Efficient computational approaches for analysis of thin and flexible multibody structures

Bulín, Radek; Hajžman, Michal

doi:10.1007/s11071-021-06225-5

Cited by 13 publications

(3 citation statements)

References 36 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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“…In order to verify the feasibility and correctness of the proposed method in analyzing the large deformation problems of incompressible hyperelastic curved beams, statics and dynamics simulations of flexible curved beams subjected only to gravity are carried out through several examples in this section. In numerical calculation, the Gaussian integral method was used to integrate the volume of the curved beam element, the Generalized-α method [28,29] was used to solve the dynamics equation ( 29), and the Newton-Raphson method was used to solve the static equation (30).…”

Section: Numerical Simulationsmentioning

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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“…An important topic is how to resolve computability problems caused by stiffness terms with strong nonlinearity. For example, the improvement of computational efficiency using precomputation of the constant part of the stiffness term (Bulín and Hajžman, 2021) and by introducing algebraic constraints in the global coordinate system and element coordinate system (Hara and Watanabe, 2018) have shown good results. In the ANCF formulation, understanding various material properties of the flexible structure such as inertia and material properties, e.g., mass density, Young's modulus, and cross-sectional shape, is necessary.…”

Section: Introductionmentioning

confidence: 99%

Method for analysis of planar motion of system with rigid and extremely flexible components via analogy with contact problem of rigid bodies

Ooshima

Sugawara

2021

Mechanical Engineering Journal

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Recent years have witnessed attempts to employ a system with rigid and extremely flexible components (SREF), usually consisting of strings, membranes, and so on, to realize huge structures for spacecraft in orbit. In general, such flexible components have two states, i.e., with and without tensional force. Previously, the authors proposed an effective method for analyzing SREF motion, which is based on an analogy between the state transitions of the SREF and contact problem of rigid bodies. The state transitions of the SREF are detected via a linear complementarity problem that is used for contact problem in the analysis method proposed by Pfeiffer et al. (Pfeiffer and Glocker, 1996). The authors had applied this method to an SREF consisting of two masses and two strings, where the motion of the system was limited to one dimension. In this study, the method is extended to an SREF having planar motion. As an analysis object, an SREF consisting of two masses and two strings is introduced. Finally, the results of numerical analyses are compared with those of an experiment under same parameters, and the validation of the proposed method is demonstrated by the comparison.

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Efficient computational approaches for analysis of thin and flexible multibody structures

Cited by 13 publications

References 36 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

Method for analysis of planar motion of system with rigid and extremely flexible components via analogy with contact problem of rigid bodies

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