Stress analysis of adhesively-bonded single stepped-lap joints based on three-parameter fractional viscoelastic foundation model

Abstract

This paper aims to develop a viscoelastic analytical model for adhesively bonded single stepped-lap joints subjected to tensile loading. The adherends are aluminum alloy A6063 and modeled as Timoshenko elastic beams and the adhesive is epoxy type B. A three-parameter fractional viscoelastic foundation (3PFVF) model is proposed to express the governing stresses in the joint and the fractional Zener model is used to model the viscoelastic behavior of the adhesive layer. The proposed 3PFVF model makes it possible to have different peel stresses between the two interfaces of adhesive and adherends. The governing differential equations are derived in the Laplace domain, and then solved and transformed simultaneously in the time domain using the Gaver-Stehfest inverse Laplace transform method. The finite element simulation with ANSYS is applied to validate the proposed method. The results show that a simple fractional viscoelastic model, which has a short differential equation, offers the same results as the classical viscoelastic models, which have higher and more complex differential equations. Moreover, the results show that the maximum shear and peel stresses in the single stepped-lap joints are about 20% less than single-lap joints.

Application of Bezier curves for description of structure shape in optimization of adhesive joints

“…У цьому випадку задача зводиться до знаходження товщини елементів конструкції в системі точок [11]. Перехід від неперервних функцій до дискретних дозволяє оптимізувати з'єднання з покроковою зміною товщини [12]. Якщо ж шукана функція є неперервною, то то її можна описати за відомими значеннями в системі точок за допомогою сплайнів [13], функцій Безьє [14,15] або рядів Фур'є [16; 17].…”

Topological optimization of a symmetrical adhesive joint. Island model of genetic algorithm

“…The description of the geometric shape of the overlay in the form of a Fourier series (15) makes it quite easy to calculate the mass of the overlay ( 8)…”

“…In this case, the problem is to find the thickness of structural elements in a system of points [13]. The transition from continuous to discrete functions makes it possible to optimize the joint with a stepped thickness change [14,15] (this solution is often used in joints of layers composites). If the desired function is implied to be continuous, in this case, it can be described by known values in the system of points using splines [16], of the Bezier functions [17,18].…”