D3PLOT 22.1

RESPONSE SPECTRUM ANALYSIS Combination Methods

RESPONSE SPECTRUM ANALYSIS Combination Methods

D3Plot provides two methods for combining the modes; Square Root Sum of Squares (SRSS) and Complete Quadratic Combination (CQC).

Square Root Sum of Squares

For each result value stored in the ptf file, the SRSS method calculates the combined total with the formula:

Where:
Are the participation factors for mode <i> in the global X, Y and Z directions. These are extracted from the 'eigout' file output from Dyna.
Are the spectral accelerations for mode <i> in the global X, Y and Z directions. These are extracted from the Time Period vs. Acceleration curves provided by the user.
Is the frequency of mode <i>.
Is a factor that is applied to the results by Dyna to make the mode shapes visible. This is extracted automatically by D3Plot from the results file.
Is the results value at mode <i>

There are two important points to note:

  1. All results values are processed this way. This will not make sense in some cases, for example, thin shell thickness will be incorrect in the combined mode.
  2. Thin shell stress tensors are rotated to the elements local coordinate system of the undeformed geometry before they are combined. They are rotated back to the global coordinate system in the combined mode.
By default the results from all the modes will be combined, but if you wish you can choose to only consider a subset of modes. To do this, press the Modes button to bring up the panel shown on the right.

Complete Quadratic Combination

The CQC method is an improvement on the SRSS method as it allows for interactions between closely spaced nodes, but it takes longer to process.

For each result value stored in the ptf file, the CQC method calculates the combined total with the formula:

Where:

Is the response for mode <i>
Is the response for mode <j>
Is the Cross Modal Coefficient for modes <i> and <j>

Where:

Are the damping ratios for modes <i> and <j>
Is the ratio of the frequencies of modes <i> and <j>

As with the SRSS method the following two points should be noted:

  1. All results values are processed this way. This will not make sense in some cases, for example, thin shell thickness will be incorrect in the combined mode.
  2. Thin shell stress tensors are rotated to the elements local coordinate system of the undeformed geometry before they are combined. They are rotated back to the global coordinate system in the combined mod

By default all modes will be processed and the damping for each mode is set to 5%. As with the SRSS method you can chose to select only a subset of modes to consider by pressing the Modes button. This will bring up the panel shown on the right.

Also in this panel different damping values can be set for each mode.




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