Abstract
Abstract. Flexible joints, sometimes called bushing elements or force elements, are found in all structural and multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of the model. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, identification of its stiffness characteristics is not so simple, specially if the joint is itself a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. This paper proposes a family of tensorial deformation measures suitable for elastic bodies of finite dimension. These families are generated by two parameters that can be used to modify the constitutive behavior of the joint, while maintaining the tensorial nature of the deformation measures. Numerical results demonstrate the objectivity of the deformations measures, a feature that is not shared by the deformations measures presently used in the literature. The impact of the choice of the two parameters on the constitutive behavior of the flexible joint is also investigated.
Highlights
Flexible joints, sometimes called bushing elements or force elements, are found in all multibody dynamics codes
Sometimes called bushing elements or force elements, are found in all multibody dynamics codes. In their simplest form, flexible joints consist of sets of three linear and three torsional springs placed between two nodes of a multibody system
The selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements
Summary
Sometimes called bushing elements or force elements, are found in all multibody dynamics codes. Much attention has been devoted to the problem of synthesizing accurate constitutive properties for the modeling of flexible bushings presenting complex, time-dependent rheological behavior, Ledesma et al (1996); Kadlowec et al (2003) It is worth stressing, that the literature seldom addresses three-dimensional joint deformations. When lumped deformable joints are used, relative displacements and rotations are often required to remain moderate, not necessarily infinitesimal Such restrictions occur when using the FIELD element of MSC/ADAMS, a linear element that implements an orthotropic torsional spring based on a constant, orthotropic constitutive matrix. The formulations and implementations of flexible joints available in research and commercial codes do not appear to allow arbitrarily large relative displacements and rotations. The motion tensors that bring frame F I to frames F k and F , denoted Ck and C , respectively can be expressed as
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