ANSYS Coupled-Field Analysis Guide phần 7 doc

Table 7.1 Coupled-Field Elements Description Element Name Coupled-field hexahedral SOLID5 Coupled-field quadrilateral PLANE13 Acoustic quadrilateral FLUID29 Acoustic hexahedral FLUID30 3

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Figure 6.14 Modal Amplitude of Mode 1 vs High Polarization Voltage

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Figure 6.15 Modal Amplitude of Mode 3 vs High Polarization Voltage

Calculated capacitances are shown in the following figures

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ANSYS Coupled-Field Analysis Guide ANSYS Release 10.0 002184 © SAS IP, Inc.

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Figure 6.16 Capacitances CAP12 and CAP13 vs High Polarization Voltage

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Figure 6.17 Capacitance CAP23 vs High Polarization Voltage

Calculation of displacements at acting element loads

! *** Calculate deflection state at acting element loads

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Figure 6.18 Expanded Displacements for Acceleration Load

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Figure 6.19 Expanded Displacements for Pressure Load

Prestressed harmonic analysis

The following example demonstrates the change of harmonic transfer functions at different polarization voltages.The higher the applied polarization voltage, the more the resonance peak shifts to the left

! *** Prestressed harmonic analysis

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Figure 6.21 Harmonic Transfer Function Phase Angle for 800 V Polarization Voltage

Nonlinear Transient Analysis

! *** Nonlinear transient analysis

cycle_t=500e-6 ! Cycle time of one saw tooth

! about 20 times the cycle time of mode 1

rise_t=cycle_t/10 ! Rise time

num_cyc=3 ! Number of cycles

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Figure 6.22 Modal Amplitudes vs Time at Saw Tooth Like Voltage Function

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Chapter 7: Direct Coupled-Field Analysis

The direct method for doing a coupled-field analysis involves a single analysis that uses a coupled-field element.

Table 7.1: “Coupled-Field Elements” lists the elements that have coupled-field capability

Table 7.1 Coupled-Field Elements

Description Element Name

Coupled-field hexahedral SOLID5

Coupled-field quadrilateral PLANE13

Acoustic quadrilateral FLUID29

Acoustic hexahedral FLUID30

3-D magneto-structural hexahedral SOLID62

Thermal-electric quadrilateral PLANE67

Thermal-electric line LINK68

Thermal-electric hexahedral SOLID69

Piezoelectric circuit CIRCU94

Coupled-field tetrahedral SOLID98

2-D Electromechanical Transducer TRANS109

Thermal-flow pipe FLUID116

General circuit CIRCU124

1-D Electromechanical Transducer TRANS126

Thermal-electric shell SHELL157

2-D surface to surface contact CONTA171

2-D/3-D node to surface contact CONTA175

Coupled-field quadrilateral PLANE223

Coupled-field hexahedral SOLID226

Coupled-field tetrahedral SOLID227

Note — Your finite element model may intermix certain coupled-field elements with the VOLT degree

of freedom To be compatible, the elements must have the same reaction force (see Element

Compatib-ility in the ANSYS Low-Frequency Electromagnetic Analysis Guide).

The coupled-field element contains all the necessary degrees of freedom It handles the field coupling by

calcu-lating the appropriate element matrices (matrix coupling) or element load vectors (load vector coupling) In linear

problems with matrix coupling, coupled-field interaction is calculated in one iteration Load vector coupling quires at least two iterations to achieve a coupled response Nonlinear problems are iterative for both matrixand load vector coupling Table 7.2: “Coupling Methods Used in Direct Coupled-Field Analyses” lists the differenttypes of coupled-field analyses available in the ANSYS Multiphysics product using the direct method, and which

re-type of coupling is present in each See the ANSYS, Inc Theory Reference for more details about matrix versus load

vector coupling

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The ANSYS Professional program supports only thermal-electric direct coupling, and the ANSYS Emag programsupports only electromagnetic and electromagnetic-circuit direct coupling.

Table 7.2 Coupling Methods Used in Direct Coupled-Field Analyses

Coupling Method Type of Analysis

Load vector Magneto-structural

Matrix Electromagnetic

Load vector Electromagnetic-thermal-structural

Load vector Electromagnetic-thermal

Matrix Piezoelectric

Load vector Piezoresistive

Matrix and load vector Thermal-pressure

Matrix Velocity-thermal-pressure

Matrix Pressure-structural (acoustic)

Load vector (and matrix, if Seebeck coefficients are defined)

Thermal-electric

Load vector Magnetic-thermal

Load vector Electrostatic-structural

Matrix Electromagnetic-circuit

Matrix Electro-structural-circuit

Matrix or load vector (and matrix, if contact elements are used)

Structural-thermal

Matrix and/or load vector Structural-thermal-electric

Matrix Thermal-piezoelectric

Note — Coupled-field elements that use load vector coupling are not valid in a substructure analysis.

Within the substructure generation pass, no iterative solution is available; therefore, the ANSYS programignores all load vector and feedback coupling effects

Because of the possible extreme nonlinear behavior of load vector coupled field elements, you may need to usethe predictor and line search options to achieve convergence Chapter 8, “Nonlinear Structural Analysis” in the

ANSYS Structural Analysis Guide describes these options.

To speed up convergence in a coupled-field transient analysis, you may turn off the time integration effects forany DOFs that are not a concern For example, if structural inertial and damping effects can be ignored in a

thermal-structural transient analysis, you can issue TIMINT,OFF,STRUC to turn off the time integration effects

for the structural DOFs

Of the analysis types listed above, this chapter explains how to do thermal-electric, piezoelectric, piezoresistive,structural-thermal, structural-thermal-electric, magneto-structural, and electrostatic-structural analyses

Electric contact is also available in ANSYS See Modeling Electric Contact in the ANSYS Contact Technology Guide

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7.9 Sample Thermoelectric Cooler Analysis (Batch or Command Method)

7.10 Sample Thermoelectric Generator Analysis (Batch or Command Method)

7.11 Sample Structural-Thermal Harmonic Analysis (Batch or Command Method)

7.12 Sample Electro-Thermal Microactuator Analysis (Batch or Command Method)

7.13 Sample Piezoelectric Analysis (Batch or Command Method)

7.14 Sample Piezoresistive Analysis (Batch or Command Method)

7.15 Sample Electromechanical Analysis (Batch or Command Method)

7.16 Sample Electromechanical Transient Analysis (Batch or Command Method)

7.17 Sample Electromechanical Hysteresis Analysis (Batch or Command Method)

7.18 Sample Electromechanical Comb Finger Analysis (Batch or Command Method)

7.19 Sample Force Calculation of Two Opposite Electrodes (Batch or Command Method)

7.20 Where to Find Other Examples

7.1 Lumped Electric Elements

ANSYS provides several lumped elements that can be applied in pure electric circuit, circuit coupled magnetic,piezoelectric and coupled electromechanical analyses This section provides a brief overview For more details

on DOF, through variables (force, reaction force), and element compatibility, refer to this guide, the ANSYS Elements

Reference, and Element Compatibility in the ANSYS Low-Frequency Electromagnetic Analysis Guide.

CIRCU94 is a circuit element with electric potential (VOLT) DOF and negative electric charge (AMPS label) throughvariable (force, reaction force) Depending on KEYOPT selection it can act like a linear resistor, capacitor, inductor,

or an independent voltage or current source CIRCU94 can be applied in connection with other ANSYS elementshaving the same DOF and through variable (force, reaction force): SOLID5, PLANE13, SOLID98, PLANE230, SOL-ID231, and SOLID232 to simulate circuit coupled piezoelectric analysis

CIRCU124 is a circuit element with electric potential (VOLT) DOF and electric current (AMPS label) through variable(force, reaction force) Depending on KEYOPT selection it can act like a linear resistor, capacitor, inductor, or anumber of circuit source or coupled circuit source options CIRCU124 can be applied in connection with otherANSYS elements having the same DOF and through variable (force, reaction force): SOLID5, PLANE67, SOLID69,SOLID98, CIRCU125, TRANS126, PLANE223, SOLID226, SOLID227, PLANE230 SOLID231, and SOLID232 CIRCU124can also work together with magnetic elements PLANE13, PLANE53, and SOLID97 to simulate circuit fed mag-netic analysis

CIRCU125 is a circuit element with electric potential (VOLT) DOF and electric current (AMPS label) through variable(force, reaction force) Depending on KEYOPT selection it can act like a regular or Zener diode circuit CIRCU125can be applied in connection with other ANSYS elements having the same DOF and through variable (force, re-action force): CIRCU124, TRANS126, PLANE67, and SOLID69

TRANS126 is an electromechanical transducer with electric potential (VOLT) as well as mechanical displacement(UX, UY, UZ) DOFs and electric current (AMPS label), as well as mechanical force (FX, FY, FZ) through variables(force, reaction force) TRANS126 can be applied in connection with other ANSYS elements having the same DOFand through variable (force, reaction force): CIRCU124, CIRCU125, PLANE67, and SOLID69 It can also be applied

in connection with all regular ANSYS mechanical elements to simulate strongly coupled electromechanical actions, a characteristic of MEMS design

inter-7–3

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7.2 Thermal-Electric Analysis

This analysis, available in the ANSYS Multiphysics product, can account for the following thermoelectric effects:

• Joule heating - Heating occurs in a conductor carrying an electric current Joule heat is proportional to the

square of the current, and is independent of the current direction

• Seebeck effect - A voltage (Seebeck EMF) is produced in a thermoelectric material by a temperature

differ-ence The induced voltage is proportional to the temperature differdiffer-ence The proportionality coefficient

is know as the Seebeck coefficient (α)

• Peltier effect - Cooling or heating occurs at the junction of two dissimilar thermoelectric materials when

an electric current flows through the junction Peltier heat is proportional to the current, and changessign if the current direction is reversed

• Thomson effect - Heat is absorbed or released in a non-uniformly heated thermoelectric material when

electric current flows through it Thomson heat is proportional to the current, and changes sign if thecurrent direction is reversed

Typical applications include heating coils, fuses, thermocouples, and thermoelectric coolers and generators For

more information, refer to Thermoelectrics in the ANSYS, Inc Theory Reference.

7.2.1 Elements Used in a Thermal-Electric Analysis

The ANSYS program includes a variety of elements you can use to model thermal-electric coupling

Table 7.3: “Elements Used in Thermal-Electric Analyses” summarizes them briefly For detailed descriptions of

the elements and their characteristics (DOFs, KEYOPT options, inputs and outputs, etc.), see the ANSYS Elements

Reference.

LINK68, PLANE67, SOLID69, and SHELL157 are special purpose thermal-electric elements The coupled-fieldelements (SOLID5, SOLID98, PLANE223, SOLID226, and SOLID227 ) require you to select the element DOFs for athermal-electric analysis: TEMP and VOLT For SOLID5 and SOLID98, set KEYOPT(1) to 0 or 1 For PLANE223,SOLID226, and SOLID227, set KEYOPT(1) to 110

Table 7.3 Elements Used in Thermal-Electric Analyses

Analysis Types Material Properties

Thermoelectric Effects Elements

Static Transient (transient thermal effects only)

KXX, KYY, KZZ RSVX, RSVY, RSVZ DENS, C, ENTH

Joule Heating LINK68 - Thermal-Electric Line

PLANE67 - Thermal-Electric Quadrilateral

SOLID69 - Thermal-Electric Hexahedral

SOLID5 - Coupled-Field Hexahedral

SOLID98 - Coupled-Field Tetrahedral

SHELL157 - Thermal-Electric Shell

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Analysis Types Material Properties

Thermoelectric Effects Elements

Static Transient (transient thermal and electrical effects)

KXX, KYY, KZZ RSVX, RSVY, RSVZ DENS, C, ENTH SBKX SBKY, SBKZ PERX, PERY, PERZ

Joule Heating Seebeck Effect Peltier Effect Thomson Effect

PLANE223 - Coupled-Field Quadrilateral

SOLID226 - Coupled-Field Hexahedral

SOLID227 - Coupled-Field Tetrahedral

7.2.2 Performing a Thermal-Electric Analysis

The analysis can be either steady-state (ANTYPE,STATIC) or transient (ANTYPE,TRANS) It follows the same

pro-cedure as a steady-state or transient thermal analysis (See Steady-State Thermal Analysis and Transient Thermal

Analysis in the ANSYS Thermal Analysis Guide.)

To perform a thermal-electric analysis, you need to specify the element type and material properties For Jouleheating effects, you must define both electrical resistivity (RSVX, RSVY, RSVZ) and thermal conductivity (KXX,KYY, KZZ) Mass density (DENS), specific heat (C), and enthalpy (ENTH) may be defined to take into accountthermal transient effects These properties may be constant or temperature-dependent

A transient analysis using PLANE223, SOLID226, or SOLID227 can account for both transient thermal and transientelectrical effects You must define electric permittivity (PERX, PERY, PERZ) to model the transient electrical effects

A transient analysis using LINK68, PLANE67, SOLID69, SOLID5, SOLID98, or SHELL157 can only account for sient thermal effects

tran-To include the Seebeck-Peltier thermoelectric effects, you need to specify a PLANE223, SOLID226, or SOLID227

element type and a Seebeck coefficient (SBKX, SBKY, SBKZ) (MP) You also need to specify the temperature offset from zero to absolute zero (TOFFST) To capture the Thomson effect, you need to specify the temperature de- pendence of the Seebeck coefficient (MPDATA).

PLANE67 and PLANE223 assume a unit thickness; they do not allow thickness input If the actual thickness (t) isnot uniform, you need to adjust the material properties as follows: multiply the thermal conductivity and density

by t, and divide the electrical resistivity by t

Be sure to define all data in consistent units For example, if the current and voltage are specified in amperesand volts, you must use units of watts/length-degree for thermal conductivity The output Joule heat will then

be in watts

For problems with convergence difficulties, activate the line search capability (LNSRCH).

See Section 7.9: Sample Thermoelectric Cooler Analysis (Batch or Command Method) and Section 7.10: SampleThermoelectric Generator Analysis (Batch or Command Method) for example problems

7.3 Piezoelectric Analysis

Piezoelectrics is the coupling of structural and electric fields, which is a natural property of materials such asquartz and ceramics Applying a voltage to a piezoelectric material creates a displacement, and vibrating apiezoelectric material generates a voltage A typical application of piezoelectric analysis is a pressure transducer.Possible piezoelectric analysis types (available in the ANSYS Multiphysics or ANSYS Mechanical products only)are static, modal, prestressed modal, harmonic, prestressed harmonic, and transient

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