A FINITE ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS WITH LOCALLY MODIFIED TRIANGULATIONS.

Area of Science:

• Computational mechanics
• Solid mechanics
• Numerical analysis

Background:

• Discontinuities in material properties and flux across interfaces pose challenges for standard numerical methods in elasticity.
• Existing finite element methods may require complex mesh generation or lead to increased computational cost when dealing with such discontinuities.

Purpose of the Study:

• To propose a novel finite element method for solving elasticity systems with discontinuities in coefficients and flux across arbitrary interfaces.
• To maintain the computational efficiency of standard finite element methods while accommodating complex interface conditions.

Main Methods:

• A finite element method based on a Cartesian mesh with local modifications.
• Local mesh adjustments create a quasi-uniform, body-fitted mesh from the initial Cartesian grid.
• Ensuring standard finite element theory and implementation remain applicable.

Main Results:

• The proposed method effectively handles systems with discontinuous material coefficients.
• Numerical examples demonstrate successful management of non-homogeneous jumps in flux across interfaces.
• The method shows efficiency in computational performance.

Conclusions:

• The developed finite element method provides an efficient and applicable solution for elasticity problems with interface discontinuities.
• Local mesh modifications on a Cartesian grid offer a practical approach to complex material interfaces.
• The technique preserves the advantages of standard finite element implementations.