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.

Dynamics and Control of Adaptive Nonlinear Piezothermoelastic Structures With Coupled Electric, Thermal and Mechanical Fields: A Finite Element Approach

2002 ◽  
Author(s):  
H. S. Tzou ◽  
D. W. Wang
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Shell Element ◽  
Shell Structures ◽  
Control Analysis ◽  
Control Force ◽  
Vibration Sensing ◽  
Dynamics And Control ◽  
And Control ◽  
Piezoelectric Shell

Piezoelectric sensors and actuators are widely used in smart structures, mechatronic and structronic systems, etc. This paper is to investigate the dynamics and control of nonlinear laminated piezothermoelastic shell structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Governing relations of nonlinear strain-displacement, electric field-electric potential, and temperature gradient-temperature field for a piezothermoelastic shell are presented in a curvilinear coordinate system. Based on the layerwise constant shear angle theory, a generic curved triangular laminated piezothermoelastic shell element is developed. Generic nonlinear finite element formulations for vibration sensing and control analysis of laminated piezoelectric shell structures are derived based on the virtual work principle. Dynamic system equations, equations of electric potential output, and feedback control force are derived and discussed. The modified Newton-Raphson method is used for efficient nonlinear dynamic analysis of complex nonlinear piezoelectric/elastic/control structural systems. For vibration sensing and control, various control algorithms are implemented. The developed nonlinear piezothermoelastic shell element and finite element code are validated and applied to analysis of nonlinear flexible structronic systems. Vibration sensing and control of constant/non-constant curvature piezoelectric shell structures are studied. Thermal effect to static deflection, dynamic response, and control is investigated.

Two-Dimensional Geometrically Nonlinear Finite Element Formulation for Analysis of Straight Pipes

2020 ◽  
Author(s):  
Saher Attia ◽  
Magdi Mohareb ◽  
Michael Martens ◽  
Nader Yoosef Ghodsi ◽  
Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Strain Tensor ◽  
Structural Response ◽  
Small Strain ◽  
Nonlinear Finite Element ◽  
Finite Element Formulation ◽  
Single Element ◽  
Element Formulation ◽  
Geometrically Nonlinear

Abstract The paper presents a new and simple geometrically nonlinear finite element formulation to simulate the structural response of straight pipes under in-plane loading and/or internal pressure. The formulation employs the Green-Lagrange strain tensor to capture finite deformation-small strain effects. Additionally, the First Piola-Kirchhoff stress tensor and Saint Venant-Kirchhoff constitutive model are adopted within the principle of virtual work framework in conjunction with a total Lagrangian approach. The formulation is applied for a cantilever beam under three loading conditions. Results are in good agreement with shell models in ABAQUS. Although the solution is based on a single element, the formulation provides reasonable displacement and stress predictions.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

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