scholarly journals Nonlinear Instability and Reliability Analysis of Composite Laminated Beams

2021 ◽  
Author(s):  
Alireza Fereidooni
Keyword(s):  
Dynamic Instability ◽  
Integral Form ◽  
Instability Region ◽  
Beam Model ◽  
Loading Frequency ◽  
Nonlinear Behaviour ◽  
Laminated Beams ◽  
Wide Range ◽  
Laminated Structures ◽  
Shear Deformable

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.

scholarly journals Nonlinear Instability and Reliability Analysis of Composite Laminated Beams

2021 ◽  
Author(s):  
Alireza Fereidooni
Keyword(s):  
Dynamic Instability ◽  
Integral Form ◽  
Instability Region ◽  
Beam Model ◽  
Loading Frequency ◽  
Nonlinear Behaviour ◽  
Laminated Beams ◽  
Wide Range ◽  
Laminated Structures ◽  
Shear Deformable

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.

Non-Newtonian pulsating blood flow-induced dynamic instability of visco-carotid artery within soft surrounding visco-tissue using differential cubature method

2015 ◽  
Vol 229 (16) ◽  
pp. 3002-3012 ◽  
Author(s):  
A Tabatabaie Arani ◽  
Ali Ghorbanpour Arani ◽  
Reza Kolahchi
Keyword(s):  
Blood Flow ◽  
Carotid Arteries ◽  
Shell Theory ◽  
Dynamic Instability ◽  
Current Model ◽  
Biomechanical Model ◽  
Realistic Model ◽  
Instability Region ◽  
Tissue Stiffness ◽  
Voigt Model

The high blood rate that often occurs in carotid arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks, and other diseases. However, dynamic analysis of carotid arteries conveying blood is lacking. The objective of this study was to present a biomechanical model for dynamic instability analysis of the embedded carotid arteries conveying pulsating blood flow. In order to present a realistic model, the carotid arteries and tissues are assumed viscoelastic using Kelvin–Voigt model. Carotid arteries are modeled as elastic cylindrical vessels based on Mindlin cylindrical shell theory (MCST). One of the main advantages of this study is considering the pulsating non-Newtonian nature of the blood flow using Carreau, Casson, and power law models. Applying energy method, Hamilton’s principle and differential cubature method (DCM), the dynamic instability region (DIR) of the visco-carotid arteries is obtained. The detailed parametric study is conducted, focusing on the combined effects of the elastic medium and non-Newtonian models on the dynamic instability of the visco-carotid arteries. It can be seen that with increasing the tissue stiffness, the natural frequency of visco-carotid arteries decreases. The current model provides a powerful tool for further experimental investigation about arterial tortuosity.

The role of exploratory mechanisms in evolution

1995 ◽  
Vol 349 (1329) ◽  
pp. 297-297
Keyword(s):  
Dynamic Instability ◽  
Specific Mechanism ◽  
Cellular Mechanisms ◽  
Selection Processes ◽  
Wide Range ◽  
Rapid Changes ◽  
Neuronal Processes ◽  
History Of ◽  
Variation And Selection

Many cellular mechanisms use a process of variation and selection to generate specific patterns. Among these, dynamic instability of microtubules has been shown to employ a specific mechanism to intentionally generate variation. In many systems the growth of neurons or neuronal processes is excessive, the final connections being established by stabilization of functional interactions. When changes in neuronal networks take place, such as in metamorphosis, use is made of the plasticity of neuronal connectivity. In the immune system, specific responses are generated by variation and selection. Processes that explore a wide range of conditions and a wide range of structures can be called exploratory processes. These are very robust and capable of responding to damage, variability in the environment and ontogenic changes in the organisms. Such robustness would be useful for adapting to changes that occur during phylogenetic changes as well. Given the extensive history of extinction and radiation in evolution, it may be supposed that these mechanisms have themselves been selected for their capacity to survive rapid changes in the organism and for their ability to generate cellular variation.

scholarly journals Drops bouncing off macro-textured superhydrophobic surfaces

2017 ◽  
Vol 824 ◽  
pp. 866-885 ◽  
Author(s):  
Ali Mazloomi Moqaddam ◽  
Shyam S. Chikatamarla ◽  
Iliya V. Karlin
Keyword(s):  
Contact Time ◽  
Numerical Study ◽  
Three Dimensional ◽  
Superhydrophobic Surfaces ◽  
Nonlinear Behaviour ◽  
Textured Surfaces ◽  
Texture Density ◽  
Wide Range ◽  
Quantitative Manner ◽  
The Impact

Recent experiments with droplets impacting macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. Here we present a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantifies the roles played by various external and internal forces. For the first time, accurate three-dimensional simulations involving realistic macro-textured surfaces are performed. After demonstrating that simulations reproduce experiments in a quantitative manner, the study is focused on analysing the flow situations beyond current experiments. We show that the experimentally observed reduction of contact time extends to higher Weber numbers, and analyse the role played by the texture density. Moreover, we report a nonlinear behaviour of the contact time with the increase of the Weber number for imperfectly coated textures, and study the impact on tilted surfaces in a wide range of Weber numbers. Finally, we present novel energy analysis techniques that elaborate and quantify the interplay between the kinetic and surface energy, and the role played by the dissipation for various Weber numbers.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

Semianalytical compressive strength criteria for unidirectional composites

2017 ◽  
Vol 37 (4) ◽  
pp. 238-246
Author(s):  
Uri Breiman ◽  
Jacob Aboudi ◽  
Rami Haj-Ali
Keyword(s):  
Experimental Data ◽  
Compressive Strength ◽  
Volume Fraction ◽  
Unidirectional Composite ◽  
Fiber Volume ◽  
Unidirectional Composites ◽  
Analysis And Design ◽  
Composite Systems ◽  
Wide Range ◽  
Laminated Structures

The compressive strength of unidirectional composites is strongly influenced by the elastic and strength properties of the fiber and matrix phases, as well as by the local geometrical properties, such as fiber volume fraction, misalignment, and waviness. In the present investigation, two microbuckling criteria are proposed and examined against a large volume of measured data of unidirectional composites taken from the literature. The first criterion is based on the compressive strength formulation using the buckling of Timoshenko’s beam. It contains a single parameter that can be determined according to the best fit to experimental data for various types of polymeric matrix composites. The second criterion is based on buckling-wave propagation analogy using the solution of an eigenvalue problem. Both criteria provide closed-form expressions for the compressive strength of unidirectional composites. We propose modifications of the two criteria by a fitting approach, for a wide range of fiber volume fractions, applied to four classes of unidirectional composite systems. Furthermore, a normalized form of the two models is presented after calibration in order to compare their prediction against experimental data for each of the material systems. The new modified criteria are shown to give a good match to a wide range of unidirectional composite systems. They can be employed as practical compression failure criteria in the analysis and design of laminated structures.

Study on mechanical properties of high damping viscoelastic dampers

2019 ◽  
Vol 22 (14) ◽  
pp. 2925-2936 ◽  
Author(s):  
Yun Chen ◽  
Chao Chen ◽  
Qianqian Ma ◽  
Huanjun Jiang ◽  
Zhiwei Wan
Keyword(s):  
Mechanical Properties ◽  
Shear Strain ◽  
Strain Amplitude ◽  
Hysteretic Behavior ◽  
Loading Frequency ◽  
Equivalent Stiffness ◽  
Viscoelastic Dampers ◽  
Wide Range ◽  
High Damping Rubber ◽  
Stiffness And Damping

The mechanical properties of the viscoelastic damper made of high damping rubber produced in China are investigated in order to provide the basis for its application. At first, the test on material properties of high damping rubber is conducted. The Mooney–Rivlin model, the Yeoh model and the Prony series are applied for simulating the nonlinear behavior of the high damping rubber with the aid of software ABAQUS. Then, three viscoelastic dampers with different sizes are tested under cyclic loading. The effects of strain amplitude and loading frequency on hysteretic behavior of dampers are analyzed. Viscoelastic dampers possess large deformation capability, stable energy-dissipation capacity and good fatigue-resisting property. The effect of strain amplitude is much more significant than loading frequency. The hysteretic behavior of the dampers is simulated by the Bouc–Wen model and the model of the equivalent stiffness and damping, respectively. The prediction results by using the Bouc–Wen model are in good agreement with the experimental results, which indicates that the Bouc–Wen model is applicable to simulate the mechanical properties of high damping viscoelastic dampers with a wide range of shear strain. As to the model of equivalent stiffness and damping, it has the advantages of clear concept and simple calculation. However, the good accuracy of prediction can be obtained only when the shear strain is not greater than 60%.

Separation in Flat Indentation of Orthotropic Laminated Beams

2001 ◽  
Author(s):  
Chun-Fu Chen
Keyword(s):  
Contact Stresses ◽  
Real Contact Area ◽  
Iteration Algorithm ◽  
Critical Aspect ◽  
Laminated Beams ◽  
Contact Conditions ◽  
Numerical Iteration ◽  
Wide Range ◽  
Solution Methods ◽  
Separation Results

Abstract Problems of indentation of orthotropic laminated beams due to flat punches arc solved. Exact solution methods for a subsidiary problem are developed first for both the simply-supported and clamped-ended cases. A numerical iteration algorithm is then employed to assess the possible separation and the real contact area and the contact stresses for a given punch width and a beam span. The contact stresses and separation results for the beams of a typical span reveal various contact conditions that depend only upon the punch width but not the magnitude of the applied load. For a symmetric lamination of the beam, a wide range of punch widths and beam spans are implemented to detect the critical punch widths rendering the onset of separation between the punch and the beam and to establish the threshold curve for the critical aspect ratio of the beam versus the relative punch width. The effects of both the end support condition and slacking sequence of the beam upon the contact and separation scenarios as well as the threshold behavior are thoroughly evaluated.

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