Overview

Test Case

A piezoceramic (PZT-4) rectangular strip occupies the region |x| l, |y| h. The material is oriented such that its polarization direction is aligned with the Y axis. The strip is subjected to the pure bending load σ_x = σ₁y at x = ± l. Determine the electro-elastic field distribution in the strip.

This test case is also solved using Ansys Mechanical. See vm-wb-mech-109.

Figure 387: Piezoelectric Strip Problem Sketch

Constitutive Matrices for PZT4 Polarized Along the Y Axis

PZT4 Dielectric Matrix [ε_r]

PZT4 Piezoelectric Matrix [e] C/m²

PZT4 Stiffness matrix [c] x 10^-10 N/m²

Analysis Assumptions and Modeling Notes

The problem is solved using three different coupled field elements, namely, PLANE13, PLANE222, and PLANE223 elements.

Only a one-quarter symmetry sector of the rectangular strip is modeled. Symmetric and antisymmetric boundary conditions are applied.

For the first case, the finite element model uses a single 4-node, 2D quadrilateral element (PLANE13) with extra displacement and potential modes to produce a correct response to the pure bending load. For the second case, the finite element model uses a single 4-node, 2D quadrilateral element (PLANE222) with enhanced strain formulation. For the third case, the finite element model uses a single, 8-node 2D quadrilateral element (PLANE223).

Results Comparison