Isogeometric analysis of two-dimensional piezoelectric structures

Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures

Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

Isogeometric Analysis (IgA) is an emerging numerical procedure conceived as a useful advancement of the traditional Finite Element Method (FEM). The essence of IgA is to bridge the current communication gap between Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) modules by employing high-order smooth spline basis functions both for geometry modelling and the construction of the solution space of analysis. As such, the method enables major benefits, namely a simplified pre-processing workflow and enhanced accuracy per degree of freedom associated with the capability of by-passing the time-consuming mesh creation stage and preserving exact geometry regardless of grid refinement. Furthermore, a user’s prerogative of selecting bases with adequate interelement continuity allows for a direct discretization of high-order differential operators, thereby avoiding stress recovery algorithms at the patch level during post-processing. In this contribution, the isogeometric approach is introduced to the detailed analysis of a ship’s structural member. In this regard, an in-house MatLab code has been developed for the structural assessment of linearly elastic isotropic continua, defined by either one or multiple NURBS patches. Within the IgA framework, the displacement approach of the mechanical problem is treated in its equivalent weak form and the obtained variational statement is discretized by means of an isogeometric Navier solid element formulation. Patch tests, involving in-plane loaded steel plates, are preliminarily performed to verify the accuracy of the numerical prediction, delivered by the present code, with respect to its analytical counterpart. A typical T-beam with associated plating is then analysed under uniform loading. It is demonstrated that the proposed approach can be recommended for engineering practice.

Isogeometric analysis (IGA) is a computational technique that integrates computer-aided design (CAD) with finite element analysis (FEA) by employing the same basis functions for both geometry representation and solution approximation. While IGA offers numerous advantages, such as improved accuracy and efficiency, it also presents several challenges related to geometric modeling. Some of these challenges include accurately representing complex geometries with NURBS (Non-Uniform Rational B-Splines) or other basis functions used in IGA and generating high-quality meshes that conform to the complex geometry represented by NURBS curves/surfaces. This paper introduces an analytical framework to provide a more efficient and theoretically grounded method for generating curvilinear configurations and its analytical solution in IGA, bridging the gap between generated data and its physical representations. This innovative approach is distinguished by integrating the NURBS parameterization in curve generation and providing a corresponding framework to achieve a broader and more accurate explanation of meshes and properties, especially constructing new coordinates and calculating the physical displacements under these conditions. Our model enables the analytical understanding of complex curves from the UIUC airfoil and superformula datasets, demonstrating a deeper dive into simulations. This study signifies a pivotal juncture wherein machine-learning-based complex geometrical formulations are synergistically combined with actual isogeometric analysis.

Shape optimization of fluid cooling channel based on Darcy reduced-order isogeometric analysis

The isogeometric analysis (IGA), which employs non-uniform rational B-splines (NURBS) basis as shape functions for both representation of geometry and approximation of the field variables, owns several inherent advantages to become an effective numerical method such as an exact geometry description with fewer control points, high-order continuity, and high accuracy. Unlike the C0-continuity shape functions in the conventional finite element method (FEM), the high-order basis functions in IGA are not confined to one element, but span on several elements instead. This property makes the programming task difficult, and more importantly they cannot be straightforwardly embedded into the existing FEM framework. In this paper, we provide an effective numerical scheme by further extending the IGA based on the Bezier extraction of NURBS to study mechanical behavior of elasto-plastic problems in three-dimension (3D). The Bezier extraction operator decomposes NURBS functions into a set of Bernstein polynomials and provides C0-continuity Bezier elements for the IGA, which are similar to Lagrange elements structure. Consequently, the implementation of IGA is now similar to that of conventional FEM, and can easily be embedded in most existing FEM codes. The merits of the proposed formulation are also demonstrated by its convergence and validation studies against reference solutions considering both simple and complicated configurations.

Many Engineering structures, including electronic component assemblies, are inherently multi-scale in nature. These structures often experience complex local nonlinear behavior such as plasticity, damage or fracture. These local behaviors eventually lead to the failure at the macro length scale. Connecting the behavior across the length scales to develop an understanding of the failure mechanism is important for developing reliable products.To solve multi-scale problems in which the critical region is much smaller than the entire structure, an iterative solution approach based on domain decomposition techniques is proposed. Two independent models are constructed to model the global and local substructures respectively. The unbalanced force at the interface is iteratively reduced to ensure force equilibrium of the overall structure in the final solution. The approach is non-intrusive since only nodal values on the interface are transferred between the global and local models. Solution acceleration using SR1 and BFGS updates is also demonstrated. Equally importantly, the two updates are applied in a non-intrusive manner, meaning that the technique is implemented without needing access to the codes using which the sub-domains are analyzed. Code- and mesh-agnostic solutions for problems with local nonlinear material behavior or local crack growth are demonstrated. Analysis in which the global and local models are solved using two different commercial codes is also demonstrated.Engineering analysis using numerical models are helpful in providing insight into the connection between the structure, loading history, behavior and failure. Specifically, Isogeometric analysis (IGA) is advantageous for engineering problems with evolving geometry compared to the traditional finite element method (FEM). IGA carries out analysis by building behavioral approximations isoparametrically on the geometrical model (commonly NURBS) and is thus a promising approach to integrating Computer-Aided Design (CAD) with Computer-Aided Engineering (CAE).In enriched isogeometric Analysis (EIGA), the solution is enriched with known behavior on lower dimensional geometrical features such as crack tips or interfaces. In the present research, enriched field approximation techniques are developed for the application of boundary conditions, coupling patches with non-matching discretizations and for modeling singular stresses in the structure.The first problem solution discussed is to apply Dirichlet and Neumann boundary conditions on boundary representation (B-rep) CAD models immersed in an underlying domain of regular grid points. The boundary conditions are applied on the degrees of freedom of the lower dimensional B-rep part directly. The solution approach for the immersed analysis uses signed algebraic level sets constructed from the B-rep surfaces to blend the enrichedfield with the underlying field. The algebraic level sets provide a surrogate for distance, are non-iteratively (or algebraically) computed and allow implicit Boolean compositions.The methodology is also applied to couple solution approximations of decomposed patches by smoothly blending incompatible geometries to an arbitrary degree of smoothness. A parametrically described frame or interface is introduced to “stitch” the adjacent patches. A hierarchical blending procedure is then developed to stitch multiple unstructured patches including those with T-junctions or extraordinary vertices.Finally, using the EIGA technique, a computational method for analyzing general multimaterial sharp corners that enables accurate estimations of the generalized stress intensity factors is proposed. Explicitly modeled geometries of material junctions, crack tips and deboned interfaces are isogeometrically and hierarchically enriched to construct approximations with the known local behavior. specifically, a vertex enrichment is used to approximate the asymptotic field near the re-entrant corner or crack tip, Heaviside function is used to approximate the discontinuous crack face and the parametric smooth stitching technique is used to approximate the behavior across material interface. The developed method allows direct extraction of generalized stress intensity factors without needing a posteriori evaluation of path independent integrals for decisions on crack propagation. The numerical implementation is validated through analysis of a bi-material corner, interface crack and growth of an inclined crack in a homogeneous solid. The developed procedure demonstrates rapid convergence to the solution stress intensity factors with relatively fewer degrees of freedom, even with uniformly coarse discretizations.

Parallel isogeometric boundary element analysis with T-splines on CUDA

Despite of the fact that in the title the analysis of two-dimensional structures is indicated, we shall be concerned with three-dimensional structures made from composite non-homogeneus anisotropic linear visco-elastic materials. The problem considered is a quasi-static one in which inertia forces due to deformation could be neglected.

Isogeometric Analysis (IGA) has emerged as a powerful computational method that seamlessly integrates computer-aided design (CAD) and finite element analysis (FEA). It provides an innovative approach for solving complex engineering problems by employing the same basis functions used in CAD representations, such as Non-Uniform Rational B-Splines (NURBS), to discretize the computational domain. However, one of the challenges in IGA is the occurrence of crosspoints, which are regions where multiple NURBS patches meet. This presents a novel development of a crosspoint modification technique for Isogeometric Analysis, leveraging the capabilities of Artificial Intelligence (AI) algorithms. The aim is to overcome the limitations posed by crosspoints and enhance the accuracy and efficiency of IGA simulations. It utilizes AI-based methods, such as deep learning and pattern recognition, to identify and modify the crosspoint regions in the NURBS-based representation. The AI model is trained on a large dataset of known crosspoint configurations and their corresponding modifications, enabling it to learn the underlying patterns and relationships between the geometry and the required modifications. This trained model is then employed to automatically identify and modify crosspoints in new IGA problems, streamlining the pre-processing stage and reducing human intervention. The crosspoint modification technique incorporates various strategies to ensure geometric continuity and smooth transition across the modified crosspoint regions. These strategies include local refinement of the NURBS control points, adaptively adjusting the degrees of the adjacent patches, and optimizing the blending functions in the crosspoint vicinity. Several numerical experiments and comparative studies are conducted. The results demonstrate that the crosspoint modification using AI significantly improves the accuracy of the IGA simulations, particularly in regions affected by crosspoints. Moreover, the computational efficiency is enhanced as the automated modification reduces the manual effort required for crosspoint handling.
 This research contributes to the advancement of Isogeometric Analysis by introducing a novel AI-based crosspoint modification technique. By effectively addressing the challenges associated with crosspoints, the proposed method enhances the accuracy and efficiency of IGA simulations. The integration of AI algorithms with IGA holds great potential for future applications in various engineering disciplines, including structural analysis, fluid dynamics, and electromagnetics.

<abstract> <p>We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples.</p> </abstract>

Structural optimization with CADO method for a three-dimensional sheet-metal vehicle body

Isogeometric analysis (IGA) has recently become popular in computational science during the past decade or so. IGA tries to to unify both geometric and field representation; in other words, both the geometry and the fields are represented using the same underlying basis set. However, while the concept of IGA for differential equations is more common, extension to an integral equation framework is significantly more challenging. In this work, we present for the first time, the IGA as applied to integral equations encountered in electromagnetics. The presented approach relies on the subdivision scheme for both geometry and function representation. Results presented attest to the viability of the method.

Shape optimization is concerned about finding optimal designs under the aspect of some cost criteria often involving the solution of a partial differential equation (PDE) over the afore said unknown shape. In general, industrial cases involve a geometric model from Computer Aided Design (CAD). However, solving PDEs requires an analysis suitable working model, typically a Finite Element (FEM) triangulation. Hence, some of the geometric properties known from the CAD model may be lost during this format change. Therefore, we employ isogeometric analysis (IGA) instead, which has a tighter connection between geometry, simulation and shape optimization. In this paper, we present a self-contained treatment of gradient based shape optimization method with isogeometric analysis, focusing on algorithmic and practical aspects like computation of shape gradients in an IGA formulation and updating B-spline and NURBS geometries.

ABSTRACTThis paper aims to optimize both the topology of microstructure and macrostructure, by using the Moving Iso‐ Surface Threshold (MIST) method under the framework of Isogeometric Analysis (IGA). To achieve this, the physical response and the equivalent properties of the microstructure are solved by IGA. The physical response functions are defined at the control points. The NURBS fitting method is used to fit the physical response function, generating a NURBS surface for describing the physical response function, that is, the explicitly described physical response function surface. An iso‐surface cut the NURBS physical response surfaces to obtain the explicitly described structure topology. In addition, the standard IGS files of the NURBS physical response surface and iso‐surface can be transferred to Computer‐Aided‐Design (CAD) software without post‐processing. The multiscale structure can be easily assembled in CAD software using the proposed method. Finally, several numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function.