ANSYS压电分析

压电分析
The capability of modeling piezoelectric response exists in the following elements:
SOLID5 - Coupled-Field Solid Element
PLANE13 - 2-D Coupled-Field Solid Element
SOLID98 - Tetrahedral Coupled-Field Solid Element
PLANE223 - 2-D 8-Node Coupled-Field Solid Element
SOLID226 - 3-D 20-Node Coupled-Field Solid Element
SOLID227 - 3-D 10-Node Coupled-Field Solid Element
The electromechanical constitutive equations for linear material behavior are:
(11–36)
(11–37)
or equivalently
(11–38) where:
{T} = stress vector (referred to as {σ} elsewhere in this manual) {D} = electric flux density vector
{S} = strain vector (referred to as {ε } elsewhere in this manual) {E} = electric field vector
[c] = elasticity matrix (evaluated at constant electric field (referred to as [D] elsewhere in this manual))
[e] = piezoelectric stress matrix
[ε] = dielectric matrix (evaluated at constant mechanical strain)
The elasticity matrix [c] is the usual [D] matrix described in Structural Fundamentals(input using the MP commands). It can also be input directly
in uninverted form [c] or in inverted form [c]-1 as a general anisotropic symmetric matrix (input using TB ,ANEL):
[c]刚度矩阵经常采用”MP ”命令输入，也可以用“TB,ANEL ”命令输入各向异性对称矩阵的形式。

(11–39)
The piezoelectric stress matrix [e] (input using TB ,PIEZ with TBOPT = 0) relates the electric field vector {E} in the order X, Y, Z to the stress vector {T} in the order X, Y, Z, XY, YZ, XZ and is of the form:
[e]压电应力矩阵采用”TB,PIEZ ”,TBOPT =0输入
(11–40)
The piezoelectric matrix can also be input as a piezoelectric strain matrix [d] (input using TB ,PIEZ with TBOPT = 1). ANSYS will automatically convert the piezoelectric strain matrix [d] to a piezoelectric stress matrix [e] using the elasticity matrix [c] at the first defined temperature:
压电矩阵也可以以压电应变矩阵[d]的形式输入，“TB,PIEZ ”with TBOPT=1 Ansys 会自动将压电应变矩阵[d]转换为压电应力矩阵
[e]
(11–41) The orthotropic dielectric matrix [ε] uses the electrical permittivities (input as PERX, PERY and PERZ on the MP commands) and is of the form:
正交各向异性介电矩阵[ε]由介电常数构成，“MP”命令的ERX, PERY and PERZ 输入：
(11–42)
The anisotropic dielectric matrix at constant strain [εS] (input used by (used by TB,DPER,,,,0 command) PLANE223, SOLID226, and SOLID227) and is of the form:
常应变时的各向异性介电矩阵[ε]可以由命令TB,DPER,,,,0 command，在PLANE223, SOLID226, and SOLID227)输入
(11–43)
The dielectric matrix can also be input as a dielectric permittivity matrix at constant stress [εT] (input using TB,DPER,,,,1). The program will automatically convert the dielectric matrix at constant stress to a dielectric matrix at constant strain:
常应力时的常应变时的介电矩阵[ε]可以由命令TB,DPER,,,,1 command输入
(11–44) where:
[εS] = dielectric permittivity matrix at constant strain
[εT] = dielectric permittivity matrix at constant stress
[e] = piezoelectric stress matrix
[d] = piezoelectric strain matrix。