Non-uniform Rational B-spline Surfaces Research Articles

Scraper Point Attitude Optimization in the Scraping Process of Aviation Composite Curved Surface

Aiming at the interference problem between the tool and the surface during the contact between the blade position and the composite material during the off-line programming scraping process of aviation composite parts, the contact effect of the blade during the scraping process of the composite surface is discussed, and a rotation projection attitude optimization strategy is proposed. Firstly, by constructing the mathematical model of the contact between the scraper and the surface, the geometric properties of the scraper and its contact on the surface are analyzed. Then, the non-uniform rational B-spline (NURBS) surface is used to reconstruct the surface, and the position information of the local area of the contact point is obtained to obtain the normal direction and curvature. In order to evaluate the contact effect of the scraper, an objective function is defined to minimize the contact error between the scraper linear trajectory and its projection on the surface, thereby quantifying the contact accuracy. By comparing the position and attitude of the scraper before and after optimization, the effectiveness of the proposed optimization method is verified. The optimized scraper posture significantly improves the contact accuracy with the composite surface, better adapts to the geometric characteristics of the complex surface, and ensures the efficiency and consistency of the scraping process. The research results provide a new perspective and method for the future development of automatic scraping process, and also provide an effective solution and technical means for other industries in the application scenario of curved scraping.

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Optimizing algorithm for high-precision imaging stitching systems based on spline surfaces

As optical systems continue to advance, non-uniform rational B-spline (NURBS) surfaces increasingly being considered in asymmetric optical systems due to their localized control characteristics. However, the representation of NURBS surfaces has complicated the analysis of these systems, leading to a significant computational burden. To address this challenge, we propose an optimizing algorithm for imaging optical systems based on high-precision ray tracing of NURBS surfaces. This method initiates with getting a knot grid as prior information, in conjunction with the Newton-Raphson algorithm, to obtain high-precision numerical solutions for the intersection of rays with a NURBS surface. Building upon this methodology, we introduce an optimization technique that includes shape evaluation to generate an evaluation function specific to NURBS surfaces. This approach is then applied within a rapid optimization process that accounted for the region of ray influence. Under consistent control point grids and sampling ray conditions, we present an off-axis four-mirror system to showcase that our algorithm has achieved a computational efficiency improvement of approximately 14 times compared to the previous method. This high-precision imaging design based on spline surfaces fulfills the need for efficient and accurate algorithms for NURBS surface applications in various imaging systems, providing guidance for practical applications.

Comparative Study on the Interest in Non-Uniform Rational B-Splines Representation versus Polynomial Surface Description in a Freeform Three-Mirror Anastigmat

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view.

Optimization and knowledge discovery of profiled end walls in a turbine stage at a low Reynolds number

To comprehensively explore flow control method of profiled end wall for turbine stage at low Reynolds numbers, a surrogate model optimization platform including non-uniform rational B-spline surface parameterization method, support vector regression, and improved chaos particle swarm optimization algorithm is integrated. Optimization designs have been carried out for stator profiled end walls, rotor profiled end wall, and combined end walls, respectively. The results indicate that under the constraint of the output power, the application of various profiled end wall design cases all can effectively improve the aerodynamic performance of the turbine stage. By organizing the flow field of downstream rotor, the profiled end wall of stator can significantly affect the stage efficiency. The flow control benefits of the profiled end wall of the rotor is from the obstruction of the cross migration of the pressure side leg of the horseshoe vortex. The application of profiled end wall on stator has the most practical engineering value. Self-organizing maps and Shapley methods are used to explore potential correlation information of aerodynamic parameters and summarize design experience. The sensitive design variables of profiled end walls are extracted. Based on the local controllability of NURBS surfaces, the regions that affect the stage efficiency are mainly concentrated in the middle of the stator passage, near the stator trailing edge and near the rotor leading edge. The regions with a significant impact on the output power of the turbine stage are near the trailing edge of the rotor and stator. The corresponding design rules of end walls modeling are summarized.

Shape optimization of non-matching isogeometric shells with moving intersections

While shape optimization using isogeometric shells exhibits appealing features by integrating design geometries and analysis models, challenges arise when addressing computer-aided design (CAD) geometries comprised of multiple non-uniform rational B-splines (NURBS) patches, which are common in practice. The intractability stems from surface intersections within these CAD models. In this paper, we develop an approach for shape optimization of non-matching isogeometric shells incorporating intersection movement. Separately parametrized NURBS surfaces are modeled using Kirchhoff–Love shell theory and coupled using a penalty-based formulation. The optimization scheme allows shell patches to move without preserving relative location with other members during the shape optimization. This flexibility is achieved through an implicit state function, and analytical sensitivities are derived for the relative movement of shell patches. The introduction of differentiable intersections expands the design space and overcomes challenges associated with large mesh distortion, particularly when optimal shapes involve significant movement of patch intersections in physical space. Throughout optimization iterations, all members within the shell structures maintain the NURBS geometry representation, enabling efficient integration of analysis and design models. The optimization approach leverages the multilevel design concept by selecting a refined model for accurate analysis from a coarse design model while maintaining the same geometry. We adopt several example problems to verify the effectiveness of the proposed scheme and demonstrate its applicability to the optimization of the internal stiffeners of an aircraft wing.

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

Three-dimensional reconstruction of industrial parts from a single image

This study proposes an image-based three-dimensional (3D) vector reconstruction of industrial parts that can generate non-uniform rational B-splines (NURBS) surfaces with high fidelity and flexibility. The contributions of this study include three parts: first, a dataset of two-dimensional images is constructed for typical industrial parts, including hexagonal head bolts, cylindrical gears, shoulder rings, hexagonal nuts, and cylindrical roller bearings; second, a deep learning algorithm is developed for parameter extraction of 3D industrial parts, which can determine the final 3D parameters and pose information of the reconstructed model using two new nets, CAD-ClassNet and CAD-ReconNet; and finally, a 3D vector shape reconstruction of mechanical parts is presented to generate NURBS from the obtained shape parameters. The final reconstructed models show that the proposed approach is highly accurate, efficient, and practical.

NURBS-based path planning for aerosol jet printing of conformal electronics

Conformal printing offers a promising capability to integrate complex electronic functionality with intricate objects consisting of curved surfaces. However, motion planning to support these printing configurations presents a challenge, in part due to conventional reliance on tessellated surface representations that limit the accuracy and scalability of the printing process. In this paper, we introduce a direct approach to conformal aerosol jet printing on topographically complex surfaces, represented using non-uniform rational B-splines (NURBS). Using the NURBS surface definition directly offers a scalable and continuous approach for toolpath generation, which is well-aligned with standard computer-aided design practices. We select a patch that directly corresponds to the area of interest on the NURBS surface and extract the associated surface points. These surface points are then appropriately connected to generate the machine code (G-code) for a 3-axis printing system. We demonstrate this capability by printing a strain gauge on a curved model of a wind turbine blade. Our approach offers a promising avenue for manufacturing printed electronics with diverse applications that require conformal printing. This approach is particularly valuable for incorporating printed circuits on intricate underlying structures, including structural health monitoring for aerospace and civil infrastructure applications.

Effect of crown retention systems and loading direction on the stress magnitude of posterior implant-supported restorations: A 3D-FEA

This study aimed to investigate the effect of four retention systems for implant-supported posterior crowns under compressive loading using three-dimensional finite element analysis. A morse-taper dental implant (4.1 × 10 mm) was designed with Computer Aided Design software based on non-uniform rational B-spline surfaces. According to International Organization for Standardization 14,801:2016, the implant was positioned at 3 mm above the crestal level. Then four models were designed with different crown retention systems: screw-retained (A), cement-retained (B), lateral-screw-retained (C), and modified lateral-screw-retained (D). The models were imported to the analysis software and mesh was generated based on the coincident nodes between the juxtaposed lines. For the boundary conditions, two loads (600 N) were applied (axial to the implant fixture and oblique at 30°) totaling 8 conditions according to retention design and loading. The von-Mises stress analysis showed that different retention systems modify the stress magnitude in the implant-supported posterior crown. There is a similar stress pattern in the implant threads. However, models C and D presented higher stress concentrations in the crown margin in comparison with A and B. The oblique loading highly increased the stress magnitude for all models. In the simulated conditions, part of the stress was concentrated at the lateral screw under axial loading for model C and oblique loading for model D. The results indicate a possible new failure origin for crown retained using lateral screws in comparison to conventional cement-retained or screw-retained systems.

Full-LSPIA: A Least-Squares Progressive-Iterative Approximation Method with Optimization of Weights and Knots for NURBS Curves and Surfaces

The Least-Squares Progressive-Iterative Approximation (LSPIA) method offers a powerful and intuitive approach for data fitting. Non-Uniform Rational B-splines (NURBS) are a popular choice for approximation functions in data fitting, due to their robust capabilities in shape representation. However, a restriction of the traditional LSPIA application to NURBS is that it only iteratively adjusts control points to approximate the provided data, with weights and knots remaining static. To enhance fitting precision and overcome this constraint, we present Full-LSPIA, an innovative LSPIA method that jointly optimizes weights and knots alongside control points adjustments for superior NURBS curves and surfaces creation. We achieve this by constructing an objective function that incorporates control points, weights, and knots as variables, and solving the resultant optimization problem. Specifically, control points are adjusted using LSPIA, while weights and knots are optimized through the LBFGS method based on the analytical gradients of the objective function with respect to weights and knots. Additionally, we present a knot removal strategy known as Decremental Full-LSPIA. This strategy reduces the number of knots within a specified error tolerance, and determines optimal knot locations. The proposed Full-LSPIA and Decremental Full-LSPIA maximize the strengths of LSPIA, with numerical examples further highlighting the superior performance and effectiveness of these methods. Compared to the classical LSPIA, Full-LSPIA offers greater fitting accuracy for NURBS curves and surfaces while maintaining the same number of control points, and automatically determines suitable weights and knots. Moreover, Decremental Full-LSPIA yields fitting results with fewer knots while maintaining the same error tolerance.

Form-finding for Free-form Reticulated Shell Structure Considering Structural Performance and Regularization of Node Connection Patterns

In this study, we propose a form-finding method for the free-formed reticulated shell structure, considering both structural performance and regularization of node connection patterns. The coordinates of the nodes of the reticulated shells are represented on the non-uniform rational B-spline (NURBS) surface. According to the principal curvature, the clustering classifies the node connection patterns into specified groups. Multi-objective optimization is performed to minimize the strain energy and maximum deviation in clusters. A multi-objective genetic algorithm is used to solve the optimization problem. The mechanical properties of the optimal solution obtained in a numerical example are discussed to confirm the effectiveness of the proposed method.

Contact Analysis for Cycloid Pinwheel Mechanism by Isogeometric Finite Element

Cycloid drives are generally used in precision machinery requiring high-reduction ratios, such as robot joint (RV) reducers. The contact stress of cycloidal gears greatly affects lifetime and transmission performance. Traditional finite element method (FEM) has less computational efficiency for contact analysis of complex surface. Therefore, in this paper, isogeometric analysis (IGA) was employed to explore the multi-tooth contact problem of the cycloid pinwheel drive. Based on the nonuniform rational B spline (NURBS) curved surface generation method, the NURBS tooth profile of the cycloid gear was reconstructed. In addition, the NURBS surface of the cycloid gear–pin tooth–output pin was generated via the element splicing method. A geometrical analysis model of cycloid pinwheel drive was established to solve the contact force of the meshing pair under different input angles and compared with the finite element method in terms of convergence, resultant accuracy, and solving timeliness. The results show that isogeometric analysis has higher accuracy and efficiency than the finite element method in calculating the contact stress and contact force. The error of the IGA is only 8.8% for 10 × 10 elements in contact, while the error of the finite element method reaches about 40%. The method can improve the contact simulation accuracy of the cycloid drive and provides a reference for the design evaluation of RV reducer.

Fast Reconstruction Model of the Ship Hull NURBS Surface with Uniform Continuity for Calculating the Hydrostatic Elements

The fast reconstruction of the ship hull nonuniform rational B-spline (NURBS) surface with uniform continuity is essential for calculating hydrostatic elements such as waterplane area and molded volume in real time. Thus, this study proposes a fast reconstruction model with uniform continuity to solve the problem of uniform continuity and splicing in the separate model of hull bow and stern surfaces. The proposed model includes the NURBS curve generation (UCG) algorithm with uniform continuity and the hybrid NURBS surface generation (HSG) algorithm. The UCG algorithm initially fits the feature points using the global interpolation algorithm and then precisely constructs straight-line segments in the curve using the improved flattening algorithm. In comparison, the HSG algorithm adaptively selects the surface knot vectors according to the parameters of the section curves. In this study, the profile of discontinuous compartments is uniformly expressed, effectively avoiding various articulation problems in separation modeling. The results of comparative experiments show that the NURBS surface generated using the HSG algorithm can accurately express the characteristics of various parts of the hull with uniform continuity, and the calculation speed of the proposed model can be increased by up to 8.314% compared with the existing best-performing algorithms. Thus, the proposed model is effective and can improve computational efficiency to a certain extent. The NURBS surfaces generated by the proposed model can be further applied to calculating the hydrostatic elements of hulls and compartments.

An integrated design approach for simultaneous shape and topology optimization of shell structures

In this work, a novel design approach is developed to carry out shape and topology optimization of shell structures simultaneously. This approach effectively integrates the IsoGeometric Analysis (IGA) method, the Adaptive Bubble Method (ABM) and the Finite Cell Method (FCM) to make full use of their respective advantages in shell structure optimization. To be specific, the IGA method using Non-Uniform Rational B-Splines (NURBS) elements is adopted to analyze the shell structure and realize shape optimization with merits of exact shell surface representation geometrically and rotation-free shell formulation physically; the ABM is utilized to insert deformable holes adaptively in the parametric domain of the NURBS surface for topology optimization of the shell structure; the FCM is employed to facilitate the optimization process by simplifying significantly the discrimination and the numerical integration processes of trimmed elements involved in fixed-mesh analysis of the holed shell structure. Based on this integrated design approach of IGA/ABM/FCM, shape optimization can be implemented by directly optimizing the control-point coordinates of the NURBS surface in the physical space, while topology optimization could be carried out simultaneously in the parametric domain as easily as for 2D planar structures. Finally, representative examples are investigated to demonstrate the effectiveness and advantages of the proposed design approach.

Isogeometric degenerated shell formulation for post-buckling analysis of composite variable-stiffness shells

Variable-stiffness (VS) laminated shells with curved fibers have gradually become a promising lightweight structural concept in the aerospace field. However, as the complexity of the shell geometry and the fiber angle increases, the traditional finite element method (FEM) requires mesh refinement to guarantee accurate discretization, which significantly increases the computational cost, especially in the post-buckling analysis with multiple solving requirements. In this study, a non-uniform rational B-Splines (NURBS)-based degenerated solid shell formulation in the total Lagrangian framework is proposed for the post-buckling analysis of VS laminated shells. Since the nonlinear function related to the rotational degrees of freedom (DOFs) is additionally introduced into the displacement field expression, the restriction on the magnitude of the nodal rotations is effectively eliminated. In addition, the paper adopts the NURBS surface reconstruction technology based on the point-line-surface features to build B-spline CAD models from the point cloud with geometric imperfect features. Then, an integrated modeling-analysis framework for predicting the post-buckling behavior of VS structures with geometric imperfections is proposed. A series of numerical examples systematically demonstrate that the framework can effectively conduct the post-buckling analysis of shell structures with geometric imperfections. Meanwhile, the accuracy and robustness of the solutions by IGA are proved to be better than FEM.

Effect of crown stiffness and prosthetic screw absence on the stress distribution in implant-supported restoration: A 3D finite element analysis.

This in-silico investigation evaluated the mechanical impact of Morse tape implant-abutment interface and retention system (with and without screw) and restorative materials (composite block and monolithic zirconia) by means of a three-dimensional finite element analysis (3D-FEA). Four 3D models were designed for the lower first molar. A dental implant (4.5 × 10 mm B&B Dental Implant Company) was digitized (micro CT) and exported to computer-aided design (CAD) software. Non-uniform rational B-spline surfaces were reconstructed, generating a 3D volumetric model. Four different models were generated with the same Morse-type connection, but with a different locking system (with and without active screw) and a different crown material made of composite block and zirconia. The D2 bone type, which contains cortical and trabecular tissues, was designed using data from the database. The implants were juxtaposed inside the model after Boolean subtraction. Implant placement depth was simulated for the implant model precisely at crestal bone level. Each acquired model was then imported into the finite element analysis (FEA) software as STEP files. The Von Mises equivalent strains were calculated for the peri-implant bone and the Von Mises stress for the prosthetic structures. The highest strain values in bone tissue occurred in the peri-implant bone interface and were comparable in the four implant models (8.2918e-004-8.6622e-004 mm/mm). The stress peak in the zirconia crown (64.4 MPa) was higher than in the composite crown (52.2 MPa) regardless of the presence of the prosthetic screw. The abutment showed the lowest stress peaks (99.71-92.28 MPa) when the screw was present (126.63-114.25 MPa). Based on this linear analysis, it is suggested that the absence of prosthetic screw increases the stress inside the abutment and implant, without effect on the crown and around the bone tissue. Stiffer crowns concentrate more stress on its structure, reducing the amount of stress on the abutment.

Isogeometric-based mapping modeling and buckling analysis of stiffened panels

Modeling and analysis of stiffened panels are two key technologies in the design of aerospace thin-walled structures. For the stiffened panels with complex geometry, classical finite element analysis (FEA) and conventional isogeometric analysis (IGA) based on explicit geometry usually require time-consuming and labor-intensive geometric processing, and additional coupling matrices to be ready for analysis. In this study, a new method for modeling and buckling analysis of stiffened panels is proposed, which provides a more efficient and simpler way. During the modeling process, the stiffeners are treated as curves on surfaces, which is not explicitly defined using the control-point-based representation of curves, but implicitly defined using parameter curves in the parametric space of the surface. Mapping modeling provides more accurate geometric description and transfer the complex modeling problems (three-dimensional space) of stiffeners on free-form surface into simple modeling problems in the regular parametric space (two-dimensional space). During the buckling analysis process, a new mapped stiffener element based on mapping modeling is proposed, which can model the section of the eccentric stiffener without changing the geometry. The precise normal information of the Non-Uniform Rational B-Splines (NURBS) surface can ensure that the stiffeners are perpendicular to the skin. In addition, the coupling of the stiffener and the skin is automatic, without any additional coupling matrix. This buckling analysis framework realizes the complete integration of modeling and analysis. Furthermore, for the stiffened panels with cutouts, the trimmed surface analysis (TSA) method is extended to be used for the numerical integration of the trimmed stiffeners, which means that no additional geometric process is required. Finally, four numerical examples of different types of stiffened panels are constructed, involving metal, trimmed surface, classical grid-stiffener, free-form surface, variable-stiffness composites, and curvilinear grid-stiffener. Several numerical examples of static and buckling analysis of stiffened panels with high fidelity demonstrate the effectiveness of the proposed framework.

Ship hull surface reconstruction from scattered points cloud using an RBF neural network mapping technology

The ship hull surface reconstruction based on three-dimensional scattered points cloud is vital to Computer-Aided Design modeling of ship reverse engineering. There are several problems with traditional methods: the preprocessing of a large-scale scattered points cloud is complicated, and the result is susceptible to noise. Because of the “black box” characteristic, the surface reconstruction based on neural networks cannot apply to the practical engineering. To address these issues, combining the Radial Basis Function neural network and Non-Uniform Rational B-Spline interpolation algorithm, a new ship hull surface reconstruction method was proposed, which can satisfy the standard geometric model description in Computer-Aided Design system. Firstly, the Radial Basis Function neural network was used to pre-fit the three-dimensional scattered points cloud. Then the mathematical model of the surface was mapped. Finally, based on the bilinear interpolation algorithm, the mathematical model was transformed to a Non-Uniform Rational B-Spline surface to apply to the ship practical engineering. In addition, by comparing our method with the traditional method, the advantages of our method in surface reconstruction quality and surface repair ability were verified, which provided a new way for the application of Radial Basis Function neural network in ship reverse engineering.

A model for gastrointestinal tract motility in a 4D imaging phantom of human anatomy.

Gastrointestinal (GI) tract motility is one of the main sources for intra/inter-fraction variability and uncertainty in radiation therapy for abdominal targets. Models for GI motility can improve the assessment of delivered dose and contribute to the development, testing, and validation of deformable image registration (DIR) and dose-accumulation algorithms. To implement GI tract motion in the 4D extended cardiac-torso (XCAT) digital phantom of human anatomy. Motility modes that exhibit large amplitude changes in the diameter of the GI tract and may persist over timescales comparable to online adaptive planning and radiotherapy delivery were identified based on literature research. Search criteria included amplitude changes larger than planning risk volume expansions and durations of the order of tens of minutes. The following modes were identified: peristalsis, rhythmic segmentation, high amplitude propagating contractions (HAPCs), and tonic contractions. Peristalsis and rhythmic segmentations were modeled by traveling and standing sinusoidal waves. HAPCs and tonic contractions were modeled by traveling and stationary Gaussian waves. Wave dispersion in the temporal and spatial domain was implemented by linear, exponential, and inverse power law functions. Modeling functions were applied to the control points of the nonuniform rational B-spline surfaces defined in the reference XCAT library. GI motility was combined with the cardiac and respiratory motions available in the standard 4D-XCAT phantom. Default model parameters were estimated based on the analysis of cine MRI acquisitions in 10 patients treated in a 1.5T MR-linac. We demonstrate the ability to generate realistic 4D multimodal images that simulate GI motility combined with respiratory and cardiac motion. All modes of motility, except tonic contractions, were observed in the analysis of our cine MRI acquisitions. Peristalsis was the most common. Default parameters estimated from cine MRI were used as initial values for simulation experiments. It is shown that in patients undergoing stereotactic body radiotherapy for abdominal targets, the effects of GI motility can be comparable or larger than the effects of respiratory motion. The digital phantom provides realistic models to aid in medical imaging and radiation therapy research. The addition of GI motility will further contribute to the development, testing, and validation of DIR and dose accumulation algorithms for MR-guided radiotherapy.