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Remanufacturing of worn blades with various defects normally requires processes such as scanning, regenerating a geometrical reference model, additive manufacturing (AM) through laser cladding, adaptive machining and polishing and quality inspection. Unlike the manufacturing process of a new part, the most difficult problem for remanufacturing such a complex surface part is that the reference model adaptive to the worn part is no longer available or useful. The worn parts may suffer from geometrical deformation, distortion and other defects because of the effects of harsh operating conditions, thereby making their original computer aided design (CAD) models inadequate for the repair process. This paper aims to regenerate the geometric models for the worn parts, which is a key issue for implementing AM to build up the parts and adaptive machining to reform the parts. Unlike straight blades with similar cross sections, the tip geometry of the worn tip of a twist blade needs to be regenerated by a different method.

This paper proposes a surface extension algorithm for the reconstruction of a twist blade tip through the extremum parameterization of a B-spline basis function. Based on the cross sections of the scanned worn blade model, the given control points and knot vectors are firstly reconstructed into a B-spline curve D. After the extremum of each control point is calculated by extremum parameterization of a B-spline basis function, the unknown control points are calculated by substituting the extremum into the curve D. Once all control points are determined, the B-spline surface of the worn blade tip can be regenerated. Finally, the extension algorithm is implemented and validated with several examples.

The proposed algorithm was implemented and verified through the exampled blades. Through the extension algorithm, the tip geometry of the worn tip of a twist blade can be regenerated. This method solved a key problem for the repair of a twist blade tip. It provides an appropriate reference model for repairing worn blade tips through AM to build up the blade tip and adaptive machining/polishing processes to reform the blade geometry.

The extension errors for different repair models are compared and analyzed. The authors found that there are several factors affecting the accuracy of the regenerated model. When the cross-section interval and the extension length are set properly, the restoration accuracy for the blade tip can be improved, which is acceptable for the repairing.

The lack of a reference geometric model for worn blades is a significant problem when implementing blade repair through AM and adaptive machining processes. Because the geometric reference model is unavailable for the repair process, reconstruction of the geometry of a worn blade tip is the first crucial step. The authors proposed a surface extension algorithm for the reconstruction of a twist blade tip. Through the implementation of the proposed algorithm, the blade tip model can be regenerated.

Remanufacturing of worn blades with various defects is highly demeaned for the aerospace enterprises considering sustainable development. Unlike straight blades, repair of twist blades encountered a very difficult problem because the geometric reference model is unavailable for the repair processes. This paper proposed a different method to generate the reference model for the repair of a twist blade tip. With this model, repair of twist blades can be implemented through AM to build up the blade tip and adaptive machining to subtract the extra material.

The authors proposed a surface extension algorithm to reconstruct the geometric model for repair of twist blades.

This paper aims to present error compensation based on surface reconstruction to improve the positioning accuracy of industrial robots.

In previous research, it has been proved that the positioning error of industrial robots is continuous on the two-dimensional manifold of six-joint space. The point cloud generated by positioning error data can be used to fit the continuous surfaces, which makes it possible to apply surface reconstruction on error compensation. The moving least-squares interpolation and the B-spline method are used for the error surface reconstruction.

The results of experiments and simulations validate the effectiveness of error compensation by the moving least-squares interpolation and the B-spline method.

The proposed methods can control the average of compensated positioning error within 0.2 mm, which meets the requirement of a tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly.

The error surface reconstruction based on the B-spline method has great superiority because fewer sample points are needed to use this method than others while keeping the compensation accuracy at the same level. The control points of the B-spline error surface can be adjusted with measured data, which can be applied for the error prediction in any temperature field.

To explore three‐dimensional scanning technology in capturing the shape of inflated parachutes for accurate estimation of surface area and volume.

The volume and surface area of an inflated round parachute are important parameters for the design and analysis of its performance. However, it is difficult to acquire the three‐dimensional (3D) surface shape of a parachute due to its flexible fabric and dynamic movement. This paper presents how we collect 3D data with a laser scanner and calculate volume and surface area of parachutes from their scans. The necessary data clean and approximation steps with non‐uniform B‐spline function are introduced and implemented. Numerical integration methods are employed to estimate surface area and volume. The approximation of the parachute based on an ellipsoid is compared with the numerical integration approach in their volumes and surface areas.

It is found that 3D scanning technology, with help of mathematic program developed, provides a feasible mean to estimate the surface area and volume of inflated parachutes. The numerical integration method derived in this paper is reliable and robust for the computation.

It is the first time that the 3D shape of an inflated parachute has been scanned with a laser scanner. The mathematical methods developed for processing of scan data are useful for others who use 3D scanning technology. The computational approach and results of surface area and volume of inflated parachutes are valuable to parachute performance modeling and design community.

Non‐linear transformation of freeform curves and surfaces is useful in computer‐aided design and computer graphics. It is highly desirable that the original and transformed curves or surfaces are defined using the same representation. But freeform curves and surfaces defined by control points are invariant only under affine transformations, and not so under non‐linear transformations. This paper develops a method that can perform non‐linear transformations of freeform curves to specific accuracies, while retaining the same representation. It involves first applying the transformation to the control points and then modifying them so that the resulting curve and the exact transformed curve are equal at a specific number of points, which is the number of control points. Refinement to the approximation is made by increasing the number of control points. A method for measuring the maximum positional error has been implemented and this is used to facilitate an algorithm for automatic refinement. Extension of the method for surfaces is also given.

The purpose of this paper is to present some of the key achievements. At DLR, a sophisticated interdisciplinary aircraft design process is being developed, using the CPACS data format (Nagel et al., 2012; Scherer and Kohlgrüber, 2016) as a means of exchanging results. Within this process, TRAFUMO (Scherer et al., 2013) (transport aircraft fuselage model), built on ANSYS and the Python programming language, is the current tool for automatic generation and subsequent sizing of global finite element fuselage models. Recently, much effort has gone into improving the tool performance and opening up the modeling chain to further finite element solvers.

Much functionality has been shifted from specific routines in ANSYS to Python, including the automatic creation of global finite element models based on geometric and structural data from CPACS and the conversion of models between different finite element codes. Furthermore, a new method for modeling and interrogating geometries from CPACS using B-spline surfaces has been introduced.

Several new modules have been implemented independently with a well-defined central data format in place for storing and exchanging information, resulting in a highly extensible framework for working with finite element data. The new geometry description proves to be highly efficient while also improving the geometric accuracy.

The newly implemented modules provide the groundwork for a new all-Python model generation chain, which is more flexible at significantly improved runtimes. With the analysis being part of a larger multidisciplinary design optimization process, this enables exploration of much larger design spaces within a given timeframe.

In the presented paper, key features of the newly developed model generation chain are introduced. They enable the quick generation of global finite element models from CPACS for arbitrary solvers for the first time.

This preliminary research revolute the conventional clothing design process by true designs from three‐dimensional (3D) rather than two‐dimensional. The aim of the research is to develop a handy 3D clothing design software tool for general garment designers. Work carried out in this paper is the preliminary result of the 3D software infrastructure. In addition, 3D collar design based on a mathematical formula is accomplished as a template for other garment portions. Object‐oriented technology is invoked as a tool for software developing. The system is divided into two major modulus, the user interface and the kernel. The user interface is used to collect messages from the users, and then send it to the kernel for further computations. Moreover, it exhibits real‐time pictures received from the kernel. The major work of the kernel is to handle the operations that are called by the user interface. In this paper two basal collars, convertible collar and shirt collar, are illustrated as diversified figurations.

Numerical instability such as spurious oscillation is an important problem in the simulation of heat wave propagation. The purpose of this study is to propose a time discontinuous Galerkin isogeometric analysis method to reduce numerical instability of heat wave propagation in the medium subjected to heat sources, particularly heat impulse.

The essential vectors of temperature and the temporal gradients are assumed to be discontinuous and interpolated individually in the discretized time domain. The isogeometric analysis method is applied to use its property of smooth description of the geometry and to eliminate the mesh-dependency. An artificial damping scheme with proportional stiffness matrix is brought into the final discretized form to reduce the numerical spurious oscillations.

The numerical spurious oscillations in the simulation of heat wave propagation are effectively eliminated. The smooth description of geometry with spline functions solves the mesh-dependency problem and improves the numerical precision.

The time discontinuous Galerkin method is applied within the isogeometric analysis framework. The proposed method is effective in the simulation of the wave propagation problems subjecting to impulse load with numerical stability and accuracy.

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

As computer simulation increasingly supports engineering design and manufacture, the requirement for a computer software environment providing an integration platform for computational engineering software increases. The potential benefits to industry are considerable. As a first step in the long‐term development of such a system, a computer software environment has been developed for pre‐ and post‐processing for unstructured grid‐based computational simulation. Arbitrary computer application software can be integrated into the environment to provide a multi‐disciplinary engineering analysis capability within one unified computational framework. Recognising the computational demands of many application areas, the environment includes a set of parallel tools to help the user maximise the potential of high performance computers and networks. The paper will present details of the environment and include an example of, and discussion about, the integration of application software.

The aim of the paper is to provide an economically viable solution for the blade repair process. There is a continual increase in the repair market, which requires an increased level of specialised technology to reduce the repair cost and to increase productivity of the process.Design/methodology/approach – This paper introduces the aerospace component defects to be repaired. Current repair technologies including building‐up and machining technology are reviewed. Through the analysis of these available technologies, this paper proposes an integrated repair strategy through information integration and processes concentration.Findings – Provides detailed description and discussion for the repair system, including 3D digitising system, repair inspection, reverse engineering‐based polygonal modelling, and adaptive laser cladding and adaptive machining process.Originality/value – This paper describes a 3D non‐contact measurement‐based repair integration system, and provides a solution to create an individual blade‐oriented nominal model to achieve adaptive repair process (laser cladding/machining) and automated inspection.