in terms of Bernstein shape functions defined over C 0 continuous isogeometric Bézier elements, and provides an element wise data structure of NURBS which makes the implementation similar to extended finite element method (XFEM). A crack in the domain is modeled by Heaviside and crack tip enrichment functions. The values of mixed-mode stress intensity factors (SIFs) are obtained by interaction integral approach using virtual cuboidal domain. Various 3-D crack problems are solved by Bézier extraction based XIGA, and the results are compared with XFEM and analytical solutions. [ABSTRACT FROM AUTHOR]

This paper presents a unified theory for modelling composite thin-walled beams (TWB) of arbitrary planar axial curvature, variable cross-section and general material layup, complemented by the development of an Isogeometric Analysis (IGA) formulation for the discretization and solution of the equilibrium equations. To this end, the standard formulation of composite TWB with rectilinear axes is combined with a general framework for describing the kinematics of arbitrary three-dimensional curves based on the Frenet-Serret frame field. The theory includes explicit terms accounting for curvature gradients within the IGA stiffness matrix, allowing for the treatment of cases with highly curved geometry. Also included is an advanced shear-modification adjustment previously derived for rectilinear TWB, here reformulated for the case of curved TWB, improving the description of the in-plane shear-strain coupling and thus increasing the accuracy for cases with axial-bending-torsional structural coupling. Results from three numerical test cases indicate that this unified formulation effectively transfers all the advantages associated with rectilinear TWB to curved TWB models, yielding an accuracy comparable to more complex models while maintaining a competitive computational economy. [ABSTRACT FROM AUTHOR]

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator–rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example. [ABSTRACT FROM AUTHOR]

A stable basis for isogeometric analysis of trimmed models is obtained by combining extended B-splines with truncated hierarchical B-splines. While extended B-splines guarantee that the condition number of system matrices is independent of the location of a trimming curve, local refinement is used to improve the robustness of the procedure and the accuracy of the numerical results. The present extended B-spline construction works in the context of Galerkin and collocation methods. The paper focuses on the latter and introduces a new collocation scheme for truncated hierarchical B-splines. A proper transition between refinement levels is assured by a novel balancing algorithm that employs a simple criterion. The enhanced performance of the locally refined stabilization is verified by scalar Laplace and linear elasticity problems analyzed by a collocation based isogeometric boundary element method. The proposed approach yields excellent results and requires few refinement levels to improve the stabilization procedure and accuracy along trimming curves. [ABSTRACT FROM AUTHOR]

We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a decrement in the interconnection between the degrees of freedom of the mesh, which allows for large computational savings during the solution of the resulting linear system. The continuity reduction results in extra degrees of freedom that modify the approximation properties of the method. The convergence rate of such refined isogeometric analysis is equivalent to that of the maximum continuity basis. We show how the breaks in continuity and inhomogeneity of the basis lead to artifacts in the frequency spectra, such as stopping bands and outliers, and present a unified description of these effects in finite element method, isogeometric analysis, and refined isogeometric analysis. Accuracy of the refined isogeometric analysis approximations can be improved by using non-standard quadrature rules. In particular, optimal quadrature rules lead to large reductions in the eigenvalue errors and yield two extra orders of convergence, as it occurs in standard isogeometric analysis. [ABSTRACT FROM AUTHOR]

In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the open-source Octave/Matlab code GeoPDEs. [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]

We present a rotation free isogeometric analysis formulation based on Kirchhoff-Love theory, which aims to address free vibration and buckling behaviors of functionally graded thin plates with in-plane material inhomogeneity. For Kirchhoff-Love thin plate analysis, construction of C 1 conforming finite element approximation is not straightforward, while isogeometric analysis with high-order continuity splines basis functions is ideally suited for Kirchhoff-Love elements. We first explain the formulations and then provide verification of the present method through numerical examples. Studies on convergence and comparison with reference solutions are demonstrated to show the effectiveness and accuracy of the proposed method. Effects on natural frequencies, critical buckling loads and mode shapes originated from the material inhomogeneity and boundary conditions are numerically investigated. [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]

An isogeometric analysis (IGA) based numerical model is presented for simulation of thermo-hydro-mechanically (THM) coupled processes in ground freezing. The momentum, mass and energy conservation equations are derived based on porous media theory. The governing equations are supplemented by a saturation curve, a hydraulic conductivity model and constitutive equations. Variational and Galerkin formulation results in a highly nonlinear system of equations, which are solved using Newton-Raphson iteration. Numerical examples on isothermal consolidation in plane strain, one-dimensional freezing and heave due to a chilled pipeline are presented. Reasonably good agreements were observed between the IGA based heave simulations and experimental results. [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]

A novel isogeometric-based cross-sectional analysis of composite beams with arbitrary cross-section geometry and a one-dimensional composite beam model is presented via the concept of dimensional reduction method. In dimensional reduction method, three-dimensional beam problem is decomposed into a two-dimensional beam cross-sectional analysis and a one-dimensional beam problem. To achieve this goal, warping displacements should be computed by solving a cross-sectional eigenvalue problem. The cross-sectional analysis is accomplished by spline basis functions to describe unknown warping fields as well as beam cross-section geometry in an isogeometric framework. The present method benefits from the exact geometric definition of beam cross-section, greatly simplifying mesh refinement and better convergence in contrast to classical finite element method. The proposed beam cross-sectional analysis is applied to a variety of beam cross-section configurations with isotropic and anisotropic materials, which show good correlation with the available results in the literature. [ABSTRACT FROM AUTHOR]

The paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties. The isogeometric analysis method is employed in the new stochastic analysis scheme which is called Stochastic IsoGeometric Analysis (SIGA). The elastic modulus and mass density are modeled as homogeneous Gaussian random fields along the plane of structure. The governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues. In order to verify proposed method, the brute force Monte Carlo simulation is employed. The mean, variance, and COV (Coefficient of Variation) predicted by SIGA and those predicted by Monte Carlo simulation show good agreement. The numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates. The correlation between elastic modulus and mass density is also observed to have significant effect on the response COV of eigenvalue. [ABSTRACT FROM AUTHOR]

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (S N ) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements. [ABSTRACT FROM AUTHOR]

Isogeometric analysis is a method for solving geometric partial differential equations (PDEs). Generating parametrizations of a PDE’s physical domain is a basic and important issue within isogeometric analysis framework. In this paper, we present a global H 1 -parametrization method for a complex planar physical domain. [ABSTRACT FROM AUTHOR]

In the context of segmenting a boundary represented solid into topological hexahedra suitable for isogeometric analysis, it is often necessary to split an existing face by constructing auxiliary curves. We consider solids represented as a collection of trimmed spline surfaces, and design a curve which can split the domain of a trimmed surface into two pieces satisfying the following criteria: the curve must not intersect the boundary of the original domain, it must not intersect itself, the two resulting pieces should have good shape, and the endpoints and the tangents of the curve at the endpoints must be equal to specified values. [ABSTRACT FROM AUTHOR]

We present a discretisation of Kirchhoff–Love thin shells based on a subdivision algorithm that generalises NURBS to arbitrary topology. The isogeometric framework combines the advantages of both subdivision and NURBS, enabling higher degree analysis on watertight meshes of arbitrary geometry, including conic sections. Because multiple knots are supported, it is possible to benefit from symmetries in the geometry for a more efficient subdivision based analysis. The use of the new subdivision algorithm is an improvement to the flexibility of current isogeometric analysis approaches and allows new use cases. [ABSTRACT FROM AUTHOR]

A spline space suitable for Isogeometric Analysis (IgA) on multi-patch domains is presented. Our construction is motivated by emerging requirements in isogeometric simulations. In particular, IgA spaces should allow for adaptive mesh refinement and they should guarantee the optimal smoothness of the discretized solution, even across interfaces of adjacent patches. Given a domain manifold M consisting of individual patches (isomorphic to the unit square or cube) that are glued together along interfaces, we present a construction of multi-patch B-splines defined on them. Their smoothness is enhanced by locally modifying or merging basis functions around the boundary of each patch. The resulting multi-patch B-splines with enhanced smoothness (MPBES) possess the property of local linear independence and form a non-negative partition of unity. Moreover, their span can be characterized as the linear space of all piecewise polynomial functions on the domain manifold that possess certain smoothness properties. Subsequently, adaptively refined MPBES are obtained by generalizing the construction of truncated hierarchical (TH) B-splines. More precisely, a nested sequence of spaces spanned by MPBES is considered, corresponding to steps of local enrichment. In addition, an inversely nested sequence of subdomains (which are submanifolds of M ) is used to specify the local refinement level of functions in these spaces. Finally, truncated hierarchical MPBES are obtained by means of the selection and truncation mechanism of THB-splines. The desired properties of linear independence and convex partition of unity are maintained. The paper presents several numerical examples which demonstrate potential applications of the new basis in isogeometric analysis. [ABSTRACT FROM AUTHOR]

We study a reformulated version of Reissner-Mindlin plate theory in which rotation variables are eliminated in favor of transverse shear strains. Upon discretization, this theory has the advantage that the "shear locking" phenomenon is completely precluded, independent of the basis functions used for displacement and shear strains. Any combination works, but due to the appearance of second derivatives in the strain energy expression, smooth basis functions are required. These are provided by Isogeometric Analysis, in particular, NURBS of various degrees and quadratic triangular NURPS. We present a mathematical analysis of the formulation proving convergence and error estimates for all physically interesting quantities, and provide numerical results that corroborate the theory. [ABSTRACT FROM AUTHOR]

In this article, we extend this approximation theory developed in (Bazilevs et al., Math Models Methods Appl Sci 16 (2006), 1031-1090) and (Beirão da Veiga et al., Comput Methods Appl Mech Eng 209-212 (2012), 1-11) to the case when the computational domain is a collection of nonuniform rational B-splines patches. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 422-438, 2015 [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]

The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a different degree. In one case, we consider an equal order pairing for which a cross point modification based on a local degree reduction is required. In the other case, the degree of the dual space is reduced by two compared to the primal. This pairing is proven to be inf–sup stable without any necessary cross point modification. Several numerical examples confirm the theoretical results and illustrate additional aspects. [ABSTRACT FROM AUTHOR]

A balancing domain decomposition by constraints (BDDC) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling, is extended to isogeometric analysis of scalar elliptic problems. This new scaling turns out to be more powerful than the standard ρ- and stiffness scalings considered in a previous isogeometric BDDC study. Our h-analysis shows that the condition number of the resulting deluxe BDDC preconditioner is scalable with a quasi-optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces. Extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings, in particular for large isogeometric polynomial degree and high regularity. [ABSTRACT FROM AUTHOR]

Abstract: GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-Splines and Non-Uniform Rational B-Splines (NURBS), while being flexible enough to allow users to implement new and more general methods with a relatively small effort. This paper presents the philosophy at the basis of the design of GeoPDEs and its relation to a quite comprehensive, abstract definition of IGA. [Copyright &y& Elsevier]

Isogeometric analysis (IGA) is a novel discretization method, introduced by Hughes et al., which is based on nonuniform rational B-splines (NURBS). Among other features, IGA uses directly the geometry description coming from computer-aided design software without approximation, and the analysis is performed using shape functions of variable (possibly high) regularity. In this paper we propose a new discretization scheme based on continuous B-splines, adapting the IGA to the solution of Maxwell's equations.We present extensive numerical results to show that our scheme is free of spurious modes, and that it approximates singular solutions in domains with reentrant corners and edges. [ABSTRACT FROM AUTHOR]

Prediction and control of the thermal deformation of the work roll is vital for enhancing product quality in hot strip and plate rolling. In this paper, the authors present an online model for the prediction of the work roll thermal profile. The model is developed on the basis of an integrated finite element model for the coupled analysis of heat transfer and deformation occurring at the bite zone and taking into account the effect of various rolling parameters on the thermal behaviour of the work roll. The validity of the model is demonstrated through comparison with measurements made in an industrial hot strip mill. In addition, an emphasis is given to the examination of the effect of some selected rolling parameters in an actual production environment. [ABSTRACT FROM AUTHOR]

The so‐called scaled boundary isogeometric analysis combines the advantages of the isogeometric analysis and the scaled boundary finite element method. Here, the parameterization of the solid follows the idea of the scaled boundary finite element method (SB‐FEM), where the boundary of the domain is scaled in respect to a specified scaling center inside the domain. In the framework of isogeometric analysis (IGA), the NURBS functions that describe the geometry also interpolate the unknown displacement field. Such a combined approach is advantageous for three‐dimensional solids, as a radial scaling parameter describes the interior of the solid and only the geometry of the boundary is required for the analysis. The motivation is therefore to fit the idea of the boundary representation modeling technique, which is the way solids are designed in CAD –namely only by their boundary surfaces. Our contribution introduces a formulation for geometrical nonlinear 2D problems. The derived formulation addresses hyperelastic material behavior for large deformations and plane strain conditions for the two‐dimensional domain. We solve the boundary value problem by applying the weak form of equilibrium in both radial scaling and circumferential direction of the boundary. Thereafter, the nonlinear deformation behavior requires a linearization and the application of the Newton‐Raphson iterative scheme. Finally, we study the performance of this approach on a numerical problem by comparison to the standard finite element method. [ABSTRACT FROM AUTHOR]

The use of a common set of basis functions for design and analysis is the main paradigm of isogeometric analysis. The characteristics of the commonly used non-uniform rational B-splines (NURBS) surfaces require methods to handle non-conforming meshes to attain an efficient computational framework. The isogeometric mortar method uses constrained approximation spaces to enforce a coupling of deformations at the interface between patches in a weak manner. This method neither requires additional degrees of freedom nor the choice of empirical parameters. The main drawback of the standard isogeometric mortar approach is the non-local support of the mortar basis functions along the interface. This yields a large number of nodes per element for elements adjacent to the interface. Thus, the computational costs increase significantly for mesh refinement. This issue is remedied by the use of dual basis functions for the mortar method, which is referred to as dual mortar method. In this contribution several choices for the dual basis functions for B-splines are proposed and compared. A special focus is set on the support of the dual basis functions and on the support of the resulting mortar basis functions. Numerical examples show the influence of the choice for the dual basis functions on the accuracy of the global stress distribution, on the fulfillment of the interface conditions and on numerical efficiency. The use of approximate dual basis functions is shown to be competitive to computations of conforming meshes in terms of accuracy and efficiency. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract: Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient‐specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid–structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient‐specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian–Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient‐specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta. [ABSTRACT FROM AUTHOR]