本人要做压电材料的Ansys分析
但不知单元和一些步骤不清楚，有高手的请给我介绍一本书，OR给我介绍一些知识，本人QQ515898072，请写上‘压电分析’，谢谢！...
但不知单元和一些步骤不清楚，有高手的请给我介绍一本书，OR给我介绍一些知识，本人QQ515898072，请写上‘压电分析’，谢谢！
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压电分析属于耦合分析，而且使用直接耦合比较多，因为其非线性本来就高一点！具体的中文的资料见的不是很多：下面是ansyshelp中关于压电的一些说明：
2.3. Piezoelectric Analysis
Piezoelectrics is the coupling of structural and electric fields, which is a natural property of materials such as quartz and ceramics. Applying a voltage to a piezoelectric material creates a displacement, and vibrating a piezoelectric 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.
To do a piezoelectric analysis, you need to use one of these element types:
PLANE13, KEYOPT(1) = 7 coupled-field quadrilateral solid
SOLID5, KEYOPT(1) = 0 or 3 coupled-field brick
SOLID98, KEYOPT(1) = 0 or 3 coupled-field tetrahedron
PLANE223, KEYOPT(1) = 1001, coupled-field 8-node quadrilateral
SOLID226, KEYOPT(1) = 1001, coupled-field 20-node brick
SOLID227, KEYOPT(1) = 1001, coupled-field 10-node tetrahedron
PLANE13, SOLID5, and SOLID98 are available in ANSYS Multiphysics, ANSYS Mechanical, and ANSYS PrepPost. PLANE223, SOLID226, and SOLID227 are available in ANSYS Multiphysics and ANSYS PrepPost.
The KEYOPT settings activate the piezoelectric degrees of freedom, displacements and VOLT. For SOLID5 and SOLID98, setting KEYOPT(1) = 3 activates the piezoelectric only option.
The piezoelectric KEYOPT settings also make large deflection and stress stiffening effects available using the NLGEOM, SSTIF, and PSTRES commands. (See the Commands Reference for more information on these commands. See the Structural Analysis Guide and Chapter 3 of the Theory Reference for ANSYS and ANSYS Workbench for more information on large deflection and stress stiffening capabilities.) For PLANE13, large deflection and stress stiffening capabilities are available for KEYOPT(1) = 7. For SOLID5 and SOLID98, large deflection and stress stiffening capabilities are available for KEYOPT(1) = 3. In addition, small deflection stress stiffening capabilities are available for KEYOPT(1) = 0.
Note
Automatic solution control is not available for a piezoelectric analysis. The SOLCONTROL default settings are only available for a pure structural or pure thermal analysis. For a large deflection piezoelectric analysis, you must use nonlinear solution commands to specify your settings. For general information on these commands, refer to Running a Nonlinear Analysis in ANSYS in the Structural Analysis Guide.
For sample analyses, see Sample Piezoelectric Analysis (Batch or Command Method) and Sample Piezoelectric Analysis with Coriolis Effect (Batch or Command Method).
2.3.1. Points to Remember
The analysis may be static, modal, prestressed modal, harmonic, prestressed harmonic, or transient. Some important points to remember are:
For modal analysis, Block Lanczos is the recommended solver. PCG Lanczos is not supported unless using Lev_Diff = 5 on the PCGOPT command.
For static, full harmonic, or full transient analysis, choose the sparse matrix (SPARSE) solver or the Jacobi Conjugate Gradient (JCG) solver. The sparse solver is the default for static and full transient analyses. Depending on the chosen system of units or material property values, the assembled matrix may become ill-conditioned. When solving ill-conditioned matrices, the JCG iterative solver may converge to the wrong solution. The assembled matrix typically becomes ill-conditioned when the magnitudes of the structural DOF and electrical DOF start to vary significantly (more than 1e15).
For transient analyses, specify ALPHA = 0.25, DELTA = 0.5, and THETA = 0.5 on the TINTP command (Main Menu> Preprocessor> Loads> Time/Frequenc>Time Integration).
A prestressed harmonic analysis can only follow a small deflection analysis.
For PLANE13, SOLID5, and SOLID98, the force label for the VOLT DOF is AMPS. For PLANE223, SOLID226, and SOLID227, the force label for the VOLT degree of freedom is CHRG. Use these labels in F, CNVTOL, RFORCE, etc.
To do a piezoelectric-circuit analysis, use CIRCU94.
The capability to model dielectric losses using the dielectric loss tangent property (input on MP,LSST) is available only for PLANE223, SOLID226, and SOLID227.
The Coriolis effect capability is available only for PLANE223, SOLID226, and SOLID227. For information on how to include this effect, see Rotating Structure Analysis in the Advanced Analysis Techniques Guide. For a sample analyses, see Sample Piezoelectric Analysis with Coriolis Effect (Batch or Command Method).
If a model has at least one piezoelectric element, then all the coupled-field elements with structural and VOLT degrees of freedom must be of piezoelectric type. If the piezoelectric effect is not desired in these elements, simply define very small piezoelectric coefficients on TB.
2.3.2. Material Properties
A piezoelectric model requires permittivity (or dielectric constants), the piezoelectric matrix, and the elastic coefficient matrix to be specified as material properties. These are explained next.
2.3.2.1. Permittivity Matrix (Dielectric Constants)
For SOLID5, PLANE13, or SOLID98 you specify relative permittivity values as PERX, PERY, and PERZ on the MP command (Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> Relative Permittivity> Orthotropic). (Refer to the EMUNIT command for information on free-space permittivity.) The permittivity values represent the diagonal components ε11, ε22, and ε33 respectively of the permittivity matrix [εS]. (The superscript "S" indicates that the constants are evaluated at constant strain.) That is, the permittivity input on the MP command will always be interpreted as permittivity at constant strain [εS].
Note
If you enter permittivity values less than 1 for SOLID5, PLANE13, or SOLID98, the program interprets the values as absolute permittivity.
For PLANE223, SOLID226, and SOLID227, you can specify permittivity either as PERX, PERY, PERZ on the MP command or by specifying the terms of the anisotropic permittivity matrix using the TB,DPER and TBDATA commands. If you choose to use the MP command to specify permittivity, the permittivity input will be interpreted as permittivity at constant strain. If you choose to use the TB,DPER command (Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> Relative Permittivity> Anisotropic), you can specify the permittivity matrix at constant strain [εS] (TBOPT = 0) or at constant stress [εT] (TBOPT = 1). The latter input will be internally converted to permittivity at constant strain [εS] using the piezoelectric strain and stress matrices. The values input on either MP,PERX or TB,DPER will always be interpreted as relative permittivity.
2.3.2.2. Piezoelectric Matrix
You can define the piezoelectric matrix in [e] form (piezoelectric stress matrix) or in [d] form (piezoelectric strain matrix). The [e] matrix is typically associated with the input of the anisotropic elasticity in the form of the stiffness matrix [c], while the [d] matrix is associated with the compliance matrix [s].
Note
ANSYS will convert a piezoelectric strain matrix [d] matrix to a piezoelectric stress matrix [e] using the elastic matrix at the first defined temperature. To specify the elastic matrix required for this conversion, use the TB,ANEL command (not the MP command).
This 6 x 3 matrix (4 x 2 for 2-D models) relates the electric field to stress ([e] matrix) or to strain ([d] matrix). Both the [e] and the [d] matrices use the data table input described below:
The TB,PIEZ and TBDATA commands are used to define the piezoelectric matrix; see your Commands Reference for the order of input of these constants.
To define the piezoelectric matrix via the GUI, use the following:
Main Menu> Preprocessor> Material Props> Material Models> Piezoelectrics> Piezoelectric matrix
For most published piezoelectric materials, the order used for the piezoelectric matrix is x, y, z, yz, xz, xy, based on IEEE standards (see ANSI/IEEE Standard 176–1987), while the ANSYS input order is x, y, z, xy, yz, xz as shown above. This means that you need to transform the matrix to the ANSYS input order by switching row data for the shear terms as shown below:
IEEE constants [e61, e62, e63] would be input as the ANSYS xy row
IEEE constants [e41, e42, e43] would be input as the ANSYS yz row
IEEE constants [e51, e52, e53] would be input as the ANSYS xz row
2.3.2.3. Elastic Coefficient Matrix
This 6 x 6 symmetric matrix (4 x 4 for 2-D models) specifies the stiffness ([c] matrix) or compliance ([s] matrix) coefficients.
Note
This section follows the IEEE standard notation for the elastic coefficient matrix [c]. This matrix is also referred to as [D] in other areas of ANSYS Help.
The elastic coefficient matrix uses the following data table input:
Use the TB,ANEL (Main Menu> Preprocessor> Material Props> Material Models> Structural> Linear> Elastic> Anisotropic) and TBDATA commands to define the coefficient matrix [c] (or [s], depending on the TBOPT settings); see the Commands Reference for the order of input of these constants. As explained for the piezoelectric matrix, most published piezoelectric materials use a different order for the [c] matrix. You need to transform the IEEE matrix to the ANSYS input order by switching row and column data for the shear terms as shown below:
IEEE terms [c61, c62, c63, c66] would be input as the ANSYS xy row
IEEE terms [c41, c42, c43, c46, c44] would be input as the ANSYS yz row
IEEE terms [c51, c52, c53, c56, c54, c55] would be input as the xz row
An alternative to the [c] matrix is to specify Young's modulus (MP,EX command) and Poisson's ratio (MP,NUXY command) and/or shear modulus (MP,GXY command). (See the Commands Reference for more information on the MP command). To specify any of these via the GUI, use the following:
Main Menu> Preprocessor> Material Props> Material Models> Structural> Linear> Elastic> Orthotropic
For micro-electromechanical systems (MEMS), it is best to set up problems in µMKSV or µMSVfA units (see Table 1.7: "Piezoelectric Conversion Factors for MKS to μMKSV" and Table 1.14: "Piezoelectric Conversion Factors for MKS to μMKSVfA").
2.3. Piezoelectric Analysis
Piezoelectrics is the coupling of structural and electric fields, which is a natural property of materials such as quartz and ceramics. Applying a voltage to a piezoelectric material creates a displacement, and vibrating a piezoelectric 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.
To do a piezoelectric analysis, you need to use one of these element types:
PLANE13, KEYOPT(1) = 7 coupled-field quadrilateral solid
SOLID5, KEYOPT(1) = 0 or 3 coupled-field brick
SOLID98, KEYOPT(1) = 0 or 3 coupled-field tetrahedron
PLANE223, KEYOPT(1) = 1001, coupled-field 8-node quadrilateral
SOLID226, KEYOPT(1) = 1001, coupled-field 20-node brick
SOLID227, KEYOPT(1) = 1001, coupled-field 10-node tetrahedron
PLANE13, SOLID5, and SOLID98 are available in ANSYS Multiphysics, ANSYS Mechanical, and ANSYS PrepPost. PLANE223, SOLID226, and SOLID227 are available in ANSYS Multiphysics and ANSYS PrepPost.
The KEYOPT settings activate the piezoelectric degrees of freedom, displacements and VOLT. For SOLID5 and SOLID98, setting KEYOPT(1) = 3 activates the piezoelectric only option.
The piezoelectric KEYOPT settings also make large deflection and stress stiffening effects available using the NLGEOM, SSTIF, and PSTRES commands. (See the Commands Reference for more information on these commands. See the Structural Analysis Guide and Chapter 3 of the Theory Reference for ANSYS and ANSYS Workbench for more information on large deflection and stress stiffening capabilities.) For PLANE13, large deflection and stress stiffening capabilities are available for KEYOPT(1) = 7. For SOLID5 and SOLID98, large deflection and stress stiffening capabilities are available for KEYOPT(1) = 3. In addition, small deflection stress stiffening capabilities are available for KEYOPT(1) = 0.
Note
Automatic solution control is not available for a piezoelectric analysis. The SOLCONTROL default settings are only available for a pure structural or pure thermal analysis. For a large deflection piezoelectric analysis, you must use nonlinear solution commands to specify your settings. For general information on these commands, refer to Running a Nonlinear Analysis in ANSYS in the Structural Analysis Guide.
For sample analyses, see Sample Piezoelectric Analysis (Batch or Command Method) and Sample Piezoelectric Analysis with Coriolis Effect (Batch or Command Method).
2.3.1. Points to Remember
The analysis may be static, modal, prestressed modal, harmonic, prestressed harmonic, or transient. Some important points to remember are:
For modal analysis, Block Lanczos is the recommended solver. PCG Lanczos is not supported unless using Lev_Diff = 5 on the PCGOPT command.
For static, full harmonic, or full transient analysis, choose the sparse matrix (SPARSE) solver or the Jacobi Conjugate Gradient (JCG) solver. The sparse solver is the default for static and full transient analyses. Depending on the chosen system of units or material property values, the assembled matrix may become ill-conditioned. When solving ill-conditioned matrices, the JCG iterative solver may converge to the wrong solution. The assembled matrix typically becomes ill-conditioned when the magnitudes of the structural DOF and electrical DOF start to vary significantly (more than 1e15).
For transient analyses, specify ALPHA = 0.25, DELTA = 0.5, and THETA = 0.5 on the TINTP command (Main Menu> Preprocessor> Loads> Time/Frequenc>Time Integration).
A prestressed harmonic analysis can only follow a small deflection analysis.
For PLANE13, SOLID5, and SOLID98, the force label for the VOLT DOF is AMPS. For PLANE223, SOLID226, and SOLID227, the force label for the VOLT degree of freedom is CHRG. Use these labels in F, CNVTOL, RFORCE, etc.
To do a piezoelectric-circuit analysis, use CIRCU94.
The capability to model dielectric losses using the dielectric loss tangent property (input on MP,LSST) is available only for PLANE223, SOLID226, and SOLID227.
The Coriolis effect capability is available only for PLANE223, SOLID226, and SOLID227. For information on how to include this effect, see Rotating Structure Analysis in the Advanced Analysis Techniques Guide. For a sample analyses, see Sample Piezoelectric Analysis with Coriolis Effect (Batch or Command Method).
If a model has at least one piezoelectric element, then all the coupled-field elements with structural and VOLT degrees of freedom must be of piezoelectric type. If the piezoelectric effect is not desired in these elements, simply define very small piezoelectric coefficients on TB.
2.3.2. Material Properties
A piezoelectric model requires permittivity (or dielectric constants), the piezoelectric matrix, and the elastic coefficient matrix to be specified as material properties. These are explained next.
2.3.2.1. Permittivity Matrix (Dielectric Constants)
For SOLID5, PLANE13, or SOLID98 you specify relative permittivity values as PERX, PERY, and PERZ on the MP command (Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> Relative Permittivity> Orthotropic). (Refer to the EMUNIT command for information on free-space permittivity.) The permittivity values represent the diagonal components ε11, ε22, and ε33 respectively of the permittivity matrix [εS]. (The superscript "S" indicates that the constants are evaluated at constant strain.) That is, the permittivity input on the MP command will always be interpreted as permittivity at constant strain [εS].
Note
If you enter permittivity values less than 1 for SOLID5, PLANE13, or SOLID98, the program interprets the values as absolute permittivity.
For PLANE223, SOLID226, and SOLID227, you can specify permittivity either as PERX, PERY, PERZ on the MP command or by specifying the terms of the anisotropic permittivity matrix using the TB,DPER and TBDATA commands. If you choose to use the MP command to specify permittivity, the permittivity input will be interpreted as permittivity at constant strain. If you choose to use the TB,DPER command (Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> Relative Permittivity> Anisotropic), you can specify the permittivity matrix at constant strain [εS] (TBOPT = 0) or at constant stress [εT] (TBOPT = 1). The latter input will be internally converted to permittivity at constant strain [εS] using the piezoelectric strain and stress matrices. The values input on either MP,PERX or TB,DPER will always be interpreted as relative permittivity.
2.3.2.2. Piezoelectric Matrix
You can define the piezoelectric matrix in [e] form (piezoelectric stress matrix) or in [d] form (piezoelectric strain matrix). The [e] matrix is typically associated with the input of the anisotropic elasticity in the form of the stiffness matrix [c], while the [d] matrix is associated with the compliance matrix [s].
Note
ANSYS will convert a piezoelectric strain matrix [d] matrix to a piezoelectric stress matrix [e] using the elastic matrix at the first defined temperature. To specify the elastic matrix required for this conversion, use the TB,ANEL command (not the MP command).
This 6 x 3 matrix (4 x 2 for 2-D models) relates the electric field to stress ([e] matrix) or to strain ([d] matrix). Both the [e] and the [d] matrices use the data table input described below:
The TB,PIEZ and TBDATA commands are used to define the piezoelectric matrix; see your Commands Reference for the order of input of these constants.
To define the piezoelectric matrix via the GUI, use the following:
Main Menu> Preprocessor> Material Props> Material Models> Piezoelectrics> Piezoelectric matrix
For most published piezoelectric materials, the order used for the piezoelectric matrix is x, y, z, yz, xz, xy, based on IEEE standards (see ANSI/IEEE Standard 176–1987), while the ANSYS input order is x, y, z, xy, yz, xz as shown above. This means that you need to transform the matrix to the ANSYS input order by switching row data for the shear terms as shown below:
IEEE constants [e61, e62, e63] would be input as the ANSYS xy row
IEEE constants [e41, e42, e43] would be input as the ANSYS yz row
IEEE constants [e51, e52, e53] would be input as the ANSYS xz row
2.3.2.3. Elastic Coefficient Matrix
This 6 x 6 symmetric matrix (4 x 4 for 2-D models) specifies the stiffness ([c] matrix) or compliance ([s] matrix) coefficients.
Note
This section follows the IEEE standard notation for the elastic coefficient matrix [c]. This matrix is also referred to as [D] in other areas of ANSYS Help.
The elastic coefficient matrix uses the following data table input:
Use the TB,ANEL (Main Menu> Preprocessor> Material Props> Material Models> Structural> Linear> Elastic> Anisotropic) and TBDATA commands to define the coefficient matrix [c] (or [s], depending on the TBOPT settings); see the Commands Reference for the order of input of these constants. As explained for the piezoelectric matrix, most published piezoelectric materials use a different order for the [c] matrix. You need to transform the IEEE matrix to the ANSYS input order by switching row and column data for the shear terms as shown below:
IEEE terms [c61, c62, c63, c66] would be input as the ANSYS xy row
IEEE terms [c41, c42, c43, c46, c44] would be input as the ANSYS yz row
IEEE terms [c51, c52, c53, c56, c54, c55] would be input as the xz row
An alternative to the [c] matrix is to specify Young's modulus (MP,EX command) and Poisson's ratio (MP,NUXY command) and/or shear modulus (MP,GXY command). (See the Commands Reference for more information on the MP command). To specify any of these via the GUI, use the following:
Main Menu> Preprocessor> Material Props> Material Models> Structural> Linear> Elastic> Orthotropic
For micro-electromechanical systems (MEMS), it is best to set up problems in µMKSV or µMSVfA units (see Table 1.7: "Piezoelectric Conversion Factors for MKS to μMKSV" and Table 1.14: "Piezoelectric Conversion Factors for MKS to μMKSVfA").
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