# solve

Solve structural analysis, heat transfer, or electromagnetic analysis problem

## Syntax

## Description

solves the structural modal analysis problem represented by the finite element
analysis model `results`

= solve(`fem`

,"FrequencyRange",`[omega1,omega2]`

)`fem`

for all modes in the frequency range
`[omega1,omega2]`

. Define `omega1`

as
slightly lower than the lowest expected frequency and `omega2`

as slightly higher than the highest expected frequency. For example, if the
lowest expected frequency is zero, then use a small negative value for
`omega1`

.

performs an eigen decomposition of a linear thermal problem represented by the
finite element analysis model `results`

= solve(`fem`

,"DecayRange",`[lambda1,lambda2]`

)`fem`

for all modes in the
decay range `[lambda1,lambda2]`

. The resulting modes enable
you to:

Use the modal superposition method to speed up a transient thermal analysis.

Extract the reduced modal system to use, for example, in Simulink

^{®}.

obtains the modal basis of a linear or nonlinear thermal problem represented by
the finite element analysis model `results`

= solve(`fem`

,"Snapshots",`Tmatrix`

)`fem`

using proper
orthogonal decomposition (POD). You can use the resulting modes to speed up a
transient thermal analysis or, if your thermal model is linear, to extract the
reduced modal system.

,
`results`

= solve(`fem`

,`tlist`

,"ModalResults",`thermalModalR`

)

,
and
`results`

= solve(`fem`

,`tlist`

,"ModalResults",`structuralModalR`

)

solve a transient thermal or structural problem or a frequency response
structural problem, respectively, by using the modal superposition method to
speed up computations. First, perform modal analysis to compute natural
frequencies and mode shapes in a particular frequency or decay range. Then, use
this syntax to invoke the modal superposition method. The accuracy of the
results depends on the modes in the modal analysis results.`results`

= solve(`fem`

,`flist`

,"ModalResults",`structuralModalR`

)

and
`results`

= solve(`fem`

,`tlist`

,"ModalResults",`structuralModalR`

,"DampingZeta",`z`

)

solve a transient or frequency response structural problem with modal damping
using the results of modal analysis. Here, `results`

= solve(`fem`

,`flist`

,"ModalResults",`structuralModalR`

,"DampingZeta",`z`

)`z`

is the modal
damping ratio.

returns the solution to the static structural analysis model represented in
`structuralStaticResults`

= solve(`structuralStatic`

)`structuralStatic`

.

returns the solution to the transient structural dynamics model represented in
`structuralTransientResults`

= solve(`structuralTransient`

,`tlist`

)`structuralTransient`

at the times specified in
`tlist`

.

returns the solution to the frequency response model represented in
`structuralFrequencyResponseResults`

= solve(`structuralFrequencyResponse`

,`flist`

)`structuralFrequencyResponse`

at the frequencies
specified in `flist`

.

returns the solution to the modal analysis model for all modes in the frequency
range `structuralModalResults`

= solve(`structuralModal`

,"FrequencyRange",`[omega1,omega2]`

)`[omega1,omega2]`

. Define `omega1`

as
slightly lower than the lowest expected frequency and `omega2`

as slightly higher than the highest expected frequency. For example, if the
lowest expected frequency is zero, then use a small negative value for
`omega1`

.

and
`structuralTransientResults`

= solve(`structuralTransient`

,`tlist`

,"ModalResults",`structuralModalR`

)

solves a transient and a frequency response structural model, respectively, by
using the modal superposition method to speed up computations. First, perform
modal analysis to compute natural frequencies and mode shapes in a particular
frequency range. Then, use this syntax to invoke the modal superposition method.
The accuracy of the results depends on the modes in the modal analysis
results.`structuralFrequencyResponseResults`

= solve(`structuralFrequencyResponse`

,`flist`

,"ModalResults",`structuralModalR`

)

returns the solution to the steady-state thermal model represented in
`thermalSteadyStateResults`

= solve(`thermalSteadyState`

)`thermalSteadyState`

.

returns the solution to the transient thermal model represented in
`thermalTransientResults`

= solve(`thermalTransient`

,`tlist`

)`thermalTransient`

at the times specified in
`tlist`

.

performs an eigen decomposition of a linear thermal model
`thermalModalResults`

= solve(`thermalModal`

,"DecayRange",`[lambda1,lambda2]`

)`thermalModal`

for all modes in the decay range
`[lambda1,lambda2]`

. The resulting modes enable you
to:

Use the modal superposition method to speed up a transient thermal analysis.

Extract the reduced modal system to use, for example, in Simulink.

obtains the modal basis of a linear or nonlinear thermal model using proper
orthogonal decomposition (POD). You can use the resulting modes to speed up a
transient thermal analysis or, if your thermal model is linear, to extract the
reduced modal system.`thermalModalResults`

= solve(`thermalModal`

,"Snapshots",`Tmatrix`

)

solves a transient thermal model by using the modal superposition method to
speed up computations. First, perform modal decomposition to compute mode shapes
for a particular decay range. Then, use this syntax to invoke the modal
superposition method. The accuracy of the results depends on the modes in the
modal analysis results.`thermalTransientResults`

= solve(`thermalTransient`

,`tlist`

,"ModalResults",`thermalModalR`

)

returns the solution to the electrostatic, magnetostatic, or DC conduction model
represented in `emagStaticResults`

= solve(`emagmodel`

)`emagmodel`

.

returns the solution to the harmonic electromagnetic analysis model represented
in `emagHarmonicResults`

= solve(`emagmodel`

,"Frequency",`omega`

)`emagmodel`

at the frequencies specified in
`omega`

.

## Examples

## Input Arguments

## Output Arguments

## Tips

When you use modal analysis results to solve a transient structural dynamics model, the

`modalresults`

argument must be created in Partial Differential Equation Toolbox™ from R2019a or newer.For a frequency response model with damping, the results are complex. Use functions such as

`abs`

and`angle`

to obtain real-valued results, such as the magnitude and phase.

## Version History

**Introduced in R2017a**