4
1 Introduction
material linear and nonlinear modeling; multi-physics coupled modeling techniques
for piezo structures; modeling techniques of piezoelectric fiber composite bonded
structures. and the vibration control of piezo smart structures.
In Chap. 3, we first introduce and compare the hypotheses that have been already
developed, which is followed by the definitions of base vectors and geometric quantities in curvilinear coordinate system. Afterwards, the strain-displacement relations
for large rotation theory with six parameters based on first-order shear deformation
hypothesis are derived, as well as those for various geometrically nonlinear shell
theories ranging from von Kármán type nonlinearity to full geometric nonlinearity.
Chapter 4 presents constitutive relations for multi-functional materials, including
piezoceramics, piezopolymers, macro-fiber composites. First the fundamental theory
of piezoelectricity in 3-dimensional space is presented for piezoelectric materials.
To deal with fiber based piezoelectric materials, a coordinate transformation law is
constructed between the structural coordinates and fiber coordinates. Afterwards, the
constitutive relations of two typical MFC patches are developed with consideration
of multi-layered structures. Finally, electroelastic coupled materially nonlinear constitutive equations are constructed for the simulation of piezoelectric materials under
strong electric filed.
Chapter 5 develops electro-mechanically coupled nonlinear finite element (FE)
models with large rotations for static and dynamic analysis of composite and piezoelectric laminated thin-walled structures. The large rotation theory has six independent kinematic parameters expressed by five nodal degrees of freedom (DOFs) using
Euler angles to represent arbitrary rotations in structures. To demonstrate the effect
of the proposed large rotation FE models, other simplified nonlinear FE models are
developed as well. Those nonlinear models are linearized by Total-Lagrangian formulations. In the last part of this chapter, several numerical algorithms are introduced
for solving the coupled static and dynamic equations.
In Chap. 6, the finite element simulations of isotropic piezoceramics or polymers
integrated smart structures are presented. The chapter first deals with the validation
test of the present large rotation FE models by several static benchmark problems,
buckling and post-buckling analysis of alloys and composite laminated thin-walled
structures. Later, the nonlinear FE models based on various geometrically nonlinear
shell theories are applied to static and dynamic analysis of piezoelectric integrated
smart structures. In the final part of the chapter, the simulations of electroelastic
materially nonlinear analysis are investigated, in the case of smart structures under
strong electric field.
In Chap. 7, the simulations of macro-fiber composite (MFC) laminated smart
structures are presented. Two types of MFC patches including MFC-d31 and MFCd33 are considered in the simulations. In order to verify the present FE model,
validation tests are conducted through a cantilevered MFC plate. Later, linear analysis
of MFC bonded structures with arbitrary piezo-fiber orientation angles are carried out
and discussed. Furthermore, applying various geometrically nonlinear shell theories,
multi-MFC bonded plates and shells are analyzed and compared with each other.
The last chapter, Chap. 8, summarizes the present work and outlines the scope of
the future work.
1 Introduction
material linear and nonlinear modeling; multi-physics coupled modeling techniques
for piezo structures; modeling techniques of piezoelectric fiber composite bonded
structures. and the vibration control of piezo smart structures.
In Chap. 3, we first introduce and compare the hypotheses that have been already
developed, which is followed by the definitions of base vectors and geometric quantities in curvilinear coordinate system. Afterwards, the strain-displacement relations
for large rotation theory with six parameters based on first-order shear deformation
hypothesis are derived, as well as those for various geometrically nonlinear shell
theories ranging from von Kármán type nonlinearity to full geometric nonlinearity.
Chapter 4 presents constitutive relations for multi-functional materials, including
piezoceramics, piezopolymers, macro-fiber composites. First the fundamental theory
of piezoelectricity in 3-dimensional space is presented for piezoelectric materials.
To deal with fiber based piezoelectric materials, a coordinate transformation law is
constructed between the structural coordinates and fiber coordinates. Afterwards, the
constitutive relations of two typical MFC patches are developed with consideration
of multi-layered structures. Finally, electroelastic coupled materially nonlinear constitutive equations are constructed for the simulation of piezoelectric materials under
strong electric filed.
Chapter 5 develops electro-mechanically coupled nonlinear finite element (FE)
models with large rotations for static and dynamic analysis of composite and piezoelectric laminated thin-walled structures. The large rotation theory has six independent kinematic parameters expressed by five nodal degrees of freedom (DOFs) using
Euler angles to represent arbitrary rotations in structures. To demonstrate the effect
of the proposed large rotation FE models, other simplified nonlinear FE models are
developed as well. Those nonlinear models are linearized by Total-Lagrangian formulations. In the last part of this chapter, several numerical algorithms are introduced
for solving the coupled static and dynamic equations.
In Chap. 6, the finite element simulations of isotropic piezoceramics or polymers
integrated smart structures are presented. The chapter first deals with the validation
test of the present large rotation FE models by several static benchmark problems,
buckling and post-buckling analysis of alloys and composite laminated thin-walled
structures. Later, the nonlinear FE models based on various geometrically nonlinear
shell theories are applied to static and dynamic analysis of piezoelectric integrated
smart structures. In the final part of the chapter, the simulations of electroelastic
materially nonlinear analysis are investigated, in the case of smart structures under
strong electric field.
In Chap. 7, the simulations of macro-fiber composite (MFC) laminated smart
structures are presented. Two types of MFC patches including MFC-d31 and MFCd33 are considered in the simulations. In order to verify the present FE model,
validation tests are conducted through a cantilevered MFC plate. Later, linear analysis
of MFC bonded structures with arbitrary piezo-fiber orientation angles are carried out
and discussed. Furthermore, applying various geometrically nonlinear shell theories,
multi-MFC bonded plates and shells are analyzed and compared with each other.
The last chapter, Chap. 8, summarizes the present work and outlines the scope of
the future work.