A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints

Abstract

comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints. (2019) Composite Structures, 215.Abstract -The interest in functionally graded adhesive (FGA) joints has been increasing in recent years. For example, FGAs offer the opportunity to optimize the strength of multimaterial bonded joints by locally tailoring the adhesive properties and without modifying the design of the adherends to be joined. The development of dedicated stress analyses to predict the stress distribution is then of the highest interest to control the strength of such joints. The Finite Element (FE) method is able to address the stress analysis of FGA joints but is computationally costly. Simplified stress analyses have then been developed. The objective of this paper is to assess the prediction of simplified stress analyses, solved through the macroelement (ME) technique, with respect to those of FE models. It is shown that the predictions of ME models are in a sufficient agreement with the FE models to be employed at a pre-sizing stage. The influence of the overlap length is then investigated by the means of the simplified 2 stress analyses. A noticeable result is the existence of an overlap length for which the adhesive peak shear stress is minimal, in the 1D-bar kinematics framework.

A methodology for the computation of the macro-element stiffness matrix for the stress analysis of a lap joint with functionally graded adhesive properties

“…The effect can be reduced by using a variable-property adhesive. By varying the adhesive stiffness along the overlap, the stress distribution is modified in the joint The configuration used for comparison is the same one as in [15] and is shown in Figure 1.…”

“…Equations (25) replace equations (11) to derive the first lines of the matrix . The same nodal-boundary conditions (13) are used to complete the matrix , while equations (15) are used to derive the matrix. Finally, notice the truncation of the adhesive shear modulus serie is the same as the displacement series.…”

“…The tests are made with a single-lap bonded joint, as visible in Figure 1. The choice is made to use the exact same set up as in [15]. Consequently, the geometry details are available in the following Table 1 and the material parameters used are described in Table 2.…”

“…First of all, in the case of the HA ME, the exact stiffness matrix and the approached stiffness matrix developed here are compared terms by terms. Then, in the case of a FGA single lap joint, the stress distributions are compared to a FE model from a previous work[15]. The geometry and the material used to perform the tests are given in the following part.…”

A Macro-element for Modeling the Non-linear Interaction of Soil-shallow Foundation under Seismic Loading

“…Macro-element models for seismic SFI problems are also available in the literature, such as those proposed by Cremer et al [5], Chatzigogos et al [6], Grange et al [7,8], Figini et al [9], Prisco et al [10], Khebizi et al [12]. Jin [13] Barari et al [14], Paroissien et al [15] and Gorini et al [16], For shallow foundations, these authors used the macro element of quasi-static monotonic loading for analyzing the structures under seismic loading. According to Paolucci [11], the superstructure was represented by a single-degree-of-freedom mass and the macroelement introduced nonlinear effects in the calculation of soil reactions through a failure criterion and plastic flow rule.…”