Finite element formulation of a third order laminated finite rotation shell element

2002 ◽  
Vol 80 (26) ◽  
pp. 1975-1990 ◽  
Author(s):  
Mohamed Balah ◽  
Hamdan N. Al-Ghamedy
Keyword(s):  
Finite Element ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Finite Rotation ◽  
Third Order

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.

scholarly journals VIBRATION OF FGSW BEAMS UNDER NONUNIFORM MOTION OF MOVING LOAD USING AN EFFICIENT THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 51
Author(s):  
Anh Thi Ngoc Le ◽  
Kien Dinh Nguyen
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Moving Load ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Nonuniform Motion

Vibration of functionally graded sandwich (FGSW) beams under nonuniform motion of a moving load is studied using a third-order shear deformation finite element formulation. The beams consists three layers, a homogeneous ceramic core and two functionally graded faces. Instead of the rotation, the finite element formulation is derived by using the transverse shear rotation as a unknown. Newmark method is used to compute the dynamic response of the beams. Numerical result reveals that the derived formulation is efficient, and it is capable to give accurate vibration characteristics by a small number of the elements. A parametric study is carried out to illustrate the effects of the material distribution, layer thickness ratio and moving load speed on the dynamic behavior of the beams. The influence of acceleration and deceleration of the moving load on the vibration of the beams is also examined and discussed.

scholarly journals VIBRATION OF FGSW BEAMS UNDER NONUNIFORM MOTION OF MOVING LOAD USING AN EFFICIENT THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 51
Author(s):  
Anh Thi Ngoc Le ◽  
Kien Dinh Nguyen
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Moving Load ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Nonuniform Motion

Vibration of functionally graded sandwich (FGSW) beams under nonuniform motion of a moving load is studied using a third-order shear deformation finite element formulation. The beams consists three layers, a homogeneous ceramic core and two functionally graded faces. Instead of the rotation, the finite element formulation is derived by using the transverse shear rotation as a unknown. Newmark method is used to compute the dynamic response of the beams. Numerical result reveals that the derived formulation is efficient, and it is capable to give accurate vibration characteristics by a small number of the elements. A parametric study is carried out to illustrate the effects of the material distribution, layer thickness ratio and moving load speed on the dynamic behavior of the beams. The influence of acceleration and deceleration of the moving load on the vibration of the beams is also examined and 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.

Sign in / Sign up

Export Citation Format

Share Document