A high-order 2D-plate macro-element model for the analysis of bonded joints

Abstract

Adhesive bonding has emerged as an attractive solution for the joining of lightweight structures, yet accurate stress analysis remains computationally demanding when relying on Finite Elements (FE). This paper introduces a novel plate Macro-Element (ME) formulation that extends previous beam-type approaches to enable three-dimensional stress analysis of bonded joints. High-order polynomial expansions are employed to describe the displacement field of the adherends, while the adhesive is modeled as an elastic foundation. Governing equations are derived using a variational principle and integrated within a standard FE framework. Through the derivation of a special stiffness matrix, a ME can simulate an entire overlap with just one element. The proposed methodology is validated against FE results for a single-lap bonded joint with a thin adhesive layer. The influence of different higher-order displacement assumptions and constitutive models is investigated. The results show that their inclusion in the formulation improves the solution accuracy.