Creo自由式曲面与T-Splines功能的对比

Creo的自由式曲面工具和Rhino的T-Splines网格建模插件非常适合于概念产品的造型,两款软件具有相同的功能,本文通过从选择方式、形状、操作、创建、皱褶、对称、多级和曲面输出等几个方面进行详细的对比,分析两曲面中各自特点,为产品的进一步完善提供有意义的指导。尤其是Creo在曲面输出方面具有重要的优势,在其他方面如能借鉴T-Splines的部分功能,其自由式建模将更加方便,会受到广大造型师的欢迎。

T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains

In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.

T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.

NUAT T-splines of odd bi-degree and local refinement

This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces （NUAT T-splines for short） of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces （NUAT B-spline surfaces）. Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix.

On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines

Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.

SOME PROPERTIES FOR ANALYSIS-SUITABLE T-SPLINES

Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.

An efficient data structure for calculation of unstructured T-spline surfaces

To overcome the topological constraints of non-uniform rational B-splines,T-splines have been proposed to define the freeform surfaces.The introduction of T-junctions and extraordinary points makes it possible to represent arbitrarily shaped models by a single T-spline surface.Whereas,the complexity and flexibility of topology structure bring difficulty in programming,which have caused a great obstacle for the development and application of T-spline technologies.So far,research literatures concerning T-spline data structures compatible with extraordinary points are very scarce.In this paper,an efficient data structure for calculation of unstructured T-spline surfaces is developed,by which any complex T-spline surface models can be easily and efficiently computed.Several unstructured T-spline surface models are calculated and visualized in our prototype system to verify the validity of the proposed method.

基于T-Spline的全自动几何拓扑修复方法

从高质量曲面网格生成的需求出发,提出了一种基于 T-Spline 的全自动几何拓扑修复方法.本文方法创新性主要可归纳为: 1)对原有计算机辅助设计(Computer aided design, CAD)几何模型不进行任何修改保留其本真,自动识别 CAD 几何模型中常见不必要的几何特征,成功解决了 CAD 几何模型中存在的几何瑕疵,如短边、窄面、退化边、退化面、非连续光滑边界及尖锐特征等,利用新生成的\虚边"、\虚面"处理几何瑕疵,同时通过虚拓扑重构 CAD 几何模型的 B-Rep;2)开发了一套 CAD/CAE 集成系统,统一了几何模型与计算分析模型,实现计算机辅助工程(Computer aided engineering, CAE)与CAD 两者的无缝集成,所有拓扑修复操作及后续 CAE 分析计算均在同一环境下进行,避免了几何模型在 CAE 与 CAD 系统间进行转换时造成的数据丢失.该方法能够对复杂实体实现全自动几何拓扑修复及网格生成,实验表明,在保证不失真的前提下,修复后的几何模型能够生成质量良好的网格且能降低网格的生成规模,验证了本文方法的实用性和有效性,以满足工程实际分析的需要.

Compact Car-Body Surface Design with T-spline Surface

Creating proper B-spline surface models is a very challenging task for designers in car-body surface design.Due to the tensor-product structure of B-spline surface,some undesirable issues of the redundant control points addition,incomplete surface definition and the difficulty of trimming boundary alteration frequently occur,when designing the car-body surface with B-spline surfaces in local-feature-lines construction,full-boundary-merging and visual surface trimming.A more efficient approach is proposed to design the car-body surface by replacing B-spline surface with classical T-spline surface.With the local refinability and multilateral definition offered by Tspline surface,those designing issues related with B-spline surface can be overcomed.Finally,modeling examples of the door,hood and rear-window are given to demonstrate the advantage of T-spline surface over B-spline surface in car-body surface design.

New Algorithm for Local Shape Preservation T-Spline Surface Skinning

Surface skinning is a widely used algorithm in CAD modeling which permits designer to pass surface through several section curves, thus providing modeling process with powerful ability to describe complex shapes and transform the 2D design intention into 3D space. This paper contributes in the combination of T-Spline technology and surface skinning modeling by introducing a new algorithm for local shape preservation T-Spline surface skinning. The examples given in the paper show that this algorithm is effective.

Research on a toolpath generation method of NC milling based on space-filling curve

Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.

使用Rhino结合T-spline插件快速创建戏装小姐头饰模型

随着戏曲艺术广泛深入到大众的休闲生活中,大量的中小戏装工厂应运而生。根据生产需求利用三维建模技术创建戏装小姐头饰模型,分析Rhino软件结合T-spline插件在头饰建模中的应用及优势。本文以头饰虚拟物的创建抛砖引玉,将数字化设计融入传统手工艺制造中,达到帮助制作人员了解戏装产品的样式和结构,创建戏装产品模型库,便于戏装产品分类管理和二次开发,节约实物存放空间等目的。

ON T-SPLINE CLASSIFICATION

The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-standard T-splines and give the proof for the semi-standard of bi-degree(1,d)and(d,1)T-splines.

A survey on the local refinable splines

This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis.

A morphing machining strategy for artificial bonet

In this work, a novel morphing machining strategy （MMS） is proposed. In the method, the workpiece is progressively carved out from the stock. Pitfalls in conventional iso-height strategy, such as sharp edges and unevenly distributed left-over materials, are overcome. Moreover, to calculate different levels in the MMS, an energy-based morphing algorithm is proposed. Finally, the proposed strategy is employed in the machining of artificial bone represented by a T-spline surface. The excellent properties of T-spline, such as expressing complex shapes with a single surface, have been well adopted to artificial bone fabri- cation. Computer simulation and the actual machining of the middle finger bone show the feasibility of the proposed strategy.