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Nonlinear Analysis

Requires: Advanced Level


Many of the features of the VisualAnalysis are inherently nonlinear in some fashion and special attention should be paid to the modeling assumptions we make and the results we get from the program. 

In the usual linear analysis we are used to dealing with, response is directly proportional to load. In a linear analysis we assume that displacements and rotations are small, supports do not settle, stress is directly proportional to strain with 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. Unfortunately, for nonlinear analysis, these assumptions are no longer true.

Essentially, 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.


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.