Analysis of Laminated Rubber Bearings with a Numerical Reduction Model Method

Abstract

In this paper, we present a reduction method for modeling slender laminated elastomeric structures, which is developed in the context of nearly incompressible hyperelasticity. This method, based on a finite element formulation, consists in projecting the unknown fields onto a polynomial basis in order to reduce the dimension of the problem and the model size. Two types of finite elements are used, one for plane-strain and the other for 3D structures. Comparisons with classical finite element models on single layers show the reliability of the present method. The method proposed successfully predicts the global and local behavior and since it reduces both the model size and the computing time. It can be used to model slender bearing consisting of several layers.

A model reduction technique for laminated solids of revolution with a curved cross-section

“…When the polynomial order is increased, the relative local kinematical error is located near the free edges. This behavior does not depend on loading and has already been observed in the case of plane layers [16]. This test shows the reliability of the reduced finite element since the response of these elements is close to 3D standard elements when the polynomial order of the projection is increased.…”

“…It can also be seen that an optimum for n u exists which depends on the number of polynomial functions involved in the discretization of the pressure field n p . This observation has been previously seen in the case of plane layers in [15,16]. Furthermore, it has to be noted that for n u fixed one can choose an optimal n p to obtain the most precise response for the pressure and avoid numerical instability or locking phenomena.…”

“…The terms C pl vol and C iso are already given in [16]. The function F j (θ ) stands for the Fourier terms sin(θ ) or cos(θ ).…”

“…The proposed method is based on a coupling of pseudo-axisymmetric and semi-analytical elements, with a view to build a 3D to 1D reduction. This process has been introduced in a previous paper [16], leading to the development of a Numerical Reduction Method (NRM). It has been shown, in the aforementioned paper, that NRM is as reliable and as precise as a classical 3D finite element model in the case of plane laminates (with an important decrease in the computing size and time).…”

“…In particular, rigid rotational conditions (on a surface) are dependent on the geometric parametrization. And finally, the question of numerical convergence and numerical stability in the context of nearly incompressible hyperelasticity has to be investigated as it is done for plane layers (see [15,16]). This paper is structured as follows: firstly, the ingredients, required to develop the model reduction method, are presented.…”