This contribution presents an isogeometric approach in three dimensions for nonlinear problems in solid mechanics and structural dynamics. The proposed approach aligns with the boundary representation modeling technique in CAD. Isogeometric analysis is combined with the parameterization of the scaled boundary finite element method. In this way, the boundary description of 3D solids in CAD can be directly utilized for the analysis in an isogeometric framework. The approximation of the solution on the boundary is based on bi‐variate NURBS. We also approximate the interior of the solid with uni‐variate B‐splines to facilitate the solution of nonlinear problems. The nonlinear case is extended to three dimensions in this present work. The method is further extended to dynamic problems. The mass and damping matrices are derived using the same basis functions. The solution of the entire solid is obtained with the Galerkin method. We study several nonlinear and dynamic problems with simple geometries and arbitrary number of boundaries. Moreover, a fiber reinforced composite serves as demonstration for complex shapes.

This contribution presents a multiscale approach for the analysis of shell structures using Reissner–Mindlin kinematics. A distinctive feature is that the thickness of the representative volume element (RVE) corresponds to the shell thickness. The main focus of this paper is on the choice of correct boundary conditions for the RVE. Three different types of boundary conditions, which fulfil the Hill–Mandel condition, are presented to bridge the two scales. A common feature is the application of zero-traction boundary conditions at the top and bottom surfaces of the RVE. Furthermore, an internal constraint is used to reduce the dependency of the stiffness components on the RVE size. The introduced boundary conditions differ mainly in the application of shear strains and their symmetry requirements on the RVE. The characteristic features are compared by means of linear-elastic benchmark tests. It is shown that the stress resultants and tangent stiffness components are obtained correctly. Moreover, the presented approach is verified using different macroscopic shell structures and different mesostructures. Both, linear and nonlinear small strain examples are compared to analytical values or full-scale solutions and demonstrate a wide applicability of the present formulation.

This contribution deals with a homogenisation approach for shell structures. A coupled multiscale approach also known as FE² is used, which satisfies the Hill‐Mandel condition. The macroscopic structure is modelled with shell elements. Assuming periodicity of the mesostructure, which fulfils the scale separation requirement, allows the definition of a representative volume element (RVE). Using the RVE, equivalent homogeneous material parameters are obtained in order to define the overall structure. The shell strains obtained on the macroscopic scale are applied to the RVE. To model the mesostructure as 3D solids, the boundary representation from CAD is adopted. Next, Isogeometric analysis (IGA) is used for the solution on the boundary. In order to analyse the interior of the solid, IGA is combined with the scaled boundary finite element method. While the boundary is approximated using NURBS functions, the interior is approximated by B‐Splines, contrary to the use of an analytical solution in classical SBFEM. As a result, nonlinear problems can be covered. Furthermore, this approach facilitates the direct use of CAD models for analysis, which is especially useful for complex geometries on the mesostructure, e.g. for modelling laminar textile structures, such as woven fabrics or laid webs. Star‐shaped domains needed for the analysis are obtained by subdivision of the overall domain. Using NURBS basis functions for the approximation of the boundary can be problematic because the position of the control points, in contrast to the nodes in FEM, does not necessarily equal the physical coordinates. To enforce prescribed boundary conditions in the framework of homogenisation, this leads to difficulties. To overcome this problem a transition element is utilized to couple the shell kinematics on the macrostructure with the 3D solid on the mesostructure. This results in a method able to use complex geometries from CAD models as representative volume elements for shell structures.

This study focuses on the development of novel evaluation methods for the analysis of thin carbon reinforced concrete (CRC) structures. CRC allows for the exploration of slender components and innovative construction techniques due to its high tensile strength. In this contribution, the authors have extended the analysis of CRC shells from existing research. The internal structure of CRC specimens was explored using microtomography. The rovings within the samples were segmented from the three-dimensional tomographic reconstructions using a 3D convolutional neural network with enhanced 3D data augmentation strategies and further analyzed using image-based techniques. The main contribution is the evaluation of the manufacturing precision and the simulation of the structural behavior by measuring the carbon grid positions inside the concrete. From the segmentations, surface point clouds were generated and then integrated into a multiscale framework using a parameterized representative volume element that captures the characteristic properties of the textile reinforcement. The procedure is presented using an example covering all necessary design steps from computed tomography to multiscale analysis. The framework is able to effectively evaluate novel construction methods and analyze the linear-elastic behavior of CRC shells.

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