Volumetric  locking  suppression  method  for  nearly  incompressible  nonlinear  elastic multi-layer  beams  using ANCF elements

Orzechowski, Grzegorz; Frączek, Janusz

doi:10.15632/jtam-pl.55.3.977

Cited by 8 publications

(3 citation statements)

References 29 publications

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“…These elements have been widely used in the nonlinear analysis of a wide range of challenging applications, some of which have complex geometry. 38…”

Section: Ancf Mesh Topologymentioning

confidence: 99%

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

Shabana

2023

Proceedings of the Institution of Mechanical Engineers, Part K:

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This article discusses a new approach for predicting and quantifying mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated mechanical systems (AMS). In this approach, the constrained equations of motion are solved simultaneously with discrete temperature equations obtained by converting heat partial-differential equation to a set of first-order ordinary differential equations. Dependence of the temperature gradients and their spatial derivatives on the position gradients, spinning motion, and curvatures is discussed. The approach captures dependence of the temperature-oscillation frequencies on the mechanical-displacement frequencies. The temperature field can be selected to ensure continuity of the temperature gradients at the nodal points. To generalize the AMS coupled thermo-elasticity formulation and capture the effect of the boundary and motion constraints (BMC) on the thermal expansion, the proposed method is based on integrating thermodynamics and Lagrange-D’Alembert principles. The absolute nodal coordinate formulation (ANCF) is used to describe continuum displacement and obtain accurate description of the reference-configuration geometry and change of this geometry due to deformations. A thermal-analysis large-displacement formulation is used to allow converting heat energy to kinetic energy, ensuring stress-free thermal expansion in case of unconstrained uniform thermal expansion. Cholesky heat coordinates are used to define an identity coefficient matrix for the efficient solution of the discretized heat equations. The approach presented is applicable to the two different forms of the heat equation used in the literature; one form is explicit function of the stresses while the other form does not depend explicitly on the stresses. Because of the need for using ANCF finite elements to achieve a higher degree of continuity in the coupled thermomechanical approach introduced in this article, the concept of the ANCF mesh topology is discussed.

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“…These elements have been widely used in the nonlinear analysis of a wide range of challenging applications, some of which have complex geometry. 38…”

Section: Ancf Mesh Topologymentioning

confidence: 99%

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

Shabana

2023

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…Luo et al [20] established hyperelastic thin-shell elements of compressible Neo-Hookean and incompressible Mooney-Rivlin materials and compared the shell dynamics response of different materials. Orzechowski and Frączek [21,22] based on their work investigated a volume-locking suppression method applied to a nonlinear hyperelastic nearly incompressible material model with fully parametric beam elements. Based on the work of [21,22], Xu et al [23,24] improved the low-order beam element (ILOBE) using a reduced integration technique and proposed an ANCF high-order beam element (HOBE) with quadratic interpolation in the transverse direction.…”

Section: Introductionmentioning

confidence: 99%

“…Orzechowski and Frączek [21,22] based on their work investigated a volume-locking suppression method applied to a nonlinear hyperelastic nearly incompressible material model with fully parametric beam elements. Based on the work of [21,22], Xu et al [23,24] improved the low-order beam element (ILOBE) using a reduced integration technique and proposed an ANCF high-order beam element (HOBE) with quadratic interpolation in the transverse direction. Two kinds of beam elements are combined with four kinds of nonlinear material models, and the accuracy of the different nonlinear material models is compared by numerical simulation arithmetic and physical experiments.…”

Section: Introductionmentioning

confidence: 99%

Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

Wang

Guo

et al. 2022

Nonlinear Dyn

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Compared with traditional linear elastic materials, the soft structure composed of incompressible hyperelastic materials has not only geometrical nonlinearity but also material nonlinearity during deformation. In this paper, the absolute nodal coordinate formulation (ANCF) is used to study the large deformations and large overall motions of incompressible hyperelastic curved beams. A novel large deformation dynamic modeling method for curved beams made of hyperelastic materials is proposed, in which a simplified Neo-Hookean model is combined with the onedimensional ANCF beam element. The elastic force vector is calculated according to the exact expression of curvature. The dynamic equations are derived by using the virtual work principle. The dynamic responses of a cantilever silica gel beam under gravity are calculated based on the present method and compared with those of the improved low-order beam element (ILOBE), high-order beam element (HOBE), and commercial finite element analysis software (ANSYS). Simulation results show that the proposed method can accurately describe the large deformation and large overall motion of the beam, and has better computational efficiency. Research in this paper provides an efficient dynamic model for the dynamics analysis of soft robot arms.

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A new absolute nodal coordinate formulation beam element with multilayer circular cross section

Peng

Tian

2019

Acta Mech. Sin.

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Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Cited by 8 publications

References 29 publications

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

A new absolute nodal coordinate formulation beam element with multilayer circular cross section

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