Abstract
Many modern applications of the flexible multibody systems require formulations that can effectively solve problems that include large displacements and deformations having the ability to model nonlinear materials. One method that allows dealing with such systems is continuum-based absolute nodal coordinate formulation (ANCF). The objective of this study is to formulate an efficient method of modeling nonlinear nearly incompressible materials with polynomial Mooney–Rivlin models and volumetric energy penalty function in the framework of the ANCF. The main part of this paper is dedicated to the examination of several ANCF fully parameterized beam elements under incompressible regime. Moreover, two volumetric suppression methods, originating in the finite element analysis, are proposed: a well-known selective reduced integration and F-bar projection. It is also presented that the use of these methods is crucial for performing reliable analysis of models with bending-dominated loads when lower-order elements are employed. The results of the simulations carried on with considered elements and proposed methods are compared with the results obtained from commercial finite element package and existing ANCF implementation. The results show important improvement as compared with previous applications and good agreement with reference results.
Highlights
In the modern design of the software and applications, the highly flexible bodies built with nonlinear materials are in common use
Element beam element 30 with trapezoidal mode (BE30T) converges to wrong over-stiff solution with noticeable error, despite that this element includes a trapezoidal displacement mode. This is probably cause by the fact that when very large deformations occur due to bending, the cross section takes the form of trapezoid but with curved sides, Nearly incompressible nonlinear material models which requires a quadratic transversal approximation that beam element 42 (BE42) provides
The absolute nodal coordinate formulation is known to be well suited for large deformation analysis of the flexible bodies
Summary
In the modern design of the software and applications, the highly flexible bodies built with nonlinear materials are in common use. The main objective of this paper is to examine the use of nonlinear, hyperelastic, nearly incompressible material models using the absolute nodal coordinate formulation beam elements. While this objective was addressed in previous publications [23], the main contribution of this paper is to show the importance of volumetric locking elimination in the applications when bending-dominated models are considered. The third element is higher-order element with thirty nodal coordinates that include trapezoidal deformation mode of the cross section that suppresses volumetric locking introduced in [24,25] This element is referred in the following as beam element 30 with trapezoidal mode (BE30T).
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