M. N. Rao

Bio: M. N. Rao is an academic researcher from RWTH Aachen University. The author has contributed to research in topics: Piezoelectricity & Finite element method. The author has an hindex of 4, co-authored 9 publications receiving 61 citations.

Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic composite structures

Abstract: A fully geometrically nonlinear finite rotation shell element for static analysis of layered magneto-electro-elastic (MEE) coupled composite structures is proposed. Reissner–Mindlin first-order shear deformation (FOSD) theory with full geometrically nonlinear strain–displacement relations and finite rotations is used to obtain the variational formulation. The scalar electric and magnetic fields are assumed along with the quasi-static behavior of MEE layers. Electric and magnetic potentials are assumed to vary quadratically in the transverse direction. Three linear constitutive relations are used describe the magneto-electro-elastic coupling. The magneto-electro-elastic composite four node shell element behavior is refined by embodying an assumed natural strain (ANS) method for transverse shear strains, and an enhanced assumed strain (EAS) method for in-plane bending strains. The developed finite element model is deployed for static analysis of layered MEE structures in sensor and actuator configurations, and results are compared with the available references. Additionally, several numerical examples are simulated to show the potentiality and predictive capabilities of the proposed finite element method.

Finite element modeling and analysis of piezo-integrated composite structures under large applied electric fields

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.

Finite rotation FE-simulation and active vibration control of smart composite laminated structures

Abstract: The present article focuses on the nonlinear finite element simulation and control of large amplitude vibrations of smart piezolaminated composite structures. Full geometrically nonlinear finite rotation strain---displacement relations and Reissner---Mindlin first-order shear deformation hypothesis to include the transverse shear effects are considered to derive the variational formulation. A quadratic variation of electric potential is assumed in transverse direction. An assumed natural strain method for the shear strains, an enhanced assumed strain method for the membrane strains and an enhanced assumed gradient method for the electric field is incorporated to improve the behavior of a four-node shell element. Numerical simulations presented in this article show the accurate prediction capabilities of the proposed method, especially for structures undergoing finite deformations and rotations, in comparison to the results obtained by simplified nonlinear models available in references and also with those obtained by using the C3D20RE solid element for piezoelectric layers in the Abaqus code.

Static and dynamic FE analysis of piezolaminated composite shells considering electric field nonlinearity under thermo-electro-mechanical loads

Abstract: The present article focuses on the static and dynamic finite element simulations of smart piezolaminated composite shell structures considering strong electric field nonlinearity under thermo-electro-mechanical loads. To model the electromechanical behaviour of piezoelectric patches or layers under large applied electric fields more efficiently, two-way coupled rotationally invariant second-order nonlinear constitutive relations are used in the variational principle approach. Furthermore, the nonlinear piezoelectric element formulations are further extended to capture the response under temperature gradients. Quadratic and cubic polynomial approximations are deemed to represent the electric potential and temperature fields, respectively. Validation of the present element formulation has been done in comparison to experimental and numerical investigations of those available in the literature. Moreover, numerical simulations are performed to study the large electric field nonlinearities of piezolaminated structures in static and dynamic as well as active vibration control problems under both mechanical and thermal loads. The numerical simulations have shown that using the piezoelectric nonlinearity, both the static shape control and vibration suppression either under mechanical or thermal loads can be accomplished at much lower actuation voltages than estimated by the linear model.

Large deflection electro-mechanical analysis of composite structures bonded with macro-fiber composite actuators considering thermal loads

Abstract: In this paper, static analysis of laminated composite plates and shells bonded with macro-fiber composite (MFC) actuators under thermo-electro-mechanical loads is considered. Most earlier studies in the literature focused on the effects of MFC actuation power and fiber orientations on shape deformation of composite plates/shells subjected to electrical voltage only. Also most of the earlier studies on MFC- $$\hbox {d}_{33}$$ bonded smart structures in literature are performed by commercial softwares like Ansys or Abaqus using the thermal strain equivalent approach to model the piezomechanical coupling. Here, our earlier developed geometrically nonlinear plate and shell finite elements considering finite rotation theory are extended for MFC actuator-bonded composite structures taking into account additionally the response to temperature gradients. An improved Reissner–Mindlin hypothesis is considered to derive the variational formulation, in which a parabolic assumption of transverse shear strains across the thickness is assumed. MFC actuators dominated by the $$\hbox {d}_{33}$$ effect (MFC- $$\hbox {d}_{33}$$ ) with arbitrary fiber orientations are considered. The numerical model is validated with composite beams and plates by comparing the results of simulations with experimental investigations existing in the literature. An angle-ply composite shell structure is studied in detail concerning geometrically nonlinear analysis of bending and twisting deformations under different MFC- $$\hbox {d}_{33}$$ fiber orientations under electric loading. Shape control of thermally induced deformations of composite plates and shells is performed using bonded MFC- $$\hbox {d}_{33}$$ actuators and the significance of the present geometrically nonlinear model is highlighted.

A review of recent research on multifunctional composite materials and structures with their applications

Abstract: In the last few years the research activity in multifunctional composite materials and structures (MFCMS) is remarkably increased. This paper is a review of journal publications that are related to multifunctional composite materials and structures. MFCMS are meant for performing a variety of functions apart from the primary structural function which provides structural functions such as strength, stiffness, stability while non-structural functions provides energy harvesting, self-healing capability, sensing and actuation and sometimes acts as a protective layer etc. Many of the recent developments focused on the applications of MFCMS such as High Altitude Airship (HAA), morphing aircraft wings, energy harvesting, nanomaterials & nanostructures, smart structures, coupled field analysis, biomechanical etc. This paper also focused on the nonlinear mechanics of MFCMS because High Altitude Airship type of problems comes under geometrically and materially nonlinear case, so to analyse this type of problems one of the effective method called Variational Asymptotic Method is used. This method solves the problem by splitting the 3-D nonlinear problem into 1-D analysis through the thickness and 2-D nonlinear shell analysis. This paper concludes with a discussion of future scope and difficulties in design and analysis of multifunctional composite structures.

Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory

Abstract: In the present work, a geometrically nonlinear finite shell element is first presented to predict nonlinear dynamic behavior of piezolaminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shell, to enrich the existing research results on FG-CNTRC structures. The governing equations are developed via an improved first-order shear deformation theory (FSDT), in which a parabolic distribution of the transverse shear strains across the shell thickness is assumed and a zero condition of the transverse shear stresses on the top and bottom surfaces is imposed. Using a micro-mechanical model on the foundation of the developed rule of mixture, the effective material properties of the FG-CNTRC structures, which are strengthened by single-walled carbon nanotubes (SWCNTs), are scrutinized. The effectiveness of the present method is demonstrated by validating the obtained results against those of other studies from literature considering shell structures. Furthermore, some novel numerical results, including the nonlinear transient deflection of smart FG-CNTRC spherical and cylindrical shells, will be presented and can be considered for future structure design.

A review on modeling techniques of piezoelectric integrated plates and shells

Abstract: Piezoelectric materials embedded into plates and shells make the structures being capable of sensing and actuation, usually called smart structures, which are frequently used for shape and vibratio...

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Abstract: This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Free vibration analysis of postbuckled arbitrary-shaped FG-GPL-reinforced porous nanocomposite plates

Abstract: Based upon the third-order shear deformation theory (TSDT) and a variational mixed formation, the postbuckling response and free vibration around buckled configurations of variously-shaped plates made of functionally graded graphene platelet (FG-GPL)-reinforced nanocomposite are numerically investigated considering the effect of porosity. The proposed numerical strategy is formulated according to the ideas of variational differential quadrature (VDQ) and finite element method (FEM), and can be employed for plates with different shapes (e.g. rectangular, skew or quadrilateral and annular) including arbitrary-shaped hole. The material properties of nanocomposite are approximated based upon the Halpin–Tsai model together with the closed-cell Gaussian Random field scheme for various distribution patterns of porosity and GPLs along the thickness direction. The governing equations are obtained according to Hamilton’s principle by novel vector-matrix relations which can be readily used in numerical methods. One of the main novelties of developed numerical approach is proposing an efficient technique according to the mixed formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used TSDT model. A number of numerical examples are given to investigate the influences of porosity coefficient/distribution pattern, GPL weight fraction/dispersion pattern, cutout and edge conditions on the free vibrations of postbuckled FG-GPL-reinforced porous nanocomposite plates.