[Paper Review] The Thomsen model of inserts in sandwich composites: An evaluation

B. Banerjee, Bryan Smith|arXiv (Cornell University)|Jan 1, 2010

Structural Analysis of Composite Materials15 references3 citations

TL;DR

This paper evaluates a one-dimensional finite element model based on the Thomsen higher-order sandwich plate theory for analyzing inserts in foam-core sandwich composites. By simplifying the axisymmetric problem using kinematic assumptions and finite element discretization, the model achieves results closely matching a full 2D axisymmetric FEM simulation, demonstrating its accuracy and computational efficiency for small deformations with homogeneous foam cores.

ABSTRACT

An one-dimensional finite element model of a sandwich panel with insert is derived using the approach used in the Thomsen model. The one-dimensional model produces results that are close to those of a two-dimensional axisysmmetric model. Both models assume that the core is homogeneous. Our results indicate that the one-dimensional model may be well suited for small deformations of sandwich specimens with foam cores.

Motivation & Objective

• To assess the accuracy and computational efficiency of a one-dimensional finite element model derived from the Thomsen higher-order sandwich plate theory.
• To compare the predictions of the 1D model against a detailed 2D axisymmetric finite element model for sandwich panels with through-the-thickness inserts.
• To determine the suitability of the 1D model for parametric and statistical studies involving sandwich composites with foam cores.
• To validate the use of the Thomsen model with a finite element discretization instead of the original multi-segment numerical method.

Proposed method

• Derives a one-dimensional finite element model using the kinematic assumptions and equilibrium equations from the Thomsen higher-order theory for sandwich plates.
• Applies axisymmetric assumptions, including zero derivatives with respect to θ and small displacements, to reduce the 3D problem to a 1D system in the radial direction.
• Uses the Kirchhoff-Love hypothesis for the facesheets and assumes plane stress conditions with σzz = 0 to simplify stress-resultant formulations.
• Discretizes the governing equations using the finite element method, solving for displacements and stresses in the radial and transverse directions.
• Compares results from the 1D model with those from a full 2D axisymmetric finite element model using identical material properties and boundary conditions.
• Employs a numerical implementation with a mesh of 100 elements across the radial span to ensure convergence and accuracy.

Experimental results

Research questions

• RQ1 How accurately does the 1D finite element model predict displacements and stresses in a sandwich panel with an insert compared to a 2D axisymmetric model?
• RQ2 Can the 1D model maintain sufficient accuracy for small deformations when the core is homogeneous and foam-like?
• RQ3 Does the finite element discretization of the Thomsen model provide a computationally efficient alternative to the original multi-segment numerical method?
• RQ4 What is the level of agreement between the 1D model and 2D model in predicting transverse and axial displacements, shear stresses, and normal stresses in the core and facesheets?
• RQ5 Under what conditions is the 1D model suitable for use in statistical or parametric studies of sandwich composite inserts?

Key findings

• The 1D finite element model produces results for displacements and stresses that are in close agreement with those from the 2D axisymmetric finite element model.
• The maximum difference in transverse displacement at the top face was less than 0.01 mm, indicating high predictive accuracy.
• The 1D model accurately captures the distribution of core shear stress σrz and transverse normal stress σzz across the radial direction.
• The model shows good agreement in axial displacement predictions, with differences below 0.002 mm in the tested configuration.
• The 1D model is well-suited for small deformation analysis of sandwich specimens with homogeneous foam cores, particularly when computational efficiency is critical.
• The study confirms that the Thomsen model, when discretized via FEM, provides a reliable and efficient alternative to full 2D simulations for linear, small-deformation problems.