Nonlinear large displacement and moderate rotational characteristics of composite beams incorporating transverse shear strain

Creaghan, Stephen G.; Palazotto, Anthony N.

doi:10.1016/0045-7949(94)90321-2

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…A time-harmonic load of 1 N acting transversely at the free end of the beam is considered to excite the first few modes of the substrate beam. The linear frequency responses for the transverse displacement at the free end of the beam Comparison of deflection (at 50 mm from tip) of a clamped-free (0 • /90 • ) 3s beam integrated with an ACLD patch of negligible thickness with that of an identical composite beam [35].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…In order to verify the accuracy of the nonlinear finite element (FE) model derived here, a cantilever beam, which was experimentally studied in [35], is considered as the substrate beam and the thickness of the patch of the ACLD treatment is assumed to be negligibly small. In figure 4, the loaddeflection curve of this beam computed by the present FE model is compared with the experimental results available in [35]. It may be observed from figure 4 that the two sets of results closely match each other.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Figure 4. Comparison of deflection (at 50 mm from tip) of a clamped-free (0 • /90 • ) 3s beam integrated with an ACLD patch of negligible thickness with that of an identical composite beam[35].…”

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confidence: 99%

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Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1–3 piezoelectric composites

Sarangi

Ray

2010

Smart Mater. Struct.

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This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composite material as the material of the constraining layer of the ACLD treatment. A nonlinear finite element model has been developed for analyzing the ACLD of laminated symmetric and antisymmetric cross-ply and angle-ply composite beams integrated with such ACLD treatment. The von Kármán-type nonlinear strain-displacement relations and the first-order shear deformation theory are used for deriving this coupled electromechanical nonlinear finite element model. The Golla-Hughes-McTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. The backbone curves of such a class of nonlinear systems are plotted to determine the excitation levels for causing geometrical nonlinearity. The numerical results reveal that the ACLD treatment significantly improves the damping characteristics of the cross-ply and antisymmetric angle-ply beams for suppressing the geometrically nonlinear transient vibrations of the beams.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1–3 piezoelectric composites

Sarangi

Ray

2010

Smart Mater. Struct.

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“…The static, free vibration and crack propagation for detecting the failure behaviours are investigated (Nguyen-Thanh et al, 2018;Li et al, 2020;Huang et al, 2022). Currently, the conventional thin shell theory (Fluegge, 1973;Love, 2013;Tzou and Howard, 1994), which is based on the Kirchhoff-Love hypothesis ignoring transverse shear deformation, is often used to study shell problems (Confalonieri et al, 2015;Kiendl et al, 2009;Zukas, 1974;Zareh and Qian, 2018;Creaghan and Palazotto, 1994), and for shell structures with small shear stiffness (i.e. prone to significant transverse shear deformation), certain errors will be introduced (Hansbo and Larson, 2011;Repin and Sauter, 2010;Weise, 2018;Rychter, 1988).…”

Section: Introductionmentioning

confidence: 99%

“…, 2015; Kiendl et al. , 2009; Zukas, 1974; Zareh and Qian, 2018; Creaghan and Palazotto, 1994), and for shell structures with small shear stiffness (i.e. prone to significant transverse shear deformation), certain errors will be introduced (Hansbo and Larson, 2011; Repin and Sauter, 2010; Weise, 2018; Rychter, 1988).…”

Section: Introductionmentioning

confidence: 99%

Mesh refinement of finite element method for free vibration analysis of variable geometrical rotating cylindrical shells

Wang

2023

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PurposeThis study aims to provide a reliable and effective algorithm that is suitable for addressing the problems of continuous orders of frequencies and modes under different boundary conditions, circumferential wave numbers and thickness-to-length ratios of moderately thick circular cylindrical shells. The theory of free vibration of rotating cylindrical shells is of utmost importance in fields such as structural engineering, rock engineering and aerospace engineering. The finite element method is commonly used to study the theory of free vibration of rotating cylindrical shells. The proposed adaptive finite element method can achieve a considerably more reliable high-precision solution than the conventional finite element method.Design/methodology/approachOn a given finite element mesh, the solutions of the frequency mode of the moderately thick circular cylindrical shell were obtained using the conventional finite element method. Subsequently, the superconvergent patch recovery displacement method and high-order shape function interpolation techniques were introduced to obtain the superconvergent solution of the mode (displacement), while the superconvergent solution of the frequency was obtained using the Rayleigh quotient computation. Finally, the superconvergent solution of the mode was used to estimate the errors of the finite element solutions in the energy norm, and the mesh was subdivided to generate a new mesh in accordance with the errors.FindingsIn this study, a high-precision and reliable superconvergent patch recovery solution for the vibration modes of variable geometrical rotating cylindrical shells was developed. Compared with conventional finite element method, under the challenging varying geometrical circumferential wave numbers, and thickness–length ratios, the optimised finite element meshes and high-precision solutions satisfying the preset error limits were obtained successfully to solve the frequency and mode of continuous orders of rotating cylindrical shells with multiple boundary conditions such as simple and fixed supports, demonstrating good solution efficiency. The existing problem on the difficulty of adapting a set of meshes to the changes in vibration modes of different orders is finally overcome by applying the adaptive optimisation.Originality/valueThe approach developed in this study can accurately obtain the superconvergent patch recovery solution of the vibration mode of rotating cylindrical shells. It can potentially be extended to fine numerical models and high-precision computations of vibration modes (displacement field) and solid stress (displacement derivative field) for general structural special value problems, which can be extensively applied in the field of engineering computations in the future. Furthermore, the proposed method has the potential for adaptive analyses of shell structures and three-dimensional structures with crack damage. Compared with conventional finite element methods, significant advantages can be achieved by solving the eigenvalues of structures with high precision and stability.

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Nonlinear finite element analysis of composite beams and arches using a large rotation theory

Miller

Palazotto

1995

Finite Elements in Analysis and Design

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Nonlinear large displacement and moderate rotational characteristics of composite beams incorporating transverse shear strain

Cited by 10 publications

References 13 publications

Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1–3 piezoelectric composites

Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1–3 piezoelectric composites

Mesh refinement of finite element method for free vibration analysis of variable geometrical rotating cylindrical shells

Nonlinear finite element analysis of composite beams and arches using a large rotation theory

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