Numerical methods for static shallow shells lying over an obstacle

Area of Science:

• Computational Mechanics
• Solid Mechanics
• Numerical Analysis

Background:

• Obstacle problems are crucial in engineering and physics.
• Shallow shell structures confined in a half space present unique analytical challenges.
• Existing numerical methods may require refinement for accuracy and convergence.

Purpose of the Study:

• To develop and analyze a finite element method for solving static shallow shell obstacle problems.
• To establish an error estimate for the approximate bilinear form.
• To prove the convergence of the proposed numerical scheme.

Main Methods:

• Finite element analysis (FEA).
• Utilizing properties of enriching operators.
• Conducting rigorous error analysis.

Main Results:

• An estimate for the approximate bilinear form was established.
• The convergence of the finite element scheme was mathematically proven.
• The proposed method provides an accurate approximation for the problem.

Conclusions:

• The presented finite element analysis is a viable and convergent numerical scheme.
• This work contributes to the accurate computational modeling of static shallow shells with obstacles.
• The findings are applicable to advanced engineering simulations.