Abstract:This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear … Show more
“…The ANS method is adopted in the current discrete model to avoid locking problems, which may improve the efficiency of the present model in the prediction of dynamic behavior. Therefore, shear strain is expressed as (Mallek et al, 2019b)…”
Section: Strain-displacement Relationsmentioning
confidence: 99%
“…Let us consider bold-italicXp and bold-italicxp to be the position vectors of one point p of the mid-surface in the reference configuration C 0 and the current configuration C t , respectively. The position vector of one point q of the shell structure located at distance z from the mid-surface can be defined as (Mellouli et al, 2019a, 2019b, 2019c)where h is the thickness; bold-italicD is the initial shell director, which is perpendicular to the undeformed mid-surface; and bold-italicd1 and bold-italicd2 represent the double director shell vectors in the deformed configuration (see Figure 2). Figure 2.Definition of the coordinate systems.…”
Section: Double Director Shell Formulationmentioning
confidence: 99%
“…The ANS method is adopted in the current discrete model to avoid locking problems, which may improve the efficiency of the present model in the prediction of dynamic behavior. Therefore, shear strain is expressed as (Mallek et al, 2019b)where, γ21(A), γ11(B), γ21(C), and γ11(D) represent, respectively, strains at the middle points of elements A , B , C , and D .…”
This research makes a first attempt to investigate the dynamic characteristics of functionally graded carbon nanotube–reinforced composite plates and shell structures with surface-bonded piezoelectric layers. A variational formulation is derived based on the linear double director shell theory to ensure realistic parabolic variation of transverse shear strain along the thickness direction. The assumed natural strains method is adopted to enhance the accuracy of the four-node piezoelectric shell element developed in this study. Numerical studies are conducted to validate the efficiency and numerical stability of the proposed model to predict the behavior of piezolaminated composite shell structures. Furthermore, dynamic responses are extended to functionally graded carbon nanotube–reinforced composite shells covered by two active layers. The host structure is reinforced by single-walled carbon nanotubes, which are assumed to be graded through the thickness direction with different types of distributions and embedded in a polymer matrix. The effect of the volume fractions, distribution type, and geometrical parameters of the carbon nanotubes is examined.
“…The ANS method is adopted in the current discrete model to avoid locking problems, which may improve the efficiency of the present model in the prediction of dynamic behavior. Therefore, shear strain is expressed as (Mallek et al, 2019b)…”
Section: Strain-displacement Relationsmentioning
confidence: 99%
“…Let us consider bold-italicXp and bold-italicxp to be the position vectors of one point p of the mid-surface in the reference configuration C 0 and the current configuration C t , respectively. The position vector of one point q of the shell structure located at distance z from the mid-surface can be defined as (Mellouli et al, 2019a, 2019b, 2019c)where h is the thickness; bold-italicD is the initial shell director, which is perpendicular to the undeformed mid-surface; and bold-italicd1 and bold-italicd2 represent the double director shell vectors in the deformed configuration (see Figure 2). Figure 2.Definition of the coordinate systems.…”
Section: Double Director Shell Formulationmentioning
confidence: 99%
“…The ANS method is adopted in the current discrete model to avoid locking problems, which may improve the efficiency of the present model in the prediction of dynamic behavior. Therefore, shear strain is expressed as (Mallek et al, 2019b)where, γ21(A), γ11(B), γ21(C), and γ11(D) represent, respectively, strains at the middle points of elements A , B , C , and D .…”
This research makes a first attempt to investigate the dynamic characteristics of functionally graded carbon nanotube–reinforced composite plates and shell structures with surface-bonded piezoelectric layers. A variational formulation is derived based on the linear double director shell theory to ensure realistic parabolic variation of transverse shear strain along the thickness direction. The assumed natural strains method is adopted to enhance the accuracy of the four-node piezoelectric shell element developed in this study. Numerical studies are conducted to validate the efficiency and numerical stability of the proposed model to predict the behavior of piezolaminated composite shell structures. Furthermore, dynamic responses are extended to functionally graded carbon nanotube–reinforced composite shells covered by two active layers. The host structure is reinforced by single-walled carbon nanotubes, which are assumed to be graded through the thickness direction with different types of distributions and embedded in a polymer matrix. The effect of the volume fractions, distribution type, and geometrical parameters of the carbon nanotubes is examined.
“…The approach was recently extended by Carrera et al [12,13] in order to locally increase the accuracy by means of node-dependent kinematics. Furthermore, both geometrically [14,15,16] and materially [17] nonlinear problems in the behavior of piezoelectric thin-walled structures were also considered in the work of many researchers.…”
Integration of classical, passive structures and active elements based on multi-functional materials resulted in a novel structural concept denoted as active structures. The new structural systems are characterized by self-sensing and actuation. Coupling the two distinctive features by means of a controller enables a number of exquisite functionalities such as vibration suppression, noise attenuation, shape control, structural health monitoring, etc. Reliable, accurate and highly efficient modeling tools are an important ingredient of the active structure design. This paper addresses the Abaqus implementation of a recently developed piezoelectric 3-node shell element. The element uses co-rotational formulation to cover geometric nonlinearities. Special techniques are used to address the issues originating from low-order interpolation functions. The discrete shear gap is used to resolve the shear locking, while the assumed natural deviatoric strain technique improves the membrane behavior. Examples are computed in Abaqus upon implementation of the developed element.
“…Recently, the use of composite materials in structures due to their applications and properties has been widely developed. Some new research studies were numerically and experimentally studied the nonlinear behavior of composite plate and shells (Pradyumna and Nanda, 2013;Sossou, 2012;Rezaiee-Pajand et al, 2018b;Tornabene and Reddy, 2013;Mallek et al, 2019a;Mallek et al, 2019b). After proposing FGMs, many articles were presented to investigate different static and dynamic behaviors of structures composed of this type of materials (Rezaiee-Pajand and Rezaiee-Pajand et al, 2018d;Tornabene and Viola, 2013;Tornabene, 2009;Viola and Tornabene, 2009;Mellouli et al, 2019).…”
Purpose
The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.
Design/methodology/approach
Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.
Findings
Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.
Research limitations/implications
A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.
Practical implications
FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.
Social implications
The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.
Originality/value
Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.
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