Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

Jonker, Jan B.

doi:10.1007/s11044-021-09777-x

Cited by 10 publications

(17 citation statements)

References 41 publications

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“…In the fourth and fifth case, the GMS is used in a spherical flexure joint and a misaligned cross-flexure to show the usefulness in flexure based mechanisms. The flexures are modeled with the beam element described in [47].…”

Section: Validationmentioning

confidence: 99%

“…Figure 14 shows an overconstrained cross-flexure with a misalignment in the overconstraint direction that was described in [49,50]. The two flexures are each modeled using eight beam elements with torsional warping (as defined in [47]) to model the thin part and one beam element to model the thick part which is used for attachment to the frame parts. The flexures are made of steel (Young's modulus 200 GPa, Poisson ratio 0.3), have a thickness Figure 15 shows the first natural frequency (in which the shuttle rotates around the indicated rotation axis) as function of the misalignment.…”

Section: Misaligned Cross-flexurementioning

confidence: 99%

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A multinode superelement in the generalized strain formulation

et al. 2022

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Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes.This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called “full approach” gives more accurate results than the so-called “corotational approach” but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.

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Section: Validationmentioning

confidence: 99%

Section: Misaligned Cross-flexurementioning

confidence: 99%

A multinode superelement in the generalized strain formulation

et al. 2022

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“…Stress resultants are the forces and moments that act on the cross-section. In this chapter, the beam element described in [103] is used to obtain the stress resultants. This beam element includes the Vlasov theory and the effect of Wagner torsion on the stiffness.…”

Section: Methodsmentioning

confidence: 99%

“…The multibody software SPACAR [101,104], which uses the generalized strain formulation [25], is well-suited for this beam-based analysis of flexure mechanisms. Sophisticated beam elements for the modelling of flexures have been developed and implemented in this software [103,105,139]. However, beam-based flexure modelling is not always sufficiently efficient and accurate and it also limits the design freedom.…”

Section: State Of the Art And Problem Statementmentioning

confidence: 99%

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Beam-based analysis of flexure mechanisms: increasing computational efficiency, accuracy and design freedom

Dwarshuis

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The use of beam elements with constant cross-section limits the design freedom. This thesis presents a formulation for beam elements with a varying cross-section, to allow for the analysis of non-prismatic flexures. Design optimizations of several flexure joints shows that this extra design freedom can result in significantly better flexure joints.Flexure joints contain parts which connect the flexures to each other. Although these socalled frame parts are intended to be very stiff, their compliance can significantly decrease the overall support stiffness of the flexure joints, reducing the performance. An accurate evaluation of the performance requires the stiffness of the frame parts to be modelled. However, frame parts typically have complex shapes, such that they can barely be modelled using beam elements. This thesis formulates a superelement by which complex shaped parts can be modelled efficiently. Examples show that flexure joints can be modelled efficiently and accurately by using the superelement to model frame parts and using beam elements to model the flexures.Very complex flexure-based mechanisms can be analysed more efficiently and more accurately by using the methods and elements that are introduced in this thesis. This may help the development of new flexure mechanisms, increasing the potential for using flexure mechanisms in practice.

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Third-order geometric stiffness formulation for improved mesh convergence of thin and wide spatial beams in the generalized strain beam formulation

Nijenhuis,

Meijaard,

Naves

et al. 2024

Comput Mech

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This paper presents the stiffness formulation of a beam element with the relevant third-order nonlinear geometric effects for relatively wide and thin rectangular beams, in particular when loaded in the plane and simultaneously deformed out of the plane. The element is initially straight in its undeformed configuration. The formulation is based on Timoshenko beam theory with nonuniform torsion and Wagner effects. The derivation is carried out by means of the Hellinger–Reissner variational principle with custom interpolation functions. The element is incorporated into the generalized strain beam formulation for multibody systems. Numerical simulations of precision flexure mechanisms show that the use of a single third-order element per flexible member can already yield adequate performance, at a significant reduction of the necessary degrees of freedom and the computation time, compared with using multiple second-order elements in the generalized strain beam formulation.

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Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

Cited by 10 publications

References 41 publications

A multinode superelement in the generalized strain formulation

A multinode superelement in the generalized strain formulation

Beam-based analysis of flexure mechanisms: increasing computational efficiency, accuracy and design freedom

Third-order geometric stiffness formulation for improved mesh convergence of thin and wide spatial beams in the generalized strain beam formulation

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