Micropolar beam-like structures under large deformation

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions.publishedVersionPeer reviewe

Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter

The estimation of the parameters of a simulation model such that the model’s behaviour matches closely with reality can be a cumbersome task. This is due to the fact that a number of model parameters cannot be directly measured, and such parameters might change during the course of operation in a real system. Friction between different machine components is one example of these parameters. This can be due to a number of reasons, such as wear. Nevertheless, if one is able to accurately define all necessary parameters, essential information about the performance of the system machinery can be acquired. This information can be, in turn, utilised for product-specific tuning or predictive maintenance. To estimate parameters, the augmented discrete extended Kalman filter with a curve fitting method can be used, as demonstrated in this paper. In this study, the proposed estimation algorithm is applied to estimate the characteristic curves of a directional control valve in a four-bar mechanism actuated by a fluid power system. The mechanism is modelled by using the double-step semi-recursive multibody formulation, whereas the fluid power system under study is modelled by employing the lumped fluid theory. In practise, the characteristic curves of a directional control valve is described by three to six data control points of a third-order B-spline curve in the augmented discrete extended Kalman filter. The results demonstrate that the highly non-linear unknown characteristic curves can be estimated by using the proposed parameter estimation algorithm. It is also demonstrated that the root mean square error associated with the estimation of the characteristic curve is 0.08% with respect to the real model. In addition, all the errors in the estimated states and parameters of the system are within the 95% confidence interval. The estimation of the characteristic curve in a hydraulic valve can provide essential information for performance monitoring and maintenance applications.Publishers versio

О величине зазора в распределительном узле аксиально-поршневых гидромашин

Тез. докл. Междунар. науч.-техн. конф. (науч. чтения, посвящ. П. О. Сухому), Гомель, 4-6 июля. 2002 г

Alleviation techniques for volumetric locking in elements based on the absolute nodal coordinate formulation

This study investigates the application of formulations employed by standard Bubnov-Galerkin Finite Elements to alleviate volumetric locking in the context of the Absolute Nodal Coordinate Formulation (ANCF). Volumetric locking is a prevalent phenomenon that occurs when linearly interpolated displacement fields are used to model incompressible phenomena. Although linear interpolations for the displacement field offer computational efficiency, their direct utilization can frequently yield erroneous solutions and slow convergence rates when applied to modeling incompressible materials. Commonly used techniques to reduce volumetric locking in classical finite elements include reduced and selective integration, mixed two/three field variational formulations, and F-bar methods. This study aims to demonstrate the efficacy of these techniques when applied to a two and three-dimensional linear ANCF-based continuum beam elements. Our findings demonstrate that most of the locking alleviation techniques yielded expected results compared to classical finite elements. Nevertheless and contrary to findings in the finite element literature, the mixed two/three field variational formulation, when used with linear ANCF-based continuum beam elements, improved the convergence rate only in the case of uniaxial tensile testing. For the bending mode, mixed ANCF elements significantly overestimated the displacements. While techniques alleviate locking for some deformation modes, the paper concludes that no definitive technique exists to completely resolve volumetric locking effects observed in linear ANCF elements, for all deformation modes.</p

An Overview of Higher-Order Beam Elements Based on the Absolute Nodal Coordinate Formulation

Abstract In this paper, beam elements with particular emphasis on higher-order elements based on the absolute nodal coordinate formulation (ANCF) are thoroughly investigated from the perspective of interpolation procedure and numerical performance. A straightforward and modularized procedure to construct the shape function is proposed. Based on the unified shape function formulation, the research examines how axial and transverse interpolation strategies impact element performance. Two beams in the pure bending scenario are analyzed. The comparison study reveals that higher-order interpolation in the axial and transverse directions is necessary to represent the highly curved deformation modes and alleviate Poisson locking. The Princeton beam and a thicker beam are then studied to assess the accuracy, convergence, and numerical stability of different beam elements. Conclusions are: (1) Higher-order beam elements are generally more accurate but converge more slowly. (2) To guarantee high accuracy, a complete set of transverse quadratic gradients must be adopted in the quadratic elements, and a higher-order transverse interpolation is necessary to capture the warping effect. (3) To avoid slow convergence, the axial order should not be lower than the transverse order. (4) Higher-order beam elements lead to a stiffness matrix with a larger condition number. With an inappropriate length to cross section ratio, the transverse cubic element results in an ill-conditioned stiffness matrix that brings numerical instability. (5) The numerical stability of higher-order beam elements are more sensitive to the length to cross section ratio of the meshed beam.</jats:p

Modeling of the Achilles Subtendons and Their Interactions in a Framework of the Absolute Nodal Coordinate Formulation

Experimental results have revealed the sophisticated Achilles tendon (AT) structure, including its material properties and complex geometry. The latter incorporates a twisted design and composite construction consisting of three subtendons. Each of them has a nonstandard cross-section. All these factors make the AT deformation analysis computationally demanding. Generally, 3D finite solid elements are used to develop models for AT because they can discretize almost any shape, providing reliable results. However, they also require dense discretization in all three dimensions, leading to a high computational cost. One way to reduce degrees of freedom is the utilization of finite beam elements, requiring only line discretization over the length of subtendons. However, using the material models known from continuum mechanics is challenging because these elements do not usually have 3D elasticity in their descriptions. Furthermore, the contact is defined at the beam axis instead of using a more general surface-to-surface formulation. This work studies the continuum beam elements based on the absolute nodal coordinate formulation (ANCF) for AT modeling. ANCF beam elements require discretization only in one direction, making the model less computationally expensive. Recent work demonstrates that these elements can describe various cross-sections and materials models, thus allowing the approximation of AT complexity. In this study, the tendon model is reproduced by the ANCF continuum beam elements using the isotropic incompressible model to present material features.peerReviewe

Performance review of locking alleviation methods for continuum ANCF beam elements

AbstractThe absolute nodal coordinate formulation (ANCF) is a nonlinear finite element approach proposed for the large deformation dynamics analysis of beam- and plate/shell-type structures. In the ANCF approach, elastic forces can be defined using three-dimensional elasticity-based continuum mechanics. This approach is often straightforward, and it makes it possible to use advanced material models in the ANCF framework. However, it has been pointed out in several studies that continuum ANCF-based elements with a full three-dimensional elasticity description can suffer from locking phenomena. In this study, a comparison between various combinations of locking alleviation techniques and their applicability to different ANCF beam variants is studied using numerical examples. Furthermore, the enhanced deformation gradient (EDG) technique, which has been proposed recently in finite element literature, is demonstrated for high-order ANCF beam elements. Based on the numerical tests, none of the currently available techniques are suitable for all types of ANCF elements. The paper also shows that the efficiency and accuracy of the techniques are case-dependent. For the ANCF beam element involving higher-order terms with respect to trapezoidal mode, however, the EDG-based techniques are preferable to reduce locking phenomena.</jats:p