Piezoelectric submodeling

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Standard

C3D8E elements

Elements tested

C3D8E

CPE8E

CPS8E

Features tested

The submodeling capability is applied to plane stress, plane strain, and three-dimensional solid piezoelectric elements. The global models consist of one element; the submodels model half of the global model and consist of two elements. Static and steady-state procedures are used.

Problem description

Model:

The global model dimensions are 7 × 7 × 7. The submodel models the right-hand half of the global model.

Material:

Young's modulus 3 × 106
Poisson's ratio 0.3
Density 10
Coeff. of thermal expansion 0.0001
Dielectric anisotropic (see input file)

Boundary conditions:

The electric charge and the displacements u1 and u3 are zero on the x = 0 plane. The electric charge and the u2 displacement are zero on the y = 0 plane.

Loading:

The initial temperature is −10 at all nodes. In the first step a distributed charge of 3000 is applied on the x = 7 plane and the y = 7 plane. In the second step a temperature of 40 is applied to all nodes.

Results and discussion

The nodal displacements and electrical potential for the driven nodes in the submodels are correctly interpolated from the global model results.

CPE8E elements

Problem description

Model:

The global model dimensions are 7 × 7 with a thickness of 1.0. The submodel models the right-hand half of the global model.

Material:

Young's modulus 3 × 106
Poisson's ratio 0.3
Density 5 × 10−5
Dielectric 5.872 × 10−9

Boundary conditions:

The electric charge and the u1 displacement are zero along the left-hand edge. Along the bottom edge the electric charge and the u2 displacement are zero.

Loading:

A distributed charge of 100 is applied on the right-hand edge. A concentrated charge of −150 is applied on the upper right-hand corner.

Results and discussion

The nodal displacements and electrical potential for the driven nodes in the submodels are correctly interpolated from the global model results.

CPS8E elements

Problem description

Model:

The global model dimensions are 7 × 7 with a thickness of 1.0. The submodel models the right half of the global model.

Material:

Young's modulus 3 × 106
Poisson's ratio 0.3
Density 5 × 10−5
Coeff. of thermal expansion 0.0001
Dielectric 5.872 × 10−9

Boundary conditions:

The electric charge and the u1 displacement are zero along the left edge. Along the bottom edge the electric charge and the u2 displacement are zero.

Loading:

In the static step distributed charges of 2000 and 3000 are applied on the right-hand edge and top edge respectively. A concentrated charge of −150 is applied at the upper right-hand corner. In the steady-state step, distributed pressures of 200 and 300 are applied on the right-hand edge and top edge, respectively.

Results and discussion

The nodal displacements and electrical potential for the driven nodes in the submodels are correctly interpolated from the global model results.