Various methods for parametric interpolation of NURBS curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a feedrate planning module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X-Y table confirm that the developed method improves contour accuracy significantly compared to previously proposed adaptive-feedrate and curvature-feedrate algorithms.

In the present investigation, static analysis of thin-walled shell-like structures based on isogeometric approach is presented. Since the higher order NURBS is well suited for describing the exact geometry and providing -continuity, so they are used as basis functions for bridging the gap between design and analysis. The IGA method has been shown that the properties of the NURBS basis functions lead in many cases to superior accuracy per degree of freedom with respect to finite element method. So several thin shell structures are investigated by two approaches of rotation free thin shell element based on Kirchhoff theory and three dimensional solid element by using higher order NURBS basis functions throughk -refinement strategy. It is observed that, 3D solid elements have no difficulties in dealing with curved edges and have good performance in modelling and analysis. For low order of NURBS basis functions, one can observe weak convergence rate, whereas for higher values of order of NURBS, the results are identical to those of shell element, which confirms that, only by applying the lengthwise of mesh refinement, the 3D solid element can have acceptable performance.

In spite of increasingly utilizing high speed machining (HSM), the conventional tool path generation methods which are based on linear/circular blocks by applying standard strategies like parallel, z constant and Iso are usually employed in practice. Even though these tool-paths are employed by non-linear interpolators they have inherent limitations for HSM applications. This paper presents a new method for tool path generation in terms of NURBS. In order to increase the continuity of machining in HSM, a helical topology tool path in terms of NURBS is developed. This method reduces the number of CNC blocks up to five times. This algorithm creates a 2D-horizontal guide plane by offsetting the contour edges of the design surface. After that the inside offset of the contour is generated at a computed distance and then the contour and all its offsets are projected on the CL-surface. Finally, the tool-paths are approximated with NURBS approximation algorithm. The algorithm is designed to minimize the number of control points. An example of proposed approach consisting the comparison of the conventional method and verification is given.

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modelling discrete cracks. Moreover, the repetition of two different control points between two patches can create a discontinuity and also demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. Various numerical simulations for edge and center cracks demonstrate the suitability of the isogeometric analysis approach to fracture mechanics.

With the advancement of the manufacturing processes and the continuing need for increasingly precise assemblies, consideration of dimensional and geometric tolerances has been of great importance in tolerance analysis of mechanical assemblies. Therefore, in recent decades, several methods have been developed and implemented for calculating the influences of geometric errors of components on the final performance of the assembly. One of the proposed methods for tolerance analysis is the Direct Linearization Method (DLM). However, DLM has significant advantages in dimensional tolerance analysis, due to simplifications used in this technique, it does not have the ability to solve assemblies including free form profiles. In this research, a new method has been proposed to consider the complex profiles in the process of DLM. In the proposed combination method, rational Bezier curves have been used to define component profiles such as elliptical profiles, cams, edge joints, and non-circular profiles that have a complex error variation. Then, by using principles of DLM and rational Bezier equations, the developed algorithm is successfully accomplished. In this way, we can not only use significant advantages of DLM in dimensional tolerance analysis but also it is possible to solve assemblies including a component with complex profiles without any simplification. The developed hybrid approach has been presented in detail by solving an example of assembly tolerance analysis. Finally, validation has been performed and the accuracy of the proposed approach was confirmed using Monte Carlo simulation.

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation jx, and/or shear strain Uxz, as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.

In this paper, the extended isogeometric analysis based on Bé zier extraction of NURBS is applied for Investigating stress intensity factor and fatigue life in the two-dimensional crack problems with thermal and mechanical cyclic loading. By transforming NURBS function to linear combination of Bernstein functions defined over C0-continuous Bé zier elements, the extended isogeometric analysis can be implemented in the extended finite element method framework. Grid points around the crack line and crack tip are identified by the level set representation. Then, discontinuous enrichment functions are added to the isogeometric analysis approximation. Thus, this method does not require remeshing. The interaction integral method and Paris law has been used to extract stress intensity factor and evaluate fatigue life, respectively. Numerical examples are examined to validate the efficiency of the proposed method. The effect of adaptive refinement strategies on computational cost and convergence is studied. Numerical examples showed that the presented method produces highly accurate results, yet it is beneficial to implement.

Introduction: In the present work, the steps of constructing hybrid phantoms have been studied. Mathematical and voxel phantoms are two various kinds of computational human body models which used in dose evaluations and estimations. In mathematical phantoms, organs contour define with mathematical equations and therefore they are not realistic, unlike voxel phantoms are image-based and more real. In turn, the disadvantage of voxel phantoms is extreme dependence of organs contour on CT and MRI image contrast. Hybrid phantoms are more realistic than mathematical phantoms and more desirable than voxel phantoms due to their flexibility in the shape and size of organs. In this approach, organs surface is defined with nonuniform rational B-spline (NURBS) surface which is a mathematical technique used in 3D graphics and animations extensively.Methods: Three steps are carried out to generate a hybrid phantom. (1) Transforming 2D images of human body to 3D model (2) Producing a 3D polygon mesh model of human body and internal organs (3) Creating NURBS. Initially, CT and MRI images for identifying soft and hard tissues are used. Then, two first steps can be constructing with software codes such as 3D-Doctor. For third step, NURBS modeling software can be used such as Rhinoceros.Results: We constructed hybrid phantoms with real CT and MRI images and the result is the Rhinoceros normal outcome file as *.rhp. It can be used for any size of human body because the size of organs is changeable. This pliability is the effect of NURBS control points which is the most important advantage of hybrid phantoms.Conclusion: We used advantages of both mathematical and voxel phantoms in constructing hybrid phantoms and thus they have the desirable shape and flexibility in organs. We should transform this phantom to voxel for applying in Monte carlo codes (MCNP). This voxelisation could be performing with MATLAB codes.Furthermore heart and respiratory motions can be simulated with this technique in 4D phantoms.

Employing the Isogeometric Analysis method for solution of nonlinear compressible elastic materials, generally known as hyperelasticity, is the subject of this article. For this purpose, the matrix of coefficients is derived and by the linearization of governing equations the discretized equilibrium equations are obtained and a solution algorithm is presented. To study the performance and accuracy of the method in compressible hyperelastic problems, the obtained results are compared with those of finite elements. The presented approach, besides providing a good flexibility in geometrical modeling, results in a smaller system of equations and consequently reducing the computational cost. Furthermore, despite having large deformations, the need for remeshings is alleviated. Also, the effects of the number of load increments, as well as, the number of Gauss integration points on the convergence of the solution are studied.