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.

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.

The objective of exploration seismology is to measure accurately reflected wavefields from subsurface interfaces in order to generate an image of the geological formations. More often the seismic data is non-uniformly sampled, i.e. the data is not acquired on an equidistantly spaced grid. This may result in artifacts during data processing that complicate interpretation. Sampling may be nonuniform because of human-related reasons such as: 1. Faulty equipment and positioning errors, 2. It may be due to environmental circumstances, such as cable feathering in marine acquisition induced by ocean currents or 3. Due to inaccessible areas in land acquisition (cities, rivers, and canyons).The generation of uniformly sampled data from nonuniformly sampled data is called reconstruction and many different methods to reconstruct seismic data have been published over the years. The method used in this paper is called reconstruction of nonuniformly sampled data with least squares Fourier transform. It is based on estimating the Fourier coefficients that describe the non-uniformly sampled data, and once these coefficients have been found the signal can be reconstructed on any suitable grid via an inverse Fourier transformation. The efficiency of the method is evaluated on both real and synthetic seismic. All necessary codes were written in MATLAB environment.

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.

In recent decades the effects of magnetic and electric fields on living cells and organisms have gained the increasedattention of researchers. In recent years, dielectrophoresis based microfluidics systems have been used to manipulatebiological micro particles, such as red blood cells, white blood cells, platelets, cancer cells, bacteria, yeast, microorganisms, proteins, DNA, etc. So most previous researchers have studied particle trajectory under theapplication of electric field in order to better design of such micro devices. In the current study the effect of nonuniformelectric field on a single cell is investigated. A neutral particle polarizes in the presence of electric field. It causes localchange in electrostatic potential distribution and local nonuniformity in electric field. These changes are ignored inprevious researches and effective dipole moment (EDM) approximation is applied to predict the DEP force exerted oncells. In the present research the effect of cell on electrostatic potential distribution and electric stresses acting on cellsurface is studied. To this end, the cell shape and internal boundary conditions on cell surface must be considered incomputational domain. To do this, Immersed Interface Method (IIM) which is a modified finite difference method isemployed. Some numerical results are presented to show the good accuracy of mentioned numerical method. Theelectric stresses on cell surface are calculated by Maxwell Stress Tensor (MST). Also some results are presented tovalidate the numerical solution and investigate the accuracy of EDM approximation. Other electrokinetic effects suchas electrophoresis and electro-osmosis are neglected in this study.

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.

A new wideband Wilkinson Power Divider which use the nonuniform substrate integrated waveguide (NSIW) method is presented in this paper. This structure utilizes NSIWs instead of the uniform quarter wavelength SIWs in conventional Wilkinson power divider. The proposed structure is analyzed by odd and even mode analysis. The proper NSIW section widths can be extracted by using even mode while the divider resistances are achieved by odd mode analysis. Moreover using of half mode structure in the NSIW and two output ports reduces the overall size of the proposed divider. Finally a wideband Wilkinson power divider is designed and simulated to verify the proposed design method. A good return loss (S11, S22) and insertion loss (S21) across a very wideband width from 10 GHz to 20 GHz is achieved. Also, the isolation (S23) is better than -10 dB from 9.5 GHz to 21.5 GHz for the designed NSIW divider.