Linear Assumptions

In a linear analysis, the response is directly proportional to the load, displacements and rotations are assumed to be small, supports do not settle, stress is directly proportional to strain (according to Young's Modulus), and loads maintain their original directions as the structure deforms. In general, equilibrium equations are written for the original support conditions, elastic stress-strain relations, load-free configuration, and load directions.

Nonlinear Issues

Unfortunately, for nonlinear analysis, the linear assumptions are no longer true. Nonlinearity makes a problem more complicated because equations that describe the solution must incorporate conditions not fully known until the solution is known - i.e. the actual configuration, loading condition, state of stress, and support condition. Therefore, the solution cannot be determined in a single step and iteration is necessary to converge on the correct solution.

In a sense a nonlinear analysis is somewhat more restrictive than a linear analysis. For example, the principle of superposition does not apply; we cannot scale results in proportion to load or combine results from different load cases as in a linear analysis. Accordingly, each individual load case requires a separate analysis. In essence, we just want you to be aware that many of these new features use nonlinear analysis techniques and the assumptions and results should be interpreted carefully.

Geometric Nonlinearity

Nonlinear problems are widely categorized in two categories; geometric and material. A common example of geometric nonlinearity is a cantilevered beam with a very large tip load. As the beam deflects it rotates and the tip load "follows" the beam thereby not acting solely in the direction it was originally applied. The cable elements are a prime example of geometrical nonlinear behavior.

Material Nonlinearity

A common example of material nonlinearity is cracking concrete. As you load a concrete member near its ultimate capacity and beyond it exhibits highly nonlinear behavior due to the concrete material. Another example is the formation of a plastic-hinge in steel.

Types of Nonlinear Analysis in VisualAnalysis

The use of some nonlinear features in VisualAnalysis will preclude the use of others in the same project. If you find an feature disabled, it could be due to other features already present in your model.

• One-Way Elements: Add tension-only or compression-only members or spring supports to the model to get an iterated first-order analysis that adds/removes elements, providing nonlinear results.
• P-Delta: Iterated first-order analysis to include 2nd-order effects
• AISC Direct Analysis: Iterated P-Delta Analysis, including out-of-alignment adjustments, reduced stiffness of steel members, and notional loading.
• Time History: Time-dependent effects (forcing function) and inertial terms. You create a TIme History Load Case to get this.
• Cable Elements: Add cable elements to the model to get a nonlinear analysis.
• Semi-Rigid Member Ends: Yielding or cracking as a function of load at the ends of a member element. Mark the end(s) of members as semi-rigid connections to get a nonlinear analysis.

References

For more about nonlinear analysis and other aspects of finite element analysis there is a good text by Cook that we recommend.

1. Finite Element Modeling for Stress Analysis by Robert D. Cook.  John Wiley & Sons, 1995 ISBN 0-471-10774-3.