Definition

An incremental load step refers to a method used in numerical analysis, particularly in finite element analysis (FEA), where a total load is applied in small, incremental steps rather than all at once. This approach is essential for solving nonlinear problems, where the relationship between load and response is not linear, and allows for a more accurate and stable solution by updating the stiffness matrix and other parameters at each step.

Calculation

During an incremental load step analysis, the total load P is divided into smaller increments ΔP, and the structure’s response is calculated iteratively at each step. The basic process involves:

• Applying a small load increment ΔPi at step i.
• Solving the equilibrium equations to determine the corresponding displacement increment Δui.
• Updating the structure’s stiffness matrix if the problem is nonlinear.
• Repeating the process until the total load P is applied.

Context of Use

Incremental load steps are crucial in various applications within geotechnical and structural engineering, particularly in the analysis of nonlinear problems:

• Nonlinear Structural Analysis: Incremental load steps are used to model the nonlinear behavior of materials, such as plastic deformation in metals or cracking in concrete.
• Soil-Structure Interaction: In geotechnical engineering, incremental load steps help simulate complex interactions between structures and soil, particularly when dealing with large deformations or nonlinear soil behavior.
• Dynamic Analysis: Incremental load steps are applied in dynamic analysis to model the time-dependent response of structures to loads such as earthquakes or wind, ensuring stability and accuracy over time.
• Staged Construction Analysis: This method is used in staged construction projects, where loads are applied in phases, such as in the construction of multi-story buildings or bridges, to simulate the actual construction process.

Advantages

• Improved Accuracy: Incremental load steps allow for more accurate modeling of complex, nonlinear behaviors by progressively adjusting the analysis based on the structure’s response.
• Enhanced Stability: Applying loads incrementally helps maintain numerical stability in simulations, particularly in highly nonlinear problems where direct application of the total load could lead to divergence or inaccurate results.

Limitations

• Increased Computational Effort: The incremental approach requires more computational time and resources, as the analysis must be repeated for each load step.
• Potential for Convergence Issues: In some cases, especially in highly nonlinear problems, the solution may not converge, requiring adjustments in load step size or other numerical parameters.

Summary

Incremental load steps are a critical technique in finite element analysis and other numerical methods, allowing for accurate and stable solutions to complex, nonlinear problems. By applying loads incrementally and updating the analysis at each step, engineers can model the behavior of structures and materials under realistic conditions, such as soil-structure interaction, staged construction, and dynamic loading. While this method increases computational effort, it is essential for ensuring the reliability and accuracy of the analysis, especially in challenging engineering scenarios.

Further Reading

• What is an incremental load step and how is it used in FEA?
• How to apply incremental load steps in nonlinear analysis using GEO5?

Need Help?

If you require further assistance, consider booking an online presentation with a 5% discount here.