Isogeometric analysis using T-splines

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities.     

A framework combining meshfree analysis and adaptive kriging for optimization of stiffened panels

Structural and Multidisciplinary Optimization - A framework is developed for structural optimization using an Element Free Galerkin (EFG) method for analyzing the structure, a kriging for surrogate...     

Isogeometric analysis for strain field measurements

In this paper, the potential of isogeometric analysis for strain field measurement by digital image correlation is investigated. Digital image correlation (DIC) is a full field kinematics measurement technique based on gray level conservation principle and the formulation we adopt allows for using arbitrary displacement bases. The high continuity properties of Non-Uniform Rational B-Spline (NURBS) functions are exploited herein as an additional regularization of the initial ill-posed problem. k-Refinement is analyzed on an artificial test case where the proposed methodology is shown to outperform the usual finite element-based DIC. Finally a fatigue tensile test on a thin aluminum sheet is analyzed. Strain localization occurs after a certain number of cycles and combination of NURBS into a DIC algorithm clearly shows a great potential to improve the robustness of non-linear constitutive law identification.     

Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.     

An innovative DoE strategy of the kriging model for structural reliability analysis

Structural and Multidisciplinary Optimization - An innovative strategy of the design of experiments (DoE) is proposed to reduce the number of calls of the performance function in the kriging-based...     

Maximization of buckling loads of composite panels using flexural lamination parameters

Unstiffened composite panels are optimized by using flexural lamination parameters as continuous design variables for the case in which the amounts of 0°, ±45°, and 90° plies are given. It is shown that for this case, the lamination parameters are located in a hexagonal domain. Continuous optimization is compared with genetic optimization for the stacking sequence that accounts for the discreteness of the design space and constraints on the number of contiguous plies of the same orientation. It is shown that only for very thin panels with low aspect ratios is there a significant difference between the continuous and discrete solutions.     

Bistatic scattering analysis for two-dimensional rough sea surfaces using an angular composite model

An angular composite model (ACM) is applied to analyse the bistatic scattering from two-dimensional sea surfaces. When the local scattered angle lies in the specular region, Kirchhoff approximation (KA) is used to evaluate the specular reflection, which predominates the total scattering in this region; the small perturbation method (SPM) is employed to deal with the diffuse reflection dominated by small roughness, as the local scattered angle is situated out of the specular region. This avoids dwelling on the tough question about how to choose the proper cut-off wave number like in the well-known two-scale model (TSM). Numerical illustrations are carried out for bistatic scattering coefficients versus wind speed, incident angle, incident frequency and polarization state, respectively. The comparison of numerical results of the ACM and other experimental and theoretical models in several configurations shows that the ACM is robust to give accurate numerical evaluations for bistatic scattering of rough sea surfaces.     

Design and analysis of stiffened composite panels including post-buckling and collapse

The European aircraft industry demands reduced development and operating costs, by 20% and 50% in the short and long term, respectively. Contributions to this aim are provided by the completed project POSICOSS (5th FP) and the running follow-up project COCOMAT (6th FP), both supported by the European Commission. As an important contribution to cost reduction a decrease in structural weight can be reached by exploiting considerable reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of post-buckling up to collapse. The POSICOSS team developed fast procedures for the post-buckling analysis of stiffened fibre composite panels, created comprehensive experimental data bases and derived suitable design guidelines. COCOMAT builds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The results comprise an extended experimental data base, degradation models, and improved certification and design tools as well as extended design guidelines.One major task of POSICOSS and COCOMAT is the development of improved analysis tools that are validated by experiments performed within the framework of the projects. Because the new tools must comprise a wide range of various aspects a considerable number of different structures had to be tested. These structures were designed under different objectives (e.g. large post-buckling region). For the design process, the consortiums applied state-of-the-art simulation tools and brought in their own design experience. This paper deals with the design process as performed within both projects and with the applied analysis procedures. It is focused on the DLR experience in the design and analysis of stringer-stiffened CFRP panels gained within the scope of these two projects.     

Life reliability assessment of twin-web disk using the active learning kriging model

Structural and Multidisciplinary Optimization - Compared with the traditional single turbine disk, the novel twin-web turbine disk (TWD) has a bright future in the application of the aero...     

Approximation of the critical buckling factor for composite panels

This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented.     

Adaptive control for manufacturing systems using infinitesimalperturbation analysis

Combining infinitesimal perturbation analysis (IPA) with stochastic approximation gives identification algorithms to estimate the optimal threshold value for failure-prone manufacturing systems consisting of one machine producing one part type. Two adaptive control schemes are proposed. The adaptive control schemes do not require the knowledge of the distribution functions of the up and down times. Under some appropriate conditions, the strong consistency, as well as the convergence rates, of the identification algorithms and the cost function is established for the adaptive control schemes. In particular, it is shown that central limit theorems hold for the identification algorithms     

基于凸优化的自适应CV模型*

针对CV模型分割精度不高、分割速度缓慢和易陷于局部最优等缺点,提出了一种新的基于凸优化的自适应CV模型。首先,引入了自适应权重项,对拟合中心的计算采用加权平均,提高了拟合中心计算的准确性;然后,在模型中加入了凸优化技术,以获取模型的全局最优解;最后,采用了Split Bregman方法进行快速求解,有效地提高了分割效率。实验结果表明,基于凸优化的自适应CV模型有效地提高了分割精度和效率,对初始化也具有较好的鲁棒性。     

Isogeometric analysis with trimming technique for problems of arbitrary complex topology

Trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to CAD files created by using NURBS. In the present work, it is shown that any complex multiply-connected NURBS domain can be described by using trimming curves only. Isogeometric analysis for linear elasticity problems of complex topology described in this way is presented. For fully communicative interaction between CAD and CAE, a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the IGES files exported from CAD system for Isogeometric analysis. Schemes for imposing essential and traction boundary conditions on trimming curves are presented. It has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated. With the examples of complex topology that could be described by employing trimming curves only, effectiveness and robustness of present method are demonstrated.     

Isogeometric contact analysis: Geometric basis and formulation for frictionless contact

This paper introduces an isogeometric framework for the numerical analysis of contact problems. In this approach, NURBS is utilized as basis for geometric representation and analysis. The contact surfaces and the underlying solids are parameterized in an identical paradigm. The use of NURBS geometry eliminates at the onset the geometric discontinuities induced by the traditional faceted approximation. Contact detection is carried out patch-wise, instead of element-wise, leading to an efficient and robust numerical algorithm. A strategy for smoothing sharp corners is also described. The algorithm does not rely on fillets but entails only a minor perturbation to the NURBS parameters. A variationally consistent surface-to-surface formulation is developed in the context of frictionless contact. Numerical examples are presented to demonstrate the performance and utility of the method.     

Adaptive driver model using a neural network

An adaptive driver model for longitudinal movements of a vehicle has been developed. It incorporates a conventional feedback brake controller, and both fixed and adaptive neural network controllers to produce the throttle demand. It has been interfaced with a vehicle model in a Simulink environment, and simulation studies indicate a high level of performance. Implementation of the adaptive driver model within a real-time environment has also been realized successfully. This work was presented in part at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002     

Adaptive isogeometric analysis using rational PHT-splines

Polynomial splines over hierarchical T-meshes (PHT-splines) have an efficient and simple local refinement algorithm, but fail to represent exactly certain complex engineering geometries. In this paper, based on the current isogeometric framework, we overcome the drawbacks of PHT-splines by extending these to Rational PHT-splines (RPHT-splines), and explore RPHT-splines as the basis for analysis. A residual-based posteriori error estimator using RPHT-splines basis functions is derived to guide the local refinement process adaptively. Numerical examples show the potential of RPHT-splines as the basis for the adaptive isogeometric analysis.