Dynamic stability of uncertain laminated beams subjected to subtangential loads

Goyal, Vijay K.; Kapania, Rakesh K.

doi:10.1016/j.ijsolstr.2007.11.024

Cited by 10 publications

(8 citation statements)

References 35 publications

(32 reference statements)

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“…Chakraborty et al (2002) presented a new refined locking free first-order shear deformable finite element and demonstrated its utility in solving the free vibration and wave propagation problems in the laminated composite beam structures with symmetric as well as asymmetric ply stacking. Goyal (2002) proposed the formulations to study the static responses, free vibration and buckling of laminated composite beams based on the first order shear deformation theory and principle of virtual work.…”

Section: Composite Laminated Beamsmentioning

confidence: 99%

“…Subramanian (2001) developed a two-node finite element of eight degrees of freedom per node, using a HSDT, for flexural analysis of symmetric laminated composite beams. Goyal (2002) developed a twenty-one degree-of-freedom beam element, based on the first order shear deformation theory, and principle of virtual work, to study the static response, free vibration and buckling of laminated composite beams. In his model and formulation, the dynamic stiffness matrix is not included in the formulation, because of that his model can not capture the effects of the dynamic part of varying time loading stiffness matrix.…”

Section: Finite Element Analysismentioning

confidence: 99%

“…The failure criterion was used to predict the failure load and the probability of failure was computed by Monte Carlo simulation. Goyal (2002) studied the reliability analysis of the composite beams with uncertain axial module of elasticity and ply angle orientation through the probabilistic finite element analysis and Monte Carlo simulation. He did not study the effects of the uncertainties on the region of dynamic instabilities.…”

Section: Probability Analysis Of Composite Beamsmentioning

confidence: 99%

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Nonlinear Instability and Reliability Analysis of Composite Laminated Beams

Fereidooni¹

2021

Preprint

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The wide range of high performance engineering applications of composite laminated structures demands a proper understanding of their dynamics performance. Due to the complexity and nonlinear behaviour of such structures, developing a mathematical model to determine the dynamic instability boundaries is indispensable and challenging. The aim of this research is to investigate the dynamic behaviour of shear deformable composite laminated beams subjected to varying time conservative and nonconservative loads. The dynamic instability behaviour of non-conservative and conservative system are dissimilar. In case of conservative loading, the instability region intersects the loading axis, but in case of non-conservative loads the region will be increased with loading increases. The extended Hamilton’s principle and the first order shear deformation theory are employed in this investigation to establish the integral form of the equation of motion of the beam. A five node beam model is presented to descritize the integral form of the governing equations. The model has the capability to capture the dynamic effects of the transverse shear stress, warping, and bending-twisting, bending-stretching, and stretching-twisting couplings. Also, the geometric and loading nonlinearities are included in the equation of system. The beam model incorporates, in full form, the non-classical effects of warping on stability and dynamic response of symmetrical and unsymmetrical composite beams. In case of nonlinear elasticity, the resonance curves are bent toward the increasing exciting frequencies. The response of the stable beam is pure periodic and follow the loading frequency. When the beam is asymptotically stable the response of the beam is aperiodic and does not follow the loading frequency. In unstable state of the beam response frequency increases with time and is higher than the loading frequency, also the amplitude of the beam will increases, end to beam failure. The amplitude of the beam subjected to substantial excitation loading parameters increases in a typical nonlinear manner and leads to the beats phenomena. The principal regions of dynamic instability are determined for various loading and boundary conditions using the Floquet’s theory. The beam response in the regions of instability is investigated. Axially loaded beam may be unstable not just in load equal to critical load and/or loading frequency equal to beam natural frequency. In fact there are infinite points in region of instability in plane load vs. frequency that the beam can be unstable. The region of instability of the shear deformable beams is wider compare to non-shear deformable beams. The lower bound of the instability region of the shear deformable beams changes faster than upper bound. Probabilistic stability analysis of the uncertain laminated beams subject to both conservative and nonconservative loads is studied. The effects of material and geometry uncertainties on dynamics instability of the beam, is investigated through a probabilistic finite element analysis and Monte Carlo Simulation methods. For non-conservative systems variations of uncertain material properties has a smaller influence than variations of geometric properties over the instability of the beam.

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Section: Composite Laminated Beamsmentioning

confidence: 99%

Section: Finite Element Analysismentioning

confidence: 99%

Section: Probability Analysis Of Composite Beamsmentioning

confidence: 99%

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Nonlinear Instability and Reliability Analysis of Composite Laminated Beams

Fereidooni¹

2021

Preprint

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“…Following several decades of deterministic studies, the aspect of considering the effect of uncertainty in material and structural attributes have recently started receiving due attention from the scientific community. Both probabilistic (Sakata et al (2008), Goyal and Kapania, (2008), Manan and Cooper (2009), Dey et al (2016aDey et al ( , 2016e, 2018bDey et al ( , 2019, , , 2017c, Naskar (2017)) as well as non-probabilistic (Dey et al (2016b), Pawar et al (2012)) approaches have been investigated to analyse the influence of variability in the material and structural attributes of composite structures. Plenty of researches have been reported based on intrusive methods to quantify the uncertainty of composite structures (Lal and Singh (2010), Scarth and Adhikari (2017)), wherein the major drawback can be identified as the requirement of intensive analytical derivation and lack of the ability to obtain complete probabilistic description of the response quantities for systems with spatially varying attributes.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic micromechanical spatial variability quantification in laminated composites

Naskar

Mukhopadhyay

Sriramula

2018

Composites Part B: Engineering

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This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loève expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/ system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.

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“…The effect of material uncertainty on vibration control of smart composite plate is studied by Umesh and Ganguli [7] by using polynomial chaos expansion. The dynamic stability of uncertain laminated beams subjected to subtangential loads studied by Goyal and Kapania [8] while Manan and Cooper [9] introduced probabilistic approach for design of composite wings including uncertainties. On the other hand, Fang and Springer [10] studied on the design of composite laminates by a Monte Carlo method while Kapania and Goyal [11] investigated on free vibration of unsymmetrically laminated beams.…”

Section: Introductionmentioning

confidence: 99%