scholarly journals A finite element formulation for piezoelectric shell structures considering geometrical and material non-linearities

2011 ◽  
Vol 87 (6) ◽  
pp. 491-520 ◽  
Author(s):  
K. Schulz ◽  
S. Klinkel ◽  
W. Wagner
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Piezoelectric Shell

Control of Largely-Deformed Nonlinear Electro/Elastic Beam and Plate Systems: Finite Element Formulation and Analysis

2002 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Nonlinear Dynamic Analysis ◽  
Elastic Beam ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Control Analysis ◽  
Control Force ◽  
Piezoelectric Shell

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generalized nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems is studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

Control of Nonlinear Electro/Elastic Beam and Plate Systems (Finite Element Formulation and Analysis)

2004 ◽  
Vol 126 (1) ◽  
pp. 63-70 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Elastic Beam ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Control Analysis ◽  
Finite Element Code ◽  
Vibration Sensing ◽  
And Control ◽  
Piezoelectric Shell

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generic nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems are studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

Advanced Finite Element Formulation for Piezoelectric Smart Shell Structures Under Consideration of Geometrical Nonlinearity

2008 ◽  
Author(s):  
Katrin Schulz ◽  
Sven Klinkel ◽  
Werner Wagner
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Degrees Of Freedom ◽  
Geometrical Nonlinearity ◽  
Shell Element ◽  
Shell Structures ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Displacement Fields ◽  
Piezoelectric Structures

A geometrically nonlinear highly accurate finite element formulation to analyze piezoelectric shell problems is presented. The formulation is based on the mixed field variational principle of Hu-Washizu including the independent fields displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The normal zero stress condition and the normal zero dielectric displacement condition for shells are enforced by the independent resultant stress and resultant dielectric displacement fields. The arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed shell element fulfills the patchtests and is able to model arbitrary curved shell structures. Some numerical examples demonstrate the applicability of the present shell element for piezoelectric systems and integrated piezoelectric structures.

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