Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements

Abstract

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators.

Nonlinear analysis of laminated composite shells with piezoelectric patches under displacement‐dependent pressure loads

“…The tangent stiffness matrix is evaluated using analytical integration based on the extended ANS method. The proposed hybrid-mixed solid-shell element is free from shear and membrane locking and passes the three-dimensional bending patch test for homogeneous, laminated and FGM plates [43,54,55], the inf-sup test for structures discretized by distorted meshes [38], the zero energy mode test for elastic and piezoelectric structures [56,57]. It is insensitive to the number of load increments [31,58,59] and can be recommended for three-dimensional stress analysis of laminated composite structures with piezoelectric patches subjected to displacement-dependent loads in a range of arbitrarily large displacements and rotations.…”

Coupled thermoelectroelastic analysis of thick and thin laminated piezoelectric structures by exact geometry solid‐shell elements based on the sampling surfaces method

“…This seems excessive for a SaS‐based four‐node solid‐shell element with 12 N SaS displacement DOF. However, there exist six dependent strain modes, which provide a correct rank of the element stiffness matrix in the purely mechanical solid‐shell element formulation 61 . In the electromechanical SaS‐based solid‐shell element formulation, there are exactly seven zero energy modes, namely six modes related to the rigid‐body motions and one to the short circuit 61 .…”

“…Such choice of unknowns with the use of Lagrange polynomials of degree I n − 1 in the through‐the‐thickness approximations of temperature, temperature gradient and heat flux vector, displacements, strains and stresses, electric potential, electric field and electric displacement vector, as well as the entropy density of the n th layer leads to a reliable higher‐order layer‐wise shell formulation, in which all basic variables are related to SaS. Recently, the SaS formulation was utilized to develop GeX four‐node solid‐shell elements for the geometrically linear and nonlinear analysis of piezoelectric shell structures 59‐61 . Here, these studies are extended to analyze coupled thermo‐electro‐mechanical fields in laminated piezoelectric shells.…”