Related papers: Isogeometric analysis for multi-patch structured K…
Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…
We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…
Isogeometric analysis was proposed to bridge the gap between computer-aided design and numerical discretization. However, standard multi-patch isogeometric analysis mandates conformal discretizations across patch interfaces, posing…
Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of $C^0$ planar multi-patch spline parametrizations called analysis-suitable $G^1$…
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…
In this paper, a novel varying order NURBS discretization method is proposed to enhance the performance of isogeometric analysis within the framework of computational contact mechanics. The method makes use of higher-order NURBS for contact…
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Numerical modeling of strength and non-destructive testing of complex structures such as buildings, space rockets or oil reservoirs often involves calculations on extremely large grids. The modeling of elastic wave processes in solids…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…
Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of…
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…
In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…