On Critical Buckling Loads of Columns under End Load Dependent on Direction

Area of Science:

• Applied Sciences
• Nonlinear Dynamics
• Structural Mechanics

Background:

• Nonlinear problems are prevalent across applied sciences.
• Analytical approximate solution techniques are crucial for solving nonlinear differential equations.
• The Homotopy analysis method (HAM) is a powerful technique for addressing such problems.

Purpose of the Study:

• To apply the Homotopy analysis method (HAM) to a specific nonlinear problem.
• To determine the critical buckling load of a column subjected to direction-dependent end loads.

Main Methods:

• Utilized the Homotopy analysis method (HAM).
• Applied HAM to analyze column buckling under complex loading conditions.

Main Results:

• Successfully obtained critical buckling load values for the specified column.
• Demonstrated excellent agreement between HAM-derived loads and existing exact analytical solutions.

Conclusions:

• The Homotopy analysis method (HAM) is effective for solving nonlinear structural mechanics problems.
• HAM provides accurate predictions for critical buckling loads in columns with direction-dependent end loads.