Can the same model be used for nonlinear analysis like in linear analysis? No, you will have to add a ton of information into the computer model to do nonlinear analysis. You will have to add stress strain curve for concrete, for steel. You will have to define backbone curves for beams. You will have to define P-M-M back bone curves for columns. You will have to define fiber elements for shear walls. You will be defining P-delta columns. You will be defining the limit states. The back bone curves for coupling beams for different aspect ratios are different. So all in all, to create and test one nonlinear model, it will take you about a month. Analysis will take a day. And processing the results will take another day.
What does program do is. It will start with the initial stiffness of the building which is right because before a building is loaded how can there be any cracks and loss in stiffness? Then the building is loaded with incremental loads. And it will go on increasing the loads till it reaches the limit of linearity. As soon as it hits the nonlinear zones, it will start iterating the model. Load the structure calculate the strains and deflections and stiffness. Loss in stiffness -> Yes? Iterate the same step. Loss in stiffness -> No? Go to the next load step and so on.
Nonlinear analysis is a complex task. It is the best example of "Half knowledge" is dangerous. If you do not know anything about nonlinearity then first learn it and then perform analysis. If you do it before that you will set up incorrect model and you will not be able to interpret the results.
Performing large displacement analysis of a geometrically non-linear frame using the Direct Stiffness Method (DSM) requires accounting for the fact that geometry (e.g., member orientation and length) changes significantly during deformation. Here's a simplified breakdown of how to do it:
🔁 Step-by-Step Procedure
1. Model the Initial Frame
- Divide the structure into elements (beams, trusses, etc.)
- Define initial nodal coordinates and element connectivity.
- Assign material properties (E, A, I) and initial geometry.
2. Use Co-Rotational Formulation (Optional but Recommended)
- In large displacement analysis, a co-rotational approach is often used: Each element has a local coordinate system that "moves" with the element. Linear stiffness can be applied in the local frame, then transformed back.
3. Compute Element Stiffness Matrix (Nonlinear)
- Use a geometrically nonlinear formulation like: Total Lagrangian (reference configuration) Updated Lagrangian (current configuration)
- Include geometric stiffness (initial stress or P–Δ effects).
4. Assemble Global Stiffness Matrix
- Combine all element stiffness matrices into a global system:K(u)u=F\mathbf{K}(\mathbf{u}) \mathbf{u} = \mathbf{F}where: K(u)\mathbf{K}(\mathbf{u}): Nonlinear global stiffness matrix u\mathbf{u}: Displacement vector F\mathbf{F}: External load vector
5. Iterative Solution (e.g., Newton-Raphson)
- Nonlinear problems require iteration: Initialize displacement u0\mathbf{u}_0 At each iteration: Compute internal forces Compute/update tangent stiffness matrix Solve for displacement increment Update displacement: ui+1=ui+Δu\mathbf{u}_{i+1} = \mathbf{u}_i + \Delta\mathbf{u} Repeat until convergence (e.g., residual force < tolerance)
6. Update Geometry
- After each load increment or iteration, update: Nodal positions Element orientations Recalculate stiffness matrices as needed
7. Apply Boundary Conditions
- Apply constraints and supports at each step correctly.
8. Post-Processing
- Extract final displacements, rotations, internal forces, and moments.
- Check for convergence and stability (buckling, etc.)
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