Academic literature on the topic 'C0 formulation'
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Journal articles on the topic "C0 formulation"
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Wells, Garth N., and Nguyen Tien Dung. "A C0 discontinuous Galerkin formulation for Kirchhoff plates." Computer Methods in Applied Mechanics and Engineering 196, no. 35-36 (July 2007): 3370–80. http://dx.doi.org/10.1016/j.cma.2007.03.008.
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Liu, Zhenqi, Alison B. Lansley, Tu Ngoc Duong, John D. Smart, and Ananth S. Pannala. "Increasing Cellular Uptake and Permeation of Curcumin Using a Novel Polymer-Surfactant Formulation." Biomolecules 12, no. 12 (November 23, 2022): 1739. http://dx.doi.org/10.3390/biom12121739.
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Several therapeutically active molecules are poorly water-soluble, thereby creating a challenge for pharmaceutical scientists to develop an active solution for their oral drug delivery. This study aimed to investigate the potential for novel polymer-surfactant-based formulations (designated A and B) to improve the solubility and permeability of curcumin. A solubility study and characterization studies (FTIR, DSC and XRD) were conducted for the various formulations. The cytotoxicity of formulations and commercial comparators was tested via MTT and LDH assays, and their permeability by in vitro drug transport and cellular drug uptake was established using the Caco-2 cell model. The apparent permeability coefficients (Papp) are considered a good indicator of drug permeation. However, it can be argued that the magnitude of Papp, when used to reflect the permeability of the cells to the drug, can be influenced by the initial drug concentration (C0) in the donor chamber. Therefore, Papp (suspension) and Papp (solution) were calculated based on the different values of C0. It was clear that Papp (solution) can more accurately reflect drug permeation than Papp (suspension). Formulation A, containing Soluplus® and vitamin E TPGs, significantly increased the permeation and cellular uptake of curcumin compared to other samples, which is believed to be related to the increased aqueous solubility of the drug in this formulation.
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Saleeb, A. F., and T. Y. Chang. "On the hybrid-mixed formulation of C0 curved beam elements." Computer Methods in Applied Mechanics and Engineering 60, no. 1 (January 1987): 95–121. http://dx.doi.org/10.1016/0045-7825(87)90131-9.
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Nguyen-Quoc, T., S. Nguyen-Hoai, and D. Mai-Duc. "An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates." International Journal of Computational Methods 16, no. 04 (May 13, 2019): 1850102. http://dx.doi.org/10.1142/s0219876218501025.
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In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.
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Briassoulis, D. "Thin element applications of a new formulation for C0 structural elements." Computers & Structures 37, no. 6 (January 1990): 1097–103. http://dx.doi.org/10.1016/0045-7949(90)90021-s.
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Kumar, Ajay, Pradeep Bhargava, and Anupam Chakrabarti. "Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method." Advanced Materials Research 585 (November 2012): 44–48. http://dx.doi.org/10.4028/www.scientific.net/amr.585.44.
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In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the present results of problems with those available in the published literature. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, new results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.
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Yu, Kai-Ming, Yu Wang, and Charlie C. L. Wang. "Smooth geometry generation in additive manufacturing file format: problem study and new formulation." Rapid Prototyping Journal 23, no. 1 (January 16, 2017): 34–43. http://dx.doi.org/10.1108/rpj-06-2015-0067.
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Purpose In the newly released ASTM standard specification for additive manufacturing file (AMF) format – version 1.1 – Hermite curve-based interpolation is used to refine input triangles to generate denser mesh with smoother geometry. This paper aims to study the problems of constructing smooth geometry based on Hermite interpolation on curves and proposes a solution to overcome these problems. Design/methodology/approach A formulation using triangular Bézier patch is proposed to generate smooth geometry from input polygonal models. Different configurations on the boundary curves in the formulation are analyzed to further enrich this formulation. Findings The study shows that the formulation given in the AMF format (version 1.1) can lead to the problems of inconsistent normals and undefined end-tangents. Research limitations/implications The scheme has requirements on the input normals of a model, only C0 interpolation can be generated on those cases with less-proper input. Originality/value To overcome the problems of smooth geometry generation in the AMF format, the authors propose an enriched scheme for computing smooth geometry by using triangular Bézier patch. For the configurations with less-proper input, the authors adopt the Boolean sum and the Nielson’s point-opposite edge interpolation for triangular Coons patch to generate the smooth geometry as a C0 interpolant.
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Martini, L., and R. Vitaliani. "On the polynomial convergent formulation of a C0 isoparametric skew beam element." Computers & Structures 29, no. 3 (January 1988): 437–49. http://dx.doi.org/10.1016/0045-7949(88)90396-3.
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Briassoulis, D. "The four-node C0 Mindlin plate bending element reformulated, Part I: Formulation." Computer Methods in Applied Mechanics and Engineering 107, no. 1-2 (August 1993): 23–43. http://dx.doi.org/10.1016/0045-7825(93)90167-v.
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Singh, S. K., and A. Chakrabarti. "Static, Vibration and Buckling Analysis of Skew Composite and Sandwich Plates Under Thermo Mechanical Loading." International Journal of Applied Mechanics and Engineering 18, no. 3 (August 1, 2013): 887–98. http://dx.doi.org/10.2478/ijame-2013-0053.
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Abstract Static, vibration and buckling behavior of laminated composite and sandwich skew plates is studied using an efficient C0 FE model developed based on refined higher order zigzag theory. The C0 FE model satisfies the interlaminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model, the first derivatives of transverse displacement have been treated as independent variables to overcome the problem of C1 continuity associated with the plate theory. The C0 continuity of the present element is compensated in the stiffness matrix formulation by adding a suitable term. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature is made consistent with the total strain field by using field consistent approach. Numerical results are presented for different static, vibration and buckling problems by applying the FE model under thermo mechanical loading, where a nine noded C0 continuous isoparametric element is used. It is observed that there are very few results available in the literature on laminated composite and sandwich skew plates based on refined theories. As such many new results are also generated for future reference
Dissertations / Theses on the topic "C0 formulation"
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SOLA, FEDERICO. "Simulation of Local Effects, Energy Absorption and Failure Mechanism in Multilayered and Sandwich Structures." Doctoral thesis, Politecnico di Torino, 2016. http://hdl.handle.net/11583/2644377.
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The present dissertation describes the research work carried out towards:
I. developing of analytical and numerical models for accurate and efficient analysis of laminates and sandwiches under different loading conditions (static analyses, impulsive loading and low velocity impacts);
II. developing of techniques to improve structural performances of composites structures by tuning their energy absorption mechanism;
A higher order theory (AD-ZZ) including zig-zag effects, transverse shear continuity, variable transverse displacement and layerwise representation is presented for analysis of laminates and sandwiches. This theory is cast in such a way that the unknowns in the model will involve only five variables like equivalent single layer models: the three displacement components and the two shear rotations of the normals on the reference surface. It is advantageous to formulate the theory in this way, as it provides the opportunity to refine its through-the-thickness representation by adding computational layers in the thickness direction without increasing the number of unknowns. After extensive evaluation of the accuracy obtained by the above mentioned theory for a variety of structures, the AD-ZZ model is enriched by adding a set of continuity functions in order to treat laminates and structures with in-plane discontinuities (e.g. bonded joints, two material wedge) under a unified approach without adding new unknowns.
Speaking of techniques to improve structural performances, two approaches are presented: variable stiffness composites and stitching. The former tool works on the strain energy of the structure computing fibre distributions that minimize unwanted energy contributions and maximize the wanted ones. The latter prescribes the insertions of transverse reinforcements in sandwich structures. The homogenized mechanical properties of this structure, required by the AD-ZZ model to perform the analysis, are evaluated through virtual material tests using a 3D FE model. The results obtained applying these techniques demonstrate that both are effective in reducing transverse stresses at critical interfaces and, in certain cases, in improving bending stiffness.
New C0 displacement-based and stress-based finite elements for analysis of laminated and sandwich plates based on the AD-ZZ model are developed. To achieve this goal, a new technique that converts derivatives of functional degrees of freedom contained in the AD-ZZ is presented. Both the elements satisfy all the requirements of computationally efficient finite element models for analysis of multilayered structures, namely 1) the number of degrees of freedom is independent from the number of layers; 2) no shear correction factors or penalty number are added in the formulation. Consistent shear fields are obtained for the present finite element formulations. Numerical results demonstrate that these new elements are robust, accurate and computationally efficient for analysis of multilayered structures.
In order to study structures subjected to impact loading a new simulation procedure is developed. It is based on the AD-ZZ model and considers the crushing behaviour of soft-like media without performing each time a detailed 3D finite element analysis. Numerical results show that the response of composites undergoing low velocity impact is very accurately predicted with low computational effort. Overall, the present procedure holds great promise for analysis of laminated and sandwich structures undergoing low velocity impact.
Conference papers on the topic "C0 formulation"
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Morandini, Marco, and Pierangelo Masarati. "Implementation and Validation of a 4-Node Shell Finite Element." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34473.
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This paper discusses the formulation and implementation of a 4-node C0 shell element within a general-purpose multibody formulation. A geometrically consistent set of strains and curvatures, defined in a co-rotational framework, is augmented by Enhanced Assumed Strains (EAS) and Assumed Natural Strains (ANS), to alleviate shear and membrane locking. The shell element formulation is validated by solving several static and dynamic problems from the open literature. The proposed element has been successfully used for the coupled structural and fluid-dynamics analysis of flapping wing micro-aerial vehicles.
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Orth, Fabian J., and Karan S. Surana. "p-Version Two Dimensional Beam Element for Geometrically Nonlinear Analysis." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0098.
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Abstract This paper presents a p-version geometrically nonlinear formulation (GNL) based on total Lagrangian approach for a three node two dimensional curved beam element. The hierarchical element approximation functions and the corresponding nodal variables are derived directly from the Lagrange family of interpolation functions. The resulting element displacement approximation is hierarchical and can be of arbitrary and different polynomial orders in the longitudinal and the transverse directions of the beam element and ensures C0 continuity. The element geometry is described by the coordinates of the nodes located on the axis of the beam (middle surface) and the nodal vectors describing the top and bottom surfaces of the element. The element properties are established using the principle of virtual work and the hierarchical element displacement approximation. In formulating the properties of the element complete two dimensional stresses and strains are considered hence the element is equally effective for very slender as well as extremely deep beams. Incremental equations of equilibrium are derived and solved using the standard Newton-Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those reported in the literature. The formulation presented here removes virtually all of the drawbacks present in the existing GNL beam finite element formulations and has many additional benefits. First, the currently available GNL beam formulations are based on fixed order of approximation for the displacements and thus are not hierarchical and have no provision for changing the order of approximation for the displacements u and v. Secondly, the element displacement approximations in the existing formulations are either based on linearized displacement field for which a true Lagrangian formulation is not possible and the incremental load step size is severely limited or are based on nonlinear nodal rotation function approach in which case even though the description of displacement for the element is exact but additional complications arise due to the noncummutative nature of nonlinear nodal rotation functions. The p-version displacement approximation used here does not involve traditional nodal rotations that have been used in the existing beam formulations, thus the difficulties associated with their use are not present in this formulation.
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Liu, Joseph H., and Karan S. Surana. "p-Version Axisymmetric Shell Element for Geometrically Nonlinear Analysis." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0097.
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Abstract This paper presents a p-version geometrically nonlinear (GNL) formulation based on total Lagrangian approach for a three node curved axisymmetric shell element. The approximation functions and the nodal variables for the element are derived directly from the Lagrange family of interpolation functions of order pξ and pη. This is accomplished by first establishing one dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three and one node equivalent configurations that correspond to pξ + 1 and pη + 1 equally spaced nodes in the ξ and η directions and then taking their products. The resulting element approximation functions and the nodal variables are hierarchical and the element approximation ensures C0 continuity. The element geometry is described by the coordinates of the nodes located on the middle surface of the element and the nodal vectors describing top and bottom surfaces of the element. The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete axisymmetric state of stresses and strains are considered hence the element is equally effective for very thin as well as extremely thick shells. The formulation presented here removes virtually all of the drawbacks present in the existing GNL axisymmetric shell finite element formulations and has many additional benefits. First, the currently available GNL axisymmetric shell finite element formulations are based on fixed interpolation order and thus are not hierarchical and have no mechanism for p-level change. Secondly, the element displacement approximations in the existing formulations are either based on linearized (with respect to nodal rotation) displacement field in which case a true Lagrangian formulation is not possible and the load step size is severely limited or are based on nonlinear nodal rotation functions approach in which case though the kinematics of deformation is exact but additional complications arise due to the noncummutative nature of nonlinear nodal rotation functions. Such limitations and difficulties do not exist in the present formulation. The hierarchical displacement approximation used here does not involve traditional nodal rotations that have been used in the existing shell element formulations, thus the difficulties associated with their use are not present in this formulation. Incremental equations of equilibrium are derived and solved using the standard Newton-Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a present tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the literature.
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Santos, Hugo. "Equilibrium-Based Finite Element Formulation for Timoshenko Curved Tapered Beams." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12567.
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Due to their excellent mechanical performance and structural efficiency, curved tapered beams have been widely used in many engineering applications, such as, bridge structures, piping systems, biomedical devices, aerospace and aeronautical structures, etc. Their complex geometries pose challenges to the development of robust approaches for the modelling of their mechanical behaviour. Among the various approaches available in the literature for their analysis, those that are based on the finite element method have been the most successful, particularly due to their versatility. Nonetheless, when applied to Timoshenko based structural models, some of these finite element approaches are prone to shear locking when the beam elements become slender and to membrane locking when the curvature of the beam centroid curves increases [1]. The aim of the present contribution is to introduce a novel, simple and effective, finite element formulation for the analysis of two-dimensional Timoshenko curved tapered beams. This formulation relies on a complementary variational approach based on a set of approximations that satisfy in strong form all equilibrium conditions of the boundary-value problem [2], resulting thus in a formulation that is free from both shear and membrane locking phenomena. The effectiveness of the formulation is numerically demonstrated through its application to a circular clamped-clamped beam subjected to a mid-span concentrated load, and the obtained results are analysed and discussed. REFERENCES [1] H. Stolarski and T. Belytschko, “Shear and membrane locking in curved C0 elements”, Comput. Meth. Appl. Mech. Eng., Vol. 41, pp. 279–296, (1983). [2] H.A.F.A. Santos, “Complementary-energy methods for geometrically non-linear structural models: an overview and recent developments in the analysis of frames”, Archives of Computational Methods in Engineering, Vol. 18, (2011): 405.
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Tabiei, Ala, Romil Tanov, and Victor Birman. "Sandwich Shell Finite Element for Dynamic Explicit Analysis." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2040.
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Abstract This work presents the finite element (FE) formulation and implementation of a higher order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement based third order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, a treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom (DOF) per node. Only C0 continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most common 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation. To assess the performance of the present shell element it is implemented in the general nonlinear explicit dynamic FE code DYNA3D. Several problems are solved and results are compared to other theoretical and numerical results. The developed sandwich shell element is much more computationally efficient for modeling sandwich shells than solid elements.
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Talha, Mohammad, and B. N. Singh. "Nonlinear Vibration Analysis of Shear Deformable Functionally Graded Ceramic-Metal Plates Using an Improved Higher Order Theory." In ASME 2010 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2010. http://dx.doi.org/10.1115/smasis2010-3619.
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In the present study, an improved higher order theory in conjunction with finite element method (FEM) is presented and is applied to study the nonlinear vibration analysis of shear deformable functionally graded material (FGMs) plates. The present structural model kinematics assumes the cubically varying in-plane displacement over the entire thickness, while the transverse displacement varies quadratically to achieve the accountability of normal strain and its derivative in calculation of transverse shear strains. The theory also satisfies zero transverse strains conditions at the top and bottom faces of the plate, and the geometric nonlinearity is based on Green-Lagrange assumptions. All higher order terms appearing from nonlinear strain displacement relations are incorporated in the formulation. The material properties of the plates are assumed to vary smoothly and continuously throughout the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. A C0 continuous isoparametric nonlinear FEM with 13 degrees of freedom per node is proposed for the accomplishment of the improved elastic continuum. Numerical results with different system parameters and boundary conditions are accomplished, to show the importance and necessity of the higher order terms in the nonlinear formulations.
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Shabana, Ahmed A., Ashraf M. Hamed, Abdel-Nasser A. Mohamed, Paramsothy Jayakumar, and Michael D. Letherwood. "Limitations of B-Spline Geometry in the Finite Element/Multibody System Analysis." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47168.
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This paper examines the limitations of using B-spline representation as an analysis tool by comparing its geometry with the nonlinear finite element absolute nodal coordinate formulation (ANCF) geometry. It is shown that while both B-spline and ANCF geometries can be used to model non-structural discontinuities using linear connectivity conditions, there are fundamental differences between B-spline and ANCF geometries. First, while B-spline geometry can always be converted to ANCF geometry, the converse is not true; that is, ANCF geometry cannot always be converted to B-spline geometry. Second, because of the rigid structure of the B-spline recurrence formula, there are restrictions on the order of the parameters and basis functions used in the polynomial interpolation; this in turn can lead to models that have significantly larger number of degrees of freedom as compared to those obtained using ANCF geometry. Third, in addition to the known fact that B-spline does not allow for straight forward modeling of T-junctions, B-spline representation cannot be used in a straight forward manner to model structural discontinuities. It is shown in this investigation that ANCF geometric description can be used to develop new spatial chain models governed by linear connectivity conditions which can be applied at a preprocessing stage allowing for an efficient elimination of the dependent variables. The modes of the deformations at the definition points of the joints that allow for rigid body rotations between ANCF finite elements are discussed. The use of the linear connectivity conditions with ANCF spatial finite elements leads to a constant inertia matrix and zero Coriolis and centrifugal forces. The fully parameterized structural ANCF finite elements used in this study allow for the deformation of the cross section and capture the coupling between this deformation and the stretch and bending. A new chain model that employs different degrees of continuity for different coordinates at the joint definition points is developed in this investigation. In the case of cubic polynomial approximation, C1 continuity conditions are used for the coordinate line along the joint axis; while C0 continuity conditions are used for the other coordinate lines. This allows for having arbitrary large rigid body rotation about the axis of the joint that connects two flexible links. Numerical examples are presented in order to demonstrate the use of the formulations developed in this paper.