Green's functions for unsymmetric composite laminates with inclusions

Area of Science:

• Composite Materials Science
• Solid Mechanics
• Computational Engineering

Background:

• Unsymmetric composite laminates exhibit coupled stretching-bending deformations under combined mechanical loads.
• Existing Green's functions for elliptical inclusions in composites suffer from displacement discontinuities due to ignored rigid body movements.
• Complex logarithmic functions in Green's functions require careful handling of branch cuts.

Purpose of the Study:

• To correct existing Green's functions for unsymmetric composite laminates with elliptical inclusions.
• To provide a method for correctly evaluating complex logarithmic functions within Green's functions.
• To derive an explicit closed-form solution for the Green's function of deflection for boundary element method (BEM) application.

Main Methods:

• Correction of established Green's functions by addressing rigid body movements.
• Development of a simplified approach for evaluating multi-valued complex logarithmic functions.
• Derivation of explicit closed-form Green's functions for deflection.

Main Results:

• The corrected Green's functions ensure displacement continuity across the matrix-inclusion interface.
• A robust method for handling complex logarithmic functions is presented.
• An explicit Green's function for deflection is derived, suitable for BEM.
• The proposed method eliminates the need for interface meshing in BEM, saving computational time.

Conclusions:

• The corrected Green's functions provide accurate solutions for composite laminates with inclusions.
• The simplified evaluation of logarithmic functions enhances the applicability of Green's functions.
• The derived deflection Green's function significantly improves BEM efficiency and accuracy for composite structures.