In order to solve the problem of the trajectory planning of robotic plasma cladding for complex surface coating, the concept of non-uniform rational B-spline (NURBS) function open-/closed-loop ...mapping is proposed firstly in this work to explore the new approach of the trajectory planning for complex NURBS surfaces. The trajectory planning is carried out by a 2D-NURBS curve
C
(
u
) on a 2D plane, which is mapped on a predefined 3D-NURBS surface
S
(
u
,
v
) using the NURBS surface function to form a 3D mapping curve named NURBS function mapping (NURBS-FM) curve. Using the fixed step (FS) interpolation, the equal chord length (ECL) interpolation, the equal arc length (EAL) interpolation, and the equal bow height (EBH) interpolation, etc., a complex curve can be interpolated. The FS/ECL/EAL/EBH can be defined as constraint. Depending on where the constraint is applied, the NURBS-FM can be divided into open-loop mapping and closed-loop mapping. The NURBS function open-loop mapping (NURBS-FOLM) is carried out along the route of
u
→
C
(
u
) →
S
(
u
,
v
), while the NURBS function closed-loop mapping (NURBS-FCLM) along the route of
u
→
C
(
u
) →
S
(
u
,
v
) →
u
→ …. The constraint is applied to the 2D-NURBS curve in NURBS-FOLM, while to the 3D NURBS-FM curve in NURBS-FCLM. The NURBS-FOLM and NURBS-FCLM can ensure that the interpolation points on the 2D-NURBS curve and 3D NURBS-FM curve have the ECL/EAL/EBH characteristics, respectively. When the 3D NURBS-FM curve is regarded as plasma cladding trajectory, the NURBS-FCLM can provide engineers with a new ECL/EAL/EBH interpolation method for cladding trajectory. Using the NURBS-FCLM approach based on the serial robotic plasma cladding, a high entropy alloy coating is prepared on Q235 substrate which employed the AlCoCrCuNiNb high entropy alloy powder with optimized parameters (Ar flow, ion gas flow, current, powder feeding speed, cladding feedrate) = (6L/min, 1.7L/min, 115A, 15 mm/s, 1.4 mm/s). The formation of the complex spacial curve coating on the complex surface is well without obvious defects. The simulation and experiment verify that the NURBS-FCLM is feasible and effective. It provides the technical and theoretical basis for the serial robotic plasma cladding trajectory planning of complex surface coating. With the increasing application of complex parts in various industries, the NURBS-FOLM and NURBS-FCLM technologies have more and more broad application prospects in the manufacturing of new complex product coatings and remanufacturing of old ones based on serial robotic laser/arc cladding platform.
This study aims to present a three-dimensional (3D) numerical solution for investigating the free vibration and buckling responses of annular plate, conical and cylindrical shell made of functionally ...graded (FG) porous rock materials. Isogeometric analysis (IGA) is utilized in order to develop the 3D numerical solution. Furthermore, the computational package is developed using C# Programming, which is an object-oriented programming language. The distribution of porosity along the thickness direction obeys the cosine function rule, for which the top surface is porosity-free, and the bottom surface is porosity-rich. The weak form for free vibration and buckling analyses are discretized and approximated through 3D NURBS based IGA. The accuracy of the present solutions is verified by the results obtained from published data. The convergence of 3D FGP solutions is checked, and it is found that a quartic NURBS element can yield high-accuracy results with the lowest computational cost. Afterward, the numerical results showed the impact of porosity of the FGP annular plate, FGP conical, and cylindrical shell on free vibration and buckling problems.
Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes ...even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and static coupled electromechanical loads. The discretization of problem domain is based on basis functions generated from NURBS, which are used for both geometric description and approximation of solution field variables. To capture the discontinuity across the crack-faces and the singularity at the crack-tip, the isogeometric approximation is locally enriched by discontinuous Heaviside function and asymptotic crack-tip branch functions. The sixfold enrichment functions particularly suitable for electromechanical crack-tip singularity of piezoelectric materials are used. To evaluate the generalized fracture parameters, a domain-form of electromechanical interaction integral is employed. For dynamic analysis, the implicit time integration scheme considering inertial effect is taken. Five numerical examples for single and mixed-modes of impermeable cracks are considered and the generalized fracture parameters under dynamic and static loads are analyzed. The accuracy and effectiveness of the proposed XIGA are illustrated through numerical investigations of the generalized dynamic and static fracture parameters. Numerical results are validated against the reference solutions derived from the boundary element methods. The effects of some numerical aspect ratios on generalized fracture parameters are also investigated. Additionally, we present some numerical results of quasi-static crack propagation in piezoelectric solids using the developed XIGA, taking fracture toughness anisotropy of polarized electroelastic materials into account, and employing the maximum modified hoop stress intensity factor criterion for predicting the growing direction of crack.
•XIGA dynamic and static fracture formulation in piezoelectricity is developed.•Crack growth modeling in brittle piezoelectric solids is presented.•Static generalized intensity factors of cracked piezoelectric solids are analyzed.•Transient dynamic responses of impermeable and permeable cracks are studied.•Effects of polarization, enrichments, meshes, loadings, etc. on GIFs are investigated.
An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple ...first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) 11, is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.
The concept of non-uniform rational B-spline (NURBS) mapping projection curves (NURBS-MPCs) is proposed in this work. A NURBS-MPC is a projection curve on a NURBS surface of a NURBS curve. The ...bisection method is used to interpolate NURBS-MPCs. Using an assigned chord, the interpolation of a NURBS-MPC can be obtained easily, and the milling precision of the NURBS-MPC can be controlled effectively. Based on the NURBS theory, the bisection method, and the parametric programming method, an online NURBS software package (NURBS-SP) for FANUC 0i-MB/MC/MD CNC system and an offline NURBS toolbox (NURBS-T) for Matlab have been developed. Using an example of a planar NURBS curve, a NURBS-MPC is created on a NURBS surface. The simulation and milling of the NURBS-MPC show that the bisection method is feasible and effective. The online NURBS-SP endows the NURBS interpolation function for those CNC systems only equipped with linear interpolation (G01) and circular interpolation (G02/G03) and extends the interpolation functions and machining capability of low-middle level three-axis milling machines. The interactive application of the NURBS-T and NURBS-SP can accomplish the design, simulation, and milling for NURBS-MPCs. This feature makes them to have broad application prospects in CNC machining industry.
•Efficient, object-oriented algorithm for evaluation of B-spline basis functions.•Software can be easily built by open-source standard tools.•Implementation suited for variety of application areas ...(viz. IGA, optimization, interpolation, visualization).•Software uses spline-type independent interface.•Software converts between common file formats of different application areas.
This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element analysis, and optimization. The library features reading and writing for various file formats and a wide range of spline manipulation algorithms. Further, a new efficient and objective-oriented algorithm for B-spline basis function evaluation is included. All features are available by a spline-type independent interface. The library is written in modern C++ with CMake as build system. This enables it for usage in typical scientific applications. It is provided as open-source library.
In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis ...(IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity. IGA features very small numerical dissipation and dispersion when compared to other methods for the solution of PDEs. The use of multiple patches allows to overcome the conventional limitations of single patch IGA, thanks to the gained flexibility in the design of the computational domain, especially when its representation is quite involved as in bioengineering applications. We propose two algorithms for the preprocessing of CAD models of complex surface and volumetric NURBS geometries with cavities, such as atria and ventricles: our purpose is to obtain geometrically and parametrically conforming NURBS multipatch models starting from CAD models. We employ those algorithms for the construction of an IGA realistic representation of a human heart. We apply IGA for the discretization of the Monodomain equation, which describes the evolution of the cardiac action potential in space and time at the tissue level. This PDE is coupled with suitable microscopic models to define the behavior at cellular scale: the Courtemanche–Ramirez–Nattel model for the atrial simulation, and the Luo–Rudy model for the ventricular one. Numerical simulations on realistic human atria and ventricle geometries are carried out, obtaining accurate and smooth excitation fronts by combining IGA with the multipatch approach for the geometrical representation of the computational domains, either surfaces for the atria or solids for the ventricles.
•Multipatch Isogeometric Analysis is applied to cardiac electrophysiology.•CAD geometries are preprocessed into conforming multipatch isogeometric NURBS.•Numerical simulations on realistic human atria and ventricles are carried out.
Boundary representations (B-reps) using Non-Uniform Rational B-splines (NURBS) are the de facto standard used in CAD, but their utility in deep learning-based approaches is not well researched. We ...propose a differentiable NURBS module to integrate NURBS representations of CAD models with deep learning methods. We mathematically define the derivatives of the NURBS curves or surfaces with respect to the input parameters (control points, weights, and the knot vector). These derivatives are used to define an approximate Jacobian used for performing the “backward” evaluation to train the deep learning models. We have implemented our NURBS module using GPU-accelerated algorithms and integrated it with PyTorch, a popular deep learning framework. We demonstrate the efficacy of our NURBS module in performing CAD operations such as curve or surface fitting and surface offsetting. Further, we show its utility in deep learning for unsupervised point cloud reconstruction and enforce analysis constraints. These examples show that our module performs better for certain deep learning frameworks and can be directly integrated with any deep-learning framework requiring NURBS.
•A differentiable NURBS module for integrating splines with machine learning.•Validation of the module with CAD operations such as curve and surface fitting.•Integration with loss functions that impose geometric constraints in deep learning.•Order of magnitude improvement over existing spline-based surface reconstruction.
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