Session: 01-01-01: Advanced Structural Mechanics and Computational Methods for Aerospace Applications

Paper Number: 177014

177014 - Finite Plate Elements Based on a Stress-Driven Reissner Mixed Variational Theorem for an Enhanced Transverse Stress Prediction in Composite Structures 

The accurate prediction of transverse stress fields and the rigorous enforcement of interlaminar equilibrium are fundamental requirements in the mechanical modeling of composite structures. Classical displacement-based formulations are well known to exhibit intrinsic limitations in this respect, often leading to poor transverse stress accuracy and violations of equilibrium conditions, particularly through the thickness. To overcome these shortcomings, mixed variational approaches have been extensively investigated, as they allow stress fields to be computed directly as primary unknowns, without relying on a posteriori stress recovery procedures.
Among these approaches, Reissner’s Mixed Variational Theorem (RMVT) has proven particularly attractive and has been widely adopted in the development of advanced finite element models. However, when relatively low-order thickness expansions of the primary variables are employed, standard RMVT-based formulations frequently yield inaccurate transverse stress predictions and may exhibit pronounced, nonphysical stress oscillations at material interfaces.

These deficiencies can be attributed to the simultaneous strong-form enforcement of interface continuity constraints on work-conjugate kinematic and static field variables. Such enforcement may introduce over-constraint into the mixed variational formulation, thereby degrading the accuracy of the resulting weak-form solutions. To address this issue, a stress-driven variant of the RMVT has been developed, in which exact interlaminar continuity of transverse stresses is enforced while allowing a relaxation of displacement continuity across layer interfaces.

In this work, an extension of the stress-driven RMVT within the Finite Element Method (FEM) framework is proposed for the first time. The objective is to broaden its applicability to a wide range of loading conditions and boundary constraints, as well as to assess the effectiveness of the resulting variational functional. The formulation is implemented using an eight-node serendipity finite element and is coupled with a variable kinematic description based on the Sublaminate Generalized Unified Formulation (sGUF). This combination enables a flexible and hierarchical representation of displacement and transverse stress fields, allowing complex structural behaviors to be accurately captured while preserving computational efficiency.

Numerical investigations performed on multilayered composite structures demonstrate that the proposed formulation leads to a substantial improvement in both the accuracy and smoothness of transverse stress distributions through the thickness. The results confirm that relaxing interlaminar displacement compatibility, together with the exact enforcement of stress continuity and boundary conditions, provides a robust and highly accurate framework for transverse stress modeling in layered composite structures.
 

Presenting Author: Girolamo Di Cara Université Paris Nanterre

Presenting Author Biography: Girolamo Di Cara is an Associate Professor (Maître de Conférences) in Mechanical Engineering at Université Paris Nanterre, France. He received his Ph.D. in Mechanical Engineering in 2022, with a focus on variable-kinematics finite element modeling of multilayered and sandwich structures. His research interests include mixed and stress-driven finite element formulations, advanced plate and beam theories, composite and smart structures, and the modeling of viscoelastic and active materials. He has contributed to the development of finite element frameworks based on the Reissner Mixed Variational Theorem (RMVT) and the Sublaminate Generalized Unified Formulation (sGUF), with applications to static, dynamic, and coupled multiphysics problems in composite structures.