Electrical Analysis

An electrical analysis involves calculation of electric potential in structures subject to electrical loads.

The basic finite element equation to be solved for structures experiencing electrical loads can be expressed as:(1)

K_{C} φ = f

Where,

$K_{C}$: Electrical conduction matrix
$φ$: Electric potential
$f$: Electric current

This is the equilibrium equation of electric currents and is solved for the unknown electric potential.

Electrical Analysis in OptiStruct

A standalone electrical analysis case in OptiStruct can be categorized into the following types:

Steady-State Electrical Conduction (SSEC)

The loading (current or enforced voltage) is time independent.

SSEC is used for Joule heating calculations, to generate Joule heating for further steady heat transfer analysis.

Example:

SUBCASE 1
   ANALYSIS ELEC
   SPC = 1
   LOAD = 2
   TEMP(MAT) = 4

Multi Steady Electrical Conduction (MSEC)

The loading (current or enforced voltage) is time dependent.

MSEC is mainly used to generate Joule heating for further transient heat transfer analysis.

Example:

SUBCASE 1
   ANALYSIS ELEC
   SPC = 1
   DLOAD = 3
   TEMP(MAT) = 4

Coupled Electrical Analysis

Electrical analysis can be coupled with heat transfer analysis.

With coupled electrical analysis, the Joule heating from electrical analysis can be passed for further heat transfer analysis (for example, defrosting of a car windshield). Coupling can be 1-way or 2-way.

Steady-State (linear/nonlinear) Heat Transfer analysis can only be coupled with SSEC.
Transient (linear/nonlinear) Heat Transfer analysis can only be coupled with MSEC.
Note: Transient (linear/nonlinear) Heat Transfer analysis can still call an SSEC subcase via a DLOAD (that refers to a TLOAD, referencing a SSEC subcase). This is not a coupling and the solution from SSEC is used as a loading, like QVOL, in this case.
For an example use case, if the electrical load is constant and the electrical material is temperature independent, this method can greatly reduce computational time. Without this method, the solution must be computed at each time-step.

1-Way Coupling

1-way coupling is sufficient when electrical material is temperature independent. Since the material property is constant, the electrical subcase can be solved once. Some examples are:

Example 1: Steady-State Heat Transfer Analysis Calls SSEC as Loading

Subcase 101
   ANALYSIS ELEC
   SPC = 20
   LOAD = 22
Subcase 102
   ANALYSIS HEAT
   SPC  = 21
   JOULE = 101
   LOAD = 25

Example 2: SSEC Uses Steady-State Heat Transfer Analysis to Update Material

SUBCASE 101
   ANALYSIS ELEC
   SPC = 20
   LOAD = 22
   TEMP(MAT) = 102
SUBCASE 102
   ANALYSIS HEAT
   SPC  = 21
   LOAD = 25

Note: At this time, MSEC cannot be used a standalone subcase. It cannot use transient heat transfer subcase to update material.

2-Way Coupling

2-way coupling is required/used when electrical material is temperature dependent. Some examples are:

SSEC Uses Steady-State Heat Transfer to Update Material

Joule heating from SSEC is applied to steady-state heat transfer analysis.

SUBCASE 101
   ANALYSIS ELEC
   SPC = 20
   LOAD = 22
   TEMP(MAT) = 102
SUBCASE 102
   ANALYSIS HEAT
   SPC  = 21
   JOULE = 101
   LOAD = 25

MSEC Uses Transient Heat Transfer Analysis to Update Material

Joule heating from MSEC is applied to transient heat transfer analysis.

SUBCASE 101
   ANALYSIS ELEC
   SPC = 20
   DLOAD = 23
   TEMP(MAT) = 102
SUBCASE 102
   ANALYSIS HEAT
   SPC  = 21
   JOULE = 101
   DLOAD = 24 $ This DLOAD cannot refer TLOAD of TYPE = JOULE
   TSTEP  = 9

Examples for 1-way and 2-way coupling can be extended to nonlinear steady-state heat transfer subcases.

The TPID and TCID fields on PCONTEC entry are available to define tables for contact pressure-dependent and contact-clearance dependent resistance per unit area. The table lookup values are multiplied by the actual contact area to calculate the resistance.

Input

A summary of the relevant input file entries in an electrical analysis.

The relevant Subcase Information Entries are:

Table 1. Subcase Information Entries
Entry	Purpose
ANALYSIS = ELEC	Defines an electrical analysis subcase
JOULE	References an electrical analysis subcase from a heat transfer subcase in a coupled thermo-electrical analysis

The relevant Bulk Data Entries are:

Table 2. Bulk Data Entries
Entry	Purpose
SPC, SPCD	Potential
CURRENT	Nodal current
CDENST4	Current density
MAT1EC	Isotropic electrical material
MAT2EC	Anisotropic electrical material
MATT1EC, MATT2EC	Temperature dependent material
PGAPEC	Electrical resistance properties for gap elements
PCONTEC	Contact Electric Resistance Coefficient (CERC) for CONTACT element

The TLOAD entry supports Joule loss density excitation (TYPE = J, JO, JOU, or JOUL). EXCITEID refers to the ID of a steady-state electrical subcase from which the Joule loss density can be applied to a transient heat transfer subcase.

Analogy

The following table summarizes the analogy of some electrical analysis entries with the existing thermal/structural analysis.

Table 3. Analogy for Electrical Analysis
Type	Electrical Analysis	Thermal Analysis	Structural Analysis
Result output	Electrical potential	Temperature	Displacement
Result output	Electrical field	Temperature Gradient	Strain
Loads and boundary conditions	CURRENT		FORCE
	CDENST4	QBDY1	PLOAD4
	SPC (Electrical potential)	SPC (Temperature)	SPC (Displacement)
	SPCD (Electrical potential)	SPCD (Temperature)	SPCD (Displacement)
Material	MAT1EC	MAT4	MAT1
	MAT2EC	MAT5	MAT9
	MATT1EC	MATT4	MATT1
	MATT2EC	MATT5	MATT9

Problem Setup

Example of an electrical analysis setup.

The following input file snippet shows an example of an electrical analysis setup:

$ *************************************************************
$ EXAMPLE TO DEMONSTRATE AN ELECTRICAL ANALYSIS SETUP
$ *************************************************************
OLOAD     = 11 
VOLTAGE   = 11    
GPCURRENT = 11    
ELECMAT   = 22 
ELECFIELD = 22    
HEAT      = 22
CURRDEN   = 22    
 
SUBCASE        1
  LABEL HEAT
  ANALYSIS HEAT
  IC =        1
  JOULE =     2
  TSTEP =     9
  DLOAD =     28
  SPC   =     12
  NLPARM =    6
  
SUBCASE        2
  LABEL ELEC
  ANALYSIS ELEC
  DLOAD   =   3
  SPC     =  10
  TEMP(MAT) = 1.

BEGIN BULK
...

Electrical Optimization

Optimization is supported for Electrical Analysis. Topology, Shape, Free-shape, Size, and Free-size optimization design variables are supported. The following responses are currently supported:

The Nodal Electric Potential response is activated by setting the RTYPE field to ELPOT on the DRESP1 Bulk Data Entry. The GRID ID can be defined on the ATTi field.
The Global Electric Compliance response is activated by setting the RTYPE field to ELCOMP on the DRESP1 Bulk Data Entry.

DRESP2 and DRESP3 Bulk Data Entries for response combinations are also supported. Optimization for electrical analysis is supported for all element types and is currently supported for linear steady-state electrical conduction analysis. Temperature-dependency and electro-thermal coupling are currently not supported.

Example

A visual example of modeling Joule heating in a Busbar system.

Busbars are commonly used in many applications to provide power to various electronic boxes.

The model consists is an electrical system with five circuits. The circuits are separated from each other using a thin di-electric layer.

An initial temperature of 20 degrees Celsius is applied to all the bodies.

Point currents are specified using the CURRENT Bulk Data Entry at the terminals, while 0V voltage is applied using SPC.

The temperature distribution on the model is:

The electric potential on the model is:

Output

Supported output requests for electrical analysis.

Currently, results are only available in .h3d format in a separate *_elecht.h3d file.

The supported output requests are:

Table 4. Supported Output Requests for Electrical Analysis
Result	Purpose	Details
VOLTAGE	Voltage	Available by default
HEAT	Joule loss density	Available by default
CURRDEN	Current density	Available by default
ELECFIELD	Electric field
ELECMAT	Conductivity and resistivity
GPCURRENT	Grid Point current
OLOAD	Applied nodal current

A current balance summary table is available in the .out file for steady-state electrical conduction analysis. This is similar to the SPCFORCE output table and consists of total applied current and SPC current.

This table is currently unavailable for MSEC analysis.