Computing constant offsets of a NURBS B-Rep

The International Journal of Advanced Manufacturing Technology, 2005

Proposed in this paper is a new approach for offset surface construction using three-dimensional (3D) distance volumes. After converting an original compound surface into a triangular mesh, the approach creates a distance volume of the triangular mesh. With this distance volume and a given offset value, it extracts the offset points in each slice to create a sequence of two dimensional (2D) cross-sections. The approach then performs offset surface construction using the serial cross-sections. For more accurate and efficient computation of the distance volume, the concept of space division is combined with the concept one of distance propagation to the whole space of interest. The resulting offset surface is a G 1 composite surface consisting of three kinds of surfaces: skinned, capped, andor branched surfaces. The proposed approach provides offset surfaces that are accurate and free of degeneracy. Some experimental results demonstrate its usefulness and quality.

Metals, 2020

The scope of this work is to present a reverse engineering (RE) methodology to achieve accurate polygon models for 3D printing or additive manufacturing (AM) applications, as well as NURBS (Non-Uniform Rational B-Splines) surfaces for advanced machining processes. The accuracy of the 3D models generated by this RE process depends on the data acquisition system, the scanning conditions and the data processing techniques. To carry out this study, workpieces of different material and geometry were selected, using X-ray computed tomography (XRCT) and a Laser Scanner (LS) as data acquisition systems for scanning purposes. Once this is done, this work focuses on the data processing step in order to assess the accuracy of applying different processing techniques. Special attention is given to the XRCT data processing step. For that reason, the models generated from the LS point clouds processing step were utilized as a reference to perform the deviation analysis. Nonetheless, the proposed ...

Journal of Manufacturing Science and Engineering, 2021

The composite sheet layup process involves stacking several layers of a viscoelastic prepreg sheet and curing the laminate to manufacture the component. Demands for automating functional tasks in the composite manufacturing processes have dramatically increased in the past decade. A simulation system representing a digital twin of the composite sheet can aid in the development of such an autonomous system for prepreg sheet layup. While finite element analysis (FEA) is a popular approach for simulating flexible materials, material properties need to be encoded to produce high-fidelity mechanical simulations. We present a methodology to predict material parameters of a thin-shell FEA model based on real-world observations of the deformations of the object. We utilize the model to develop a digital twin of a composite sheet. The method is tested on viscoelastic composite prepreg sheets and fabric materials such as cotton cloth, felt, and canvas. We discuss the implementation and develo...

A new approach to model the actual machining result as a NURBS surface is presented, which explicitly expresses the geometry and topology of the final product and increases the clarity in the mathematical representation of quasistatic machining errors. Most of the available models that estimate interaction of quasistatic machining errors present the actual position of individual machined points and are unable to explicitly describe the resulting machined surface. During the machining process, the desired geometry is mapped from the ideal computer-aided design (CAD) vector space into the machine tool’s vector subspaces. Using a Jacobian of the deformed geometry, it is shown that for a variety of three-axis machine tool configurations, a linear operator can be found to express this transformation. Classified error operators for all different configurations of three-axis machine tools are derived and the applicability of the developed method is illustrated by simulating the machining process using case studies. The developed model can be utilised in virtual machining and simulation of the machining process, modification of the design within a design for a manufacturing platform, and also in on-line error compensation during the machining process.

Finite Elements in Analysis and Design, 2016

International Journal for Numerical Methods in Engineering, 1989

Finite element models of the continuumsbased theories and two-dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the thirdorder are presented in a single theory. Results of linear and non-linear bending, natural vibration and stability of composite laminates are presented for various boundary.conditbns and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non-linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non-linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative. I. INTRODUCTION Increased utilization of composite materials in a variety of structures, including space and underwater vehicles, autotnotive parts, electronic and medicai devices, and sports equipment, has led to increased research activity in the mechanical characterization, structural modelling, and failure and damage assessment of composite materials. While composite materials offer many desirable structural properties over conventional materials, they also present challenging technical problems in the understanding of their structural behaviour, manufacturing, and in the damage and failure modes developed during their service:The subject of composite materials is an interdisciplinary area where chemists, materials scientists, chemical 'engineers, mechanical engineers, structural engineers and manufacturing engineers contribute to the overall product. From computational mechanics considerations, the study of composite materials involves modelling of fabrication processes (heat and mass transfer, and fluid flow) and structural response including micromechanics aspects, inelasticity and damage. Laminated composites consist of two or more different composite materials that are bonded together to achieve the best properties of the constituent layers. Most composite laminates are made of layers of the same orthotropic material, with the material coordinates of each layer oriented differently with respect to the laniinate coordinates .

Composite Structures, 2003

Some optimization methods have recently been developed to deal with discrete variable problems such as that involving the ply angles and stacking sequence of composite laminates. However, much calculation is still required for the algorithms. A regression equation of the response surface would allow the finite element analysis to be replaced with the regression equation, saving much time in optimization design. The response surface of composite laminated structures is estimated using regression analysis in this study. The information of the surface can be obtained quickly and accurately. Usually, simple polynomials are used as base functions in regression, but the results obtained unsatisfactory in this work. Considering the periodic and directional property of the design variables (ply angles), trigonometric functions are used as base functions in regression and they fit the surface very well. According to the characteristics of ply angle and trigonometric function, the value of variable can be chosen to smoothen the response surface, greatly increasing the accuracy of the regression. This study first establishes the regression procedure, and then applies it to examples of a marine propeller and a rotor wing. The regression is used with a genetic algorithm to search for optimum ply angles in the examples, saving much time while maintaining accuracy.

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011

International Journal of Computer Aided Engineering and Technology, 2008

In this paper, numerical slicing of parametric B-Rep solids has been proposed based on the concepts of virtual cloud points and Delaunay triangulation for the purpose of layered manufacturing. The layer geometry thus obtained readily lent itself to application of an optimum hatching algorithm that minimises the build time. The problem has been treated as intersection of parametric surfaces. The purpose is to estimate the slice geometry, both its domain and boundary, which will enable in building an automatic database of each slice for the purpose of finding the optimum hatching direction. The algorithm and Matlab™ code have been developed for a general parametric B-Rep solid. The proposed slicing methodology has been implemented and presented here for two different B-Rep solids, namely, a non-rational Bezier solid and a NURBS solid. It was observed that developments in this direction will ensure further automation and streamlining of the layered manufacturing process with an integration established from CAD solid model to the actual layering in the machine.