scholarly journals A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications

2008 ◽  
Vol 86 (1-2) ◽  
pp. 38-46 ◽  
Author(s):  
Sven Klinkel ◽  
Werner Wagner
Keyword(s):  
Variational Formulation ◽  
Shell Element ◽  
Solid Shell ◽  
Mixed Variational Formulation ◽  
Piezoelectric Solid ◽  
Linear And Nonlinear

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

2019 ◽  
Vol 31 (1) ◽  
pp. 53-70
Author(s):  
GM Kulikov ◽  
SV Plotnikova ◽  
E Carrera
Keyword(s):  
Shell Element ◽  
Middle Surface ◽  
Solid Shell ◽  
Modeling And Analysis ◽  
Lagrange Polynomials ◽  
Shell Elements ◽  
Exact Geometry ◽  
Piezoelectric Solid ◽  
Assumed Natural Strain ◽  
Shell Formulation

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.

A mixed variational formulation for a class of contact problems in viscoelasticity

2017 ◽  
Vol 97 (8) ◽  
pp. 1340-1356 ◽  
Author(s):  
A. Matei ◽  
S. Sitzmann ◽  
K. Willner ◽  
B. I. Wohlmuth
Keyword(s):  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Variational Formulation
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