Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials

Shabana, Ahmed A.; Eldeeb, Ahmed E.

doi:10.1007/s11071-020-05839-5

Cited by 11 publications

(5 citation statements)

References 21 publications

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“…The exible beams are modeled by ANCF, which is a well-known rigid-exible coupled modelling method that is able to deal with large-deformation and large-rotation cases [28-30] such as soft robot [31], exible membrane system [32] and uid materials [33][34][35]. The two-dimensional two-node Euler-Bernoulli ANCF beam element is adopted [36].…”

Section: Simulation Modelling Methodsmentioning

confidence: 99%

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Influences of space perturbations on robotic assembly process of ultra-large structures

Yang

Zhang

et al. 2023

Nonlinear Dyn

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The space assembly of two exible beams by a dual-arm space robot is a typical assembly scenario to construct ultra-large space structure. Yet, previous studies mainly focused on the assembly of small structures, neglecting the in uences of space perturbations. In this paper, two modelling methods are proposed to study the in uences of space perturbations on the space assembly process of ultra-large space structures. Firstly, a theoretical modelling method is proposed based on quasi-static hypothesis and linear structural mechanics. The theoretical model can be utilized for analytically estimating the transverse and axial distributed forces of the exible beams, structural vibrations, and the control moments of the space robot. An orbit-attitude-structure coupled simulation model is then established to validate the theoretical model and study the dynamic behaviours more accurately, using absolute nodal coordinate formulation and natural coordinate formulation. Finally, the effects of the attitude angle, orbital radius, and lengths of beams on the dynamic responses during assembly are investigated.Theoretical and simulation results show that the control moments and structural vibration amplitude increase dramatically with the length of the beams. The effects of Coriolis force and gravity gradient must be considered for ultra-large space structures during assembly, otherwise the control moments and structural vibrations would be substantially underestimated. The results are instructive to the assembly strategy design as well as modular component design of ultra-large space structures.

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Section: Simulation Modelling Methodsmentioning

confidence: 99%

“…12, the theoretical control moments at t = 0 are nonzero due to the axial distributed gravity-gradient force, as shown in Eqs. ( 31), (34), and (36)- (41). The nonzero control moments at the beginning can be provided by the feedforward control moments for Case 1, which leads to the high control accuracies.…”

mentioning

confidence: 99%

Influences of space perturbations on robotic assembly process of ultra-large structures

Yang

Zhang

et al. 2023

Nonlinear Dyn

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“…Shabana and Eldeeb [17] pointed out that if only one gradient vector is used to construct an orthogonal triad, the relative rotation around this vector cannot be eliminated, resulting in singularities in the constraint Jacobian matrix. Therefore, for ANCF shell elements containing only one gradient vector as nodal variables, it usually becomes quite difficult to deal with connections between ANCF shell elements with discontinuous slopes.…”

Section: Joint Constraint Equationsmentioning

confidence: 99%

“…Sugiyama et al [16] presented two formulations for constructing the nodal coordinate system of ANCF beam elements and discussed constraint equations for rotating, rigid and sliding joints. [17] proposed a formulation of the orientation constraints using two gradient vectors, and pointed out that the constraint Jacobian matrices are singular if a single gradient vector is used to construct an orthogonal basis at the constrained joint. So far, the treatment of connections between ANCF gradient-deficient shell elements has not been adequately discussed, and the reliability of joint constraint equations for ANCF shell elements has seldom been tested.…”

Section: Introductionmentioning

confidence: 99%

Weak form quadrature shell elements based on absolute nodal coordinate formulation

He,

Li,

Zhong

2024

Preprint

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Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Nodal variables of the element consist of the position vector, the transverse gradient vector and the transverse derivatives thereof at the shell mid-surface. In-plane gradient vectors which are not taken as nodal variables are obtained with the aid of the differential quadrature analog. Using the transverse gradient vector and one in-plane gradient vector, joint constraint equations for shells with discontinuous slopes are established. Simplified equations of motion with constant mass matrix result. The elements are applicable to analysis of shell structures undergoing large displacements and rotations. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

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“…There will be no Coriolis force and centrifugal force, and the elastic force is the only nonlinear term. The simplicity of programming in solving large deformation problems has greater advantages and has achieved more widespread applications [5,6].…”

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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Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials

Cited by 11 publications

References 21 publications

Influences of space perturbations on robotic assembly process of ultra-large structures

Influences of space perturbations on robotic assembly process of ultra-large structures

Weak form quadrature shell elements based on absolute nodal coordinate formulation

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

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