scholarly journals Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

2020 ◽  
Author(s):  
Lander Vertonghen ◽  
Saullo G. P. Castro
Keyword(s):  
Variable Thickness ◽  
Plane Surface ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Variable Stiffness ◽  
Element Model ◽  
Analytical Models ◽  
Thickness Variation ◽  
Wide Range ◽  
Modelling Strategies

Previous research has hinted on further improvements of the buckling behaviour of variable-stiffness laminates by incorporating overlaps, resulting in a variable thickness profile that is non-linearly coupled to the steering angles. The present study compares two modelling strategies to consider the variable thickness distribution: 1) as manufactured with discrete thicknesses; and 2) smoothed with a continuous thickness distribution. The as-manufactured discrete thickness created by overlapping tows is obtained by means of virtually manufactured laminates. The smeared approximation is much simpler to implement, whereby the local thickness is a non-linear function of the local steering angle. Linear buckling analyses are performed by means of fast semi-analytical models based on the Ritz method using hierarchical polynomials and classical plate formulation. By assuming a smooth manufacturing mould on one side, a one-sided thickness variation is produced, resulting in non-symmetric laminates for which the mid-plane surface is varied accordingly. Modelling guidelines are provided regarding the use of the smeared model in a study covering a wide range of geometries, loading and boundary conditions. With these guidelines, one can apply the smeared thickness technique in semi-analytical models to reach a correlation within ±5% compared to a costly discrete-thickness finite element model.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

Selection and implementation of optimal magnetorheological brake design for a variable impedance exoskeleton robot joint

2016 ◽  
Vol 231 (5) ◽  
pp. 941-960 ◽  
Author(s):  
Ozgur Baser ◽  
Mehmet Alper Demiray
Keyword(s):  
Volume Ratio ◽  
Variable Stiffness ◽  
Humanoid Robots ◽  
Performance Comparison ◽  
Analytical Models ◽  
Exoskeleton Robot ◽  
Wide Range ◽  
Braking Torque ◽  
Variable Damping ◽  
Variable Stiffness Actuators

Next-generation exoskeleton and humanoid robots are expected to behave similar to the human neuro-muscular system to perform stable, flexible, and biomimetic movements. To achieve this goal, the variable stiffness actuators have been widely used in various robots. Using variable damping actuators along with variable stiffness actuators will be extremely beneficial for wide range of stable movements. Magnetorheological (MR) brakes are one of the most promising electromagnetic structures that can provide such variable damping in a relatively small actuator volume. In this paper, we focused on the design, characterization, selection and implementation of T-shaped, inner coil and outer coil multi-pole MR brakes to the ankle of an exoskeleton robot. Analytical models are developed using the magnetic circuit analysis to determine the braking torque. Then, magnetic finite element models are developed and coupled with an optimization algorithm to determine the optimal set of parameters of each MR brake design. Prototypes are manufactured in same size and tested experimentally to characterize the actuators’ torque-to-volume ratio, transient response, hysteresis, torque tracking, energy consumption, and damping performances. The performance comparison of the brakes showed T-shaped multi-pole MR brake design has superior characteristics compared to two other designs. Therefore, T-shaped multi-pole MR brake design is coupled with a variable stiffness actuator and implemented in an ankle joint of an exoskeleton robot and experimentally tested. The results show that the developed new hybrid robot joint is capable of stable movement with a simple control algorithm by changing its stiffness and damping independently.

A Numerical Solution for Vibration Analysis of the Stiffened Variable-Thickness Conical Shells

2015 ◽  
Vol 757 ◽  
pp. 121-125
Author(s):  
Wei Ning ◽  
Feng Sheng Peng ◽  
Nan Wang ◽  
Dong Sheng Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variable Thickness ◽  
Conical Shell ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Free Vibrations ◽  
Conical Shells ◽  
Linear Eigenvalue Problem ◽  
Element Method

The free vibrations of the stiffened hollow conical shells with different variable thickness distribution modes are investigated in detail in the context of Donnel-Mushtari conical shell theory. Two sets of boundary conditions have been considered. The algebraic energy equations of the conical shell and the stiffeners are established separately. The Rayleigh-Ritz method is used to equate maximum strain energy to maximum kinetic energy which leads to a standard linear eigenvalue problem. Numerical results are presented graphically for different geometric parameters. The parametric study reveals the characteristic behavior which is useful in selecting the shell thickness distribution modes and the stiffener type. The comparison between the present results and those of finite element method shows that the present results agree well with those of finite element method.

Application of the ASME Code SEC III Pressure Design Requirements on Locally Thinned Tight Radius Pipe Bends

2010 ◽  
Author(s):  
Usama Abdelsalam
Keyword(s):  
Wall Thickness ◽  
Thickness Distribution ◽  
Element Model ◽  
Thickness Variation ◽  
Pipe Bend ◽  
Linear Elastic ◽  
Primary Stress ◽  
Asme Code ◽  
Wall Thickness Variation ◽  
Code Compliance

This paper addresses the primary stress requirements for the pressure loading of tight radius pipe bends according to the ASME Code SEC III NB-3200 (Design by Analysis). Solid FEA models are constructed to represent a tight radius pipe bend with general and local internal wall thinning. The wall thickness variation is considered using uniform and non-uniform axial and circumferential profiles. It is demonstrated that for a tight radius bend with wall thickness equal to the pressure based thickness of the corresponding straight pipe, the linear elastic criteria of NB-3221 are significantly exceeded. Results are presented to show the minimum acceptable wall thickness using uniform thickness distributions. The allowable wall thickness criterion of the ASME Code SEC XI Code Case N-597-2 is examined using a finite element model implementing the recommended thickness distribution along the circumferential direction. It is demonstrated that this distribution achieves a uniform stress intensity over the entire bend (uniform strength). A local thin area (LTA) centered at the intrados of the bend is super-imposed on a general thinned area and the axial and circumferential extents are varied. FEA results are presented to demonstrate Code compliance and its dependency on the axial and circumferential extents of the LTA and the thickness of the surrounding material.

Vibration of Nonhomogeneous Orthotropic Elliptic and Circular Plates With Variable Thickness

2006 ◽  
Vol 129 (2) ◽  
pp. 256-259 ◽  
Author(s):  
S. Chakraverty ◽  
Ragini Jindal ◽  
V. K. Agarwal
Keyword(s):  
Variable Thickness ◽  
Ritz Method ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Material ◽  
Orthotropic Plates ◽  
Various Boundary Conditions ◽  
Vibrational Characteristics ◽  
Schmidt Orthogonalization ◽  
Orthogonalization Procedure

In this paper, study of nonhomogeneity as well as variable thickness in elliptic and circular orthotropic plates is undertaken. Nonhomogeneity of plate material is assumed to be a quadratic variation of Young’s modulii and density whereas shear modulus, is considered to vary linearly along both the axes. The quadratic thickness variation in orthotropic nonhomogeneous plates is also considered. Effect of variation of these parameters on vibrational characteristics are analyzed for various boundary conditions at the edges. Results are obtained using boundary characteristic orthogonal polynomials generated by using Gram-Schmidt orthogonalization procedure in Rayleigh-Ritz method.

Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

2005 ◽  
Vol 109 (1091) ◽  
pp. 23-33
Author(s):  
S. Tizzi
Keyword(s):  
Variational Principles ◽  
Thickness Distribution ◽  
Minimum Weight ◽  
Ritz Method ◽  
Numerical Procedure ◽  
Critical Conditions ◽  
Uniform Structure ◽  
Thickness Variation ◽  
Reference Structure ◽  
Algebraic Equations

Abstract A numerical procedure, which utilises polynomial power series expansions for the optimisation of multipanel wing structures in idealised critical flutter conditions, is introduced and developed. It arises from the Rayleigh-Ritz method and employes trial polynomial describing functions both for the flexural displacement and for the thickness variation over the multipanel surface. An idealised structural plate model, according to the Kirchhoff’s theory, together with a linearised supersonic aerodynamic approach, are supposed. The classical Euler-Lagrange optimality criterion, based on variational principles, has been utilised for the optimisation operations, where by imposing the stationary conditions of the Lagrangian functional expression, a nonlinear algebraic equations system is obtained, whose solution is found by an appropriate algorithm. By utilising an iterative process it is possible to reach the reference structure critical conditions, with an optimised thickness distribution throughout the multipanel surface. The final part of the work consists in searching the minimum weight of the multipanel planform wing structure with optimised thickness profile vs the flutter frequency, considered as a variable imput parameter, for fixed flutter speed and equal to the critical one of the reference uniform structure.

scholarly journals On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications

Actuators ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 86 ◽  
Author(s):  
Mario Torres Melgarejo ◽  
Maximilian Darnieder ◽  
Sebastian Linß ◽  
Lena Zentner ◽  
Thomas Fröhlich ◽  
...  
Keyword(s):  
Finite Element ◽  
Accurate Determination ◽  
Three Dimensional ◽  
Beam Theory ◽  
Element Model ◽  
Bending Stiffness ◽  
Analytical Models ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Wide Range

Compliant mechanisms based on flexure hinges are widely used in precision engineering applications. Among those are devices such as precision balances and mass comparators with achievable resolutions and uncertainties in the nano-newton range. The exact knowledge of the mechanical properties of notch hinges and their modeling is essential for the design and the goal-oriented adjustment of these devices. It is shown in this article that many analytical equations available in the literature for calculating the bending stiffness of thin semi-circular flexure hinges cause deviations of up to 12% compared to simulation results based on the three-dimensional finite element model for the considered parameter range. A close examination of the stress state within the loaded hinge reveals possible reasons for this deviation. The article explains this phenomenon in detail and shows the limitations of existing analytical models depending on specific geometric ratios. An accurate determination of the bending stiffness of semi-circular flexure hinges in a wide range of geometric parameters without the need for an elaborate finite element analysis is proposed in form of FEM-based correction factors for analytical equations referring to Euler-Bernoulli’s beam theory.

Free Vibration Analysis of Stiffened Conical Shell with Variable Thickness Distribution

2014 ◽  
Vol 614 ◽  
pp. 7-11 ◽  
Author(s):  
Wei Ning ◽  
Dong Sheng Zhang ◽  
Ji Ling Jia
Keyword(s):  
Variable Thickness ◽  
Conical Shell ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Conical Shells ◽  
Linear Eigenvalue Problem ◽  
Standard Linear ◽  
Energy Equations

The free vibrations of the stiffened hollow conical shells with different variable thickness distribution modes are investigated in detail in the context of Donnel-Mushtari conical shell theory. Two sets of boundary conditions have been considered. The algebraic energy equations of the conical shell and the stiffeners are established separately. The Rayleigh-Ritz method is used to equate maximum strain energy to maximum kinetic energy which leads to a standard linear eigenvalue problem. Numerical results are presented graphically for different geometric parameters. The parametric study reveals the characteristic behavior which is usefulis inuseful in selecting the shell thickness distribution modes and the stiffener type.

scholarly journals Universal mobility characteristics of graphene originating from charge scattering by ionised impurities

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jonathan H. Gosling ◽  
Oleg Makarovsky ◽  
Feiran Wang ◽  
Nathan D. Cottam ◽  
Mark T. Greenaway ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Carrier Density ◽  
Carrier Mobility ◽  
Carrier Transport ◽  
Analytical Models ◽  
Pristine Graphene ◽  
High Electron ◽  
Boltzmann Transport ◽  
Transport Parameters ◽  
Wide Range

AbstractPristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and provides a way to predict a priori all key transport parameters of graphene devices. Our results open a route for controlling the transport properties of graphene by doping and for engineering the properties of 2D materials and heterostructures.

scholarly journals Development of Permeability Models for Saturated Fluid Flow across Arrays of Fibre Clusters

2002 ◽  
Vol 11 (3) ◽  
pp. 096369350201100
Author(s):  
E.M. Gravel ◽  
T.D. Papathanasiou
Keyword(s):  
Analytical Models ◽  
Dual Porosity ◽  
Hydraulic Permeability ◽  
Fibrous Media ◽  
Fibre Bundles ◽  
Hexagonal Packing ◽  
Composites Manufacturing ◽  
Starting Point ◽  
Wide Range ◽  
Flow Through

Dual porosity fibrous media are important in a number of applications, ranging from bioreactor design and transport in living systems to composites manufacturing. In the present study we are concerned with the development of predictive models for the hydraulic permeability ( Kp) of various arrays of fibre bundles. For this we carry out extensive computations for viscous flow through arrays of fibre bundles using the Boundary Element Method (BEM) implemented on a multi-processor computer. Up to 350 individual filaments, arranged in square or hexagonal packing within bundles, which are also arranged in square of hexagonal packing, are included in each simulation. These are simple but not trivial models for fibrous preforms used in composites manufacturing – dual porosity systems characterised by different inter- and intra-tow porosities. The way these porosities affect the hydraulic permeability of such media is currently unknown and is elucidated through our simulations. Following numerical solution of the governing equations, ( Kp) is calculated from the computed flowrate through Darcy's law and is expressed as function of the inter- and intra-tow porosities (φ, φt) and of the filament radius ( Rf). Numerical results are also compared to analytical models. The latter form the starting point in the development of a dimensionless correlation for the permeability of such dual porosity media. It is found that the numerically computed permeabilities follow that correlation for a wide range of φ i, φt and Rf.

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