scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Linear and Nonlinear Analysis of a Smart Beam Using General Electrothermoelastic Formulation

01 Apr 2004-AIAA Journal (American Institute of Aeronautics and Astronautics)-Vol. 42, Iss: 4, pp 840-849
TL;DR: In this article, coupled electrothermoelastic equations applicable to the analysis of smart structures have been derived from first principles, and applying a layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential.
Abstract: Coupled electrothermoelastic equations applicable to the analysis of smart structures have been derived from first principles. Using the equations and applying a layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and nonpiezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarization and electric field in the piezo continuum leads to nonlinear distributed body force and nonsymmetric stress tensor. These nonlinear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multipatch smart beams have also been investigated.
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, a general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented, which is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter.
Abstract: A general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented The dimensional reduction is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter In the proposed scheme, the coupled linear electroelastic equations are solved at the cross-sectional level using the finite element method Furthermore, modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis, and arbitrary electric modes are used to define applied electric fields at the cross section This results in a general definition of a coupled electroelastic stiffness, which can be used in virtually all composite and active beam formulations, as well as in the development of new low-order high-accuracy reduced models for active structures Finally, the formulation also yields recovery relations for the elastic and electric fields in the original three-dimensional solid, once the one-dimensional problem is solved The method has been implemented in a computer program (UM/VABS) and numerical results are presented for active anisotropic beam cross sections of simple geometries, which are shown to compare very well with three-dimensional finite element analysis

107 citations

Journal ArticleDOI
TL;DR: In this article, coupled electro-thermo-elastic equations applicable for the analysis of smart structures with piezoelectric patches/layers have been derived from the fundamental principles of mass, linear momentum, angular momentum, energy and charge conservation.
Abstract: Coupled electro-thermo-elastic equations applicable for the analysis of smart structures with piezoelectric patches/layers have been derived from the fundamental principles of mass, linear momentum, angular momentum, energy and charge conservation. The relevant constitutive equations have been obtained by using the second law of thermodynamics. The interaction of the electric field and polarization introduces distributed non-linear body force in the piezo material, and in addition renders the stress tensor non-symmetric due to distributed couple. Using the linear equations, and applying a layer-by-layer finite element model, the induced electric potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical, electrical and thermal loadings. The mathematical formulation and the solution technique have been validated by comparing the results of the present study with those available in the literature. It is also shown that piezo patches can be effectively used for shape control.

32 citations

Journal ArticleDOI
TL;DR: In this paper, Cimento revisited some variational principles for the fundamental equations of a regular region of piezoelectric, thermopiez-olectric and hygrothermopiezoellectric materials in the elastic range.
Abstract: In this paper some variational principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar variational principles of piezoelectricity are cited.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields for active piezolaminated plates considering thermopiezoelastic behaviors.
Abstract: Nonlinear dynamics of active piezolaminated plates are investigated considering snap-through thermopiezoelastic behaviors. For highly deformed structures with small strain, the incremental total Lagrangian formulation is presented based on Hamilton's variational principles. A multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap-through phenomena, the implicit Newmark-beta scheme with the Newton–Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. To validate the new finite element formulation and code, dynamic analyses of nonlinear elastic plates are compared with published data, resulting in good agreements and better solutions. The bifurcate buckling and sling-shot buckling of the symmetric and eccentric structural models are first investigated and the characteristics of piezoelectric active responses are studied to find snap-through piezoelectric potentials and the load-path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap-through phenomena with several attractors are proved using the nonlinear time responses for initial conditions and damping loss factors. Present results show that the snap-through phenomena should be investigated with respect to nonlinear dynamics for shape control of piezolaminated buckled plates by using piezoelectric materials.

25 citations

Journal ArticleDOI
TL;DR: In this paper, the second-order nonlinear constitutive equations are used in the variational principle approach to develop a nonlinear finite element (FE) model for piezoelectric laminated composite plates and shells.
Abstract: In this article, we focus on static finite element (FE) simulation of piezoelectric laminated composite plates and shells, considering the nonlinear constitutive behavior of piezoelectric materials under large applied electric fields. Under the assumptions of small strains and large electric fields, the second-order nonlinear constitutive equations are used in the variational principle approach, to develop a nonlinear FE model. Numerical simulations are performed to study the effect of material nonlinearity for piezoelectric bimorph and laminated composite plates as well as cylindrical shells. In comparison to the experimental investigations existing in the literature, the results predicted by the present model agree very well. The importance of the present nonlinear model is highlighted especially in large applied electric fields, and it is shown that the difference between the results simulated by linear and nonlinear constitutive FE models cannot be omitted.

23 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, a scaling analysis is performed to demonstrate that the effectiveness of actuators is independent of the size of the structure and evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure.
Abstract: This work presents the analytic and experimental development of piezoelectric actuators as elements of intelligent structures, i.e., structures with highly distributed actuators, sensors, and processing networks. Static and dynamic analytic models are derived for segmented piezoelectric actuators that are either bonded to an elastic substructure or embedded in a laminated composite. These models lead to the ability to predict, a priori, the response of the structural member to a command voltage applied to the piezoelectric and give guidance as to the optimal location for actuator placement. A scaling analysis is performed to demonstrate that the effectiveness of piezoelectric actuators is independent of the size of the structure and to evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure. Three test specimens of cantilevered beams were constructed: an aluminum beam with surface-bonded actuators, a glass/epoxy beam with embedded actuators, and a graphite/epoxy beam with embedded actuators. The actuators were used to excite steady-state resonant vibrations in the cantilevered beams. The response of the specimens compared well with those predicted by the analytic models. Static tensile tests performed on glass/epoxy laminates indicated that the embedded actuator reduced the ultimate strength of the laminate by 20%, while not significantly affecting the global elastic modulus of the specimen.

2,719 citations

Book
01 Jan 1990

1,325 citations

Journal ArticleDOI
TL;DR: In this paper, the formulation of the basic field equations, boundary conditions and constitutive equations of simple micro-elastic solids is discussed. And explicit expressions of constitutive expressions of several simple micro elastic solids are given and applied to some special problems.

1,309 citations

Journal ArticleDOI
TL;DR: In this article, a finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings.
Abstract: A finite element formulation is presented for modeling the dynamic as well as static response of laminated composites containing distributed piezoelectric ceramics subjected to both mechanical and electrical loadings. The formulation was derived from the variational principle with consideration for both the total potential energy of the structures and the electrical potential energy of the piezoceramics. An eight-node three-dimensional composite brick element was implemented for the analysis, and three-dimensional incompatible modes were introduced to take into account the global bending behavior resulting from the local deformations of the piezoceramics. Experiments were also conducted to verify the analysis and the computer simulations. Overall, the comparisons between the predictions and the data agreed fairly well. Numerical examples were also generated by coupling the analysis with simple control algorithms to control actively the response of the integrated structures in a closed loop.

472 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an overview and assessment of the technology leading to the development of intelligent structures, which are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning and power amplification electronics.
Abstract: HIS article presents an overview and assessment of the technology leading to the development of intelligent structures. Intelligent structures are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning, and power amplification electronics. Such actuating, sensing, and signal processing elements are incorporated into a structure for the purpose of influencing its states or characteristics, be they mechanical, thermal, optical, chemical, electrical, or magnetic. For example, a mechanically intelligent structure is capable of altering both its mechanical states (its position or velocity) or its mechanical characteristics (its stiffness or damping). An optically intelligent structure could, for example, change color to match its background.17 Definition of Intelligent Structures Intelligent structures are a subset of a much larger field of research, as shown in Fig. I.123 Those structures which have actuators distributed throughout are defined as adaptive or, alternatively, actuated. Classical examples of such mechanically adaptive structures are conventional aircraft wings with articulated leading- and trailing-edge control surfaces and robotic systems with articulated manipulators and end effectors. More advanced examples currently in research include highly articulated adaptive space cranes. Structures which have sensors distributed throughout are a subset referred to as sensory. These structures have sensors which might detect displacements, strains or other mechanical states or properties, electromagnetic states or properties, temperature or heat flow, or the presence or accumulation of damage. Applications of this technology might include damage detection in long life structures, or embedded or conformal RF antennas within a structure. The overlap structures which contain both actuators and sensors (implicitly linked by closed-loop control) are referred to as controlled structures. Any structure whose properties or states can be influenced by the presence of a closed-loop control system is included in this category. A subset of controlled structures are active structures, distinguished from controlled structures by highly distributed actuators which have structural functionality and are part of the load bearing system.

470 citations