# Presentation: 108875

## Software Tools for Analysis of Bonded Joints

*Farhad Tahmasebi, Ph.D.*
- NASA/GSFC - Code 542

## Outline

- Spring modeling
- Procedure
- Spring stiffness values
- Description of the adhesive stress program
- Description of the adhesive strain program
- Inputs to & outputs from the programs
- NASTRAN input & output files Program inputs
- Mathematica 3D plots

## Spring Modeling Procedure (1/3)

- A fine mesh of grids is created in the mid-plane of the bonded joint.
- For every grid in the mid-plane mesh, an initially-coincident grid is created.
- Three springs are placed between each pair of initially-coincident
- grids.
- These springs act in the X, Y, and Z directions.
- X and Y axes are parallel to the overlap plane of the bonded joint.
- Z axis is defined by the right-hand-rule.
- Rigid elements are used to connect the mid-plane grids to the corner grids of the plate elements which represent the adherends.

## Spring Modeling Procedure (2/3)

## Spring Modeling Procedure (3/3)

## Spring Stiffness Values (Shear)

- Z

## Spring Stiffness Values (Peel)

## Description of the Adhesive Stress Program (1/2)

- 1 - Prompts the user for the name of NASTRAN input and output files.
- 2 - Locates and stores all of the spring ID's, the corresponding grid ID's, and the corresponding grid coordinates in the NASTRAN input file.
- 3 - Identifies the pairs of grids which are coincident in the unloaded model.
- 4 - Identifies the spring triplets (X, Y, and Z) for the pairs of initially-coincident grids.
- 5 - Locates and stores the spring forces in the corresponding NASTRAN output file.

## Description of the Adhesive Stress Program (2/2)

- 6 - Assigns the stored spring forces to the appropriate springs in the triplets identified in step 4.
- 7 - Determines adhesive shear and peel stresses at the mid-plane grids using the following equations.
- 8 - Sorts the shear and peel stresses in descending order and writes them to an output file.
- 9 - Writes the coordinates of the mid-plane grid points and their corresponding shear and peel stresses to plot files.

## Description of the Adhesive Strain Program (1/2)

- Starts by executing steps 1 through 4 that the Adhesive Stress program goes through. Next, performs the following operations.
- 1 - Locates and stores the mid-plane grid point displacements in the NASTRAN output file.
- 2 - Calculates and stores the adhesive spring deformations from the grid point displacements obtained in the previous step.
- 3 - Assigns the stored spring deformations to the appropriate elements in the spring triplets corresponding to the pairs of initially-coincident grids

## Description of the Adhesive Strain Program (2/2)

- 4 - Calculates adhesive shear and normal strains at the mid-plane grids using the following equations.
- 5 - Sorts the shear and normal strains in descending order and writes them to an output file.
- 6 - Writes the coordinates of the mid-plane grid points and their corresponding shear and normal strains to plot files.

## Inputs & Outputs

- Inputs
- NASTRAN input file
- NASTRAN output file
- Spring forces
- Displacements of the adhesive mid-plane grids
- Element area (adhesive stress program)
- Adhesive thickness (adhesive strain program)
- Outputs
- .ad_strs (sorted stresses) & .ad_strn (sorted strains) files
- .tau, .sigma, .gamma, & .epsilon Mathematica plot files
_*The grids and springs can be numbered*__* in any order.*_

## Sample 3D Mathematica Plot (Shear Strain)

## Sample 3D Mathematica Plot (Shear Stress)

## Sample Output File (.ad_strn)

## Sample Output File (.ad_strs)

## References

- K.R. Loss and K.T. Keyward, Modeling and Analysis of Peel and Shear Stresses in Adhesively Bonded Joints, AIAA paper 84-0913.
- L.J. Hart-Smith, Adhesive-Bonded Double-Lap Joints, Technical Report NASA CR112235, Contract NAS1-11234, McDonnell Douglas/Douglas Aircraft Co., Jan. 1973.
- L.J. Hart-Smith, Design Methodology for Bonded-Bolted Composite Joints, Final Technical Report AFWAL-TR-81-3154, Vol. I, Contract F33615-79-C-3212, McDonnell Douglas/Douglas Aircraft Co., Feb. 1982.