Linear barycentric rational collocation method to solve plane elasticity problems

Area of Science:

• Numerical analysis
• Computational mechanics
• Applied mathematics

Background:

• Solving equilibrium equations is crucial in various scientific and engineering fields.
• Traditional methods may face challenges with complex geometries or boundary conditions.
• Polar coordinate systems are essential for problems with radial symmetry.

Purpose of the Study:

• To develop and analyze a novel linear barycentric rational collocation method.
• To apply this method to equilibrium equations formulated in polar coordinates.
• To establish the convergence rate of the proposed numerical technique.

Main Methods:

• Formulation of equilibrium equations in polar coordinates.
• Discretization of continuous equations into a matrix form using a linear barycentric rational collocation approach.
• Analysis of interpolation error in barycentric polar coordinates to determine convergence.
• Implementation of numerical examples for validation.

Main Results:

• The discrete linear equations were successfully transformed into matrix forms.
• The convergence rate of the method was theoretically established.
• Numerical examples demonstrated the effectiveness and accuracy of the proposed method.

Conclusions:

• The linear barycentric rational collocation method provides an effective approach for solving equilibrium equations in polar coordinates.
• The theoretical analysis and numerical results confirm the method's convergence properties.
• This method offers a valuable tool for computational analysis in relevant scientific domains.