# Large deformation in modal analysis

• Mohamed_Wael
In summary, the conversation discusses the use of Ansys Modal analysis to simulate a rhombus compliant mechanism. The concern is that the deformation values are extremely large, but the expert advises to focus on the mode shapes and frequencies rather than the deformation values. They explain how the mode shapes are normalized and how this affects the comparison of deflections between different modes. The reason for this choice is for convenience in dynamic analysis.
Mohamed_Wael
Hi all,
I have been simulating the following rhombus compliant mechanism using Ansys Modal analysis to have a quick understanding about its mode shapes,,,, the problem is that the deformation is extremely large you can see this as the scale is (*10^-5 ) . This result is for sure unrealistic but what does it indicate or what might be my mistake in the modeling https://goo.gl/WbQcxJ

Last edited:
Hi Mohamed,

As a general rule I would pay attention to the mode shapes and frequencies but ignore the deformation values in a modal FEA analysis. The amplitude of the individual modes is a mass-normalized value which doesn't typically allow for apples-to-apples comparisons between nodes. See here:

AlephZero said:
The simple-minded answer is, you can only compare the relative deflections at different points in the same mode shape. You can't compare the size of the deflections at the same point in two different modes - unless the deflection is zero at that point in one of the modes.

The less-simple-minded answer is, it depends how the different mode shapes are "normalized" when they are output. There are two "common sense" methods that are sometimes used:

1. Make the biggest deflection in each mode = 1.0 (wherever it occurs, usually at a different place in each mode)
2. Make the deflection at a place that you specify in the input = 1.0, for all the modes. (The deflection at other places in the structure maybe bigger than 1, of course).

But more likely, the mode shapes will be "mass normalized", which means the product ##x^TMx = 1## where ##x## is the mode shape vector and ##M## is the mass matrix of the structure. That means the internal energy (potential + kinetic) in different modes is proportional to the frequency squared, for the values of the displacements that are output.

The reason for this choice is because it is very convenient for using the mode shapes as generalized coordinates (in the sense of Lagrangian mechanics) for dynamic analysis both in the time domain (transient dynamics analysis) and the frequency domain (steady state response analysis). Most course notes / web sites / textbooks on dynamics of multi degree of freedom (MDOF) systems will have some of the math behind this, for "simple" systems modeled by point masses connected by springs. The basic ideas are exactly the same for finite element models - the only difference is that the finite element mass and stiffness are formulated in a more general way.

Mohamed_Wael

## What is large deformation in modal analysis?

Large deformation in modal analysis refers to the analysis of structures that undergo significant displacements and deformations during their operation. This can be caused by external forces, such as earthquakes or wind, or internal forces, such as thermal expansion or fluid flow. It is an important aspect of structural analysis as it allows for a more accurate representation of the behavior of a structure under real-world conditions.

## How is large deformation different from small deformation in modal analysis?

Small deformation in modal analysis assumes that the structure's deformations are relatively small compared to its original size. This simplifies the analysis process and allows for the use of linear equations. Large deformation, on the other hand, takes into account the non-linear behavior of the structure and requires the use of non-linear equations to accurately model the deformations.

## What factors can cause large deformation in a structure?

Several factors can contribute to large deformation in a structure, including external forces, material properties, and geometric non-linearity. External forces, such as seismic activity or wind, can cause significant displacements and deformations in a structure. Material properties, such as non-linear stress-strain relationships, can also contribute to large deformations. Lastly, geometric non-linearity, such as large rotations or changes in the structure's shape, can also cause large deformation.

## How is large deformation in modal analysis calculated?

Large deformation in modal analysis is typically calculated using numerical methods, such as the finite element method. This involves dividing the structure into smaller elements and solving a set of non-linear equations to determine the displacements and deformations at each element. The results are then combined to obtain the overall behavior of the structure.

## Why is it important to consider large deformation in modal analysis?

Large deformation is important to consider in modal analysis as it provides a more accurate representation of how a structure will behave under real-world conditions. Neglecting large deformation can lead to significant errors in the analysis and design of structures, potentially resulting in failures or safety hazards. Therefore, considering large deformation is crucial in ensuring the structural integrity and safety of a system.

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