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.

An analytical model for the response of carbon/epoxy-aluminum honeycomb core sandwich structures under quasi-static indentation loading

2017 ◽  
Vol 21 (6) ◽  
pp. 1930-1952 ◽  
Author(s):  
Abhendra K Singh ◽  
Barry D Davidson ◽  
Alan T Zehnder ◽  
Benjamin PJ Hasseldine
Keyword(s):  
Analytical Model ◽  
Sandwich Structures ◽  
Plate Theory ◽  
Ritz Method ◽  
Design Tool ◽  
Face Sheet ◽  
Total System ◽  
Honeycomb Core ◽  
Static Indentation ◽  
Aluminum Honeycomb

An analytical model is developed to predict the loading and unloading response, as well as the residual dent diameter and dent depth, of carbon/epoxy-aluminum honeycomb core composite sandwich structures undergoing quasi-static indentation loading. The model considers damage created using spherical indenters and is valid up to the barely visible external damage threshold. The initial low load regime (until the onset of core crushing) is modeled using a combination of local Hertzian indentation of an elastic half-space and small deflection plate theory of a circular plate on an elastic foundation. For loads above those required to cause core crushing, the model uses the Rayleigh-Ritz method of energy minimization with the total system energy determined using a combination of face sheet bending energy, face sheet membrane energy and work done to the core during both elastic deformation and crushing. Degraded face sheet properties are used in the model beyond the onset of face sheet delamination, which is predicted using Griffith’s energy criterion. The model is validated using experimental results for sandwich structures consisting of quasi-isotropic 8- (thin) and 16- (thick) ply carbon/epoxy face sheets and aluminum honeycomb cores. The results show that the overall mechanics of the model are fundamentally correct and reflective of physical behavior. Thus, in its present form the model shows promise as a preliminary design tool.

Buckling and Vibration of Orthotropic Nonhomogeneous Rectangular Plates With Bilinear Thickness Variation

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Yajuvindra Kumar ◽  
R. Lal
Keyword(s):  
Orthogonal Polynomials ◽  
Plate Theory ◽  
Ritz Method ◽  
Cartesian Product ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Two Dimensional ◽  
Classical Plate Theory ◽  
Simply Supported

An analysis and numerical results are presented for buckling and transverse vibration of orthotropic nonhomogeneous rectangular plates of variable thickness using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh–Ritz method on the basis of classical plate theory when uniformly distributed in-plane loading is acting at two opposite edges clamped/simply supported. The Gram–Schmidt process has been used to generate orthogonal polynomials. The nonhomogeneity of the plate is assumed to arise due to linear variations in elastic properties and density of the plate material with the in-plane coordinates. The two dimensional thickness variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Effect of various plate parameters such as nonhomogeneity parameters, aspect ratio together with thickness variation, and in-plane load on the natural frequencies has been illustrated for the first three modes of vibration for four different combinations of clamped, simply supported, and free edges correct to four decimal places. Three dimensional mode shapes for a specified plate for all the four boundary conditions have been plotted. By allowing the frequency to approach zero, the critical buckling loads in compression for various values of plate parameters have been computed correct to six significant digits. A comparison of results with those available in the literature has been presented.

Analysis of Electromechanical Performance of Energy Harvesting Skin Based on the Kirchhoff Plate Theory

2014 ◽  
Author(s):  
Heonjun Yoon ◽  
Byeng D. Youn ◽  
Heung S. Kim
Keyword(s):  
Energy Harvesting ◽  
Differential Equations ◽  
Analytical Model ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Electrical Circuit ◽  
Kirchhoff Plate ◽  
Mode Shapes ◽  
Kirchhoff Plate Theory

As a compact and durable design concept, energy harvesting skin (EH skin), which consists of piezoelectric patches directly attached onto the surface of a vibrating structure as one embodiment, has been recently proposed. This study aims at developing an electromechanically-coupled analytical model of the EH skin so as to understand its electromechanical behavior and get physical insights about important design considerations. Based on the Kirchhoff plate theory, the Hamilton’s principle is used to derive the differential equations of motion. The Rayleigh-Ritz method is implemented to calculate the natural frequency and the corresponding mode shapes of the EH skin. The electrical circuit equation is derived by substituting the piezoelectric constitutive relation into Gauss’s law. Finally, the steady-state output voltage is obtained by solving the differential equations of motion and electrical circuit equation simultaneously. The results of the analytical model are verified by comparing those of the finite element analysis (FEA) in a hierarchical manner.

A Semi-Analytical Model of Shape-Control in an Adaptive Air Foil Bearing

2018 ◽  
Author(s):  
Hossein Sadri ◽  
Alexander Kyriazis ◽  
Henning Schlums ◽  
Michael Sinapius
Keyword(s):  
Analytical Model ◽  
Shape Control ◽  
Plate Theory ◽  
Dynamic Properties ◽  
Ritz Method ◽  
Experimental Tests ◽  
Elastic Suspension ◽  
Aerodynamic Pressure ◽  
Foil Bearing ◽  
Lift Off

The aerodynamic foil bearing is a special type of air bearing in which the flexible foil structure between rotor and rigid housing supports the rotor bearing system with a greater robustness against thermal distortion and production misalignments. In such bearings, the generation of an aerodynamic pressure in the lubricating film after reaching the lift-off speed prevents the solid contact between rotor and foil structure. Since many static and dynamic properties of air foil bearings strongly depend on the inner contour of the bearing, the idea of an adaptive air foil bearing (AAFB) is developed to optimize the bearing’s performance at different operating points. This paper concentrates on a semi-analytical model based on plate theory using Ritz method for simulating the static shape control of piezoelectrically actuatable supporting segments for an AAFB under different loading conditions. The elastic suspension of the supporting segments and symmetries of the bearing are considered in the modeling. After validation by means of FEM analyses and experimental tests the influence of geometry and material is examined in a parametric study. Later on, the model is used for parameter optimization in order to achieve the most effective shape morphing.

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.

Stress-Strain Analysis of Single-Lap Composite Joints Under Tension

1996 ◽  
Vol 118 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Chihdar Yang ◽  
Su-Seng Pang
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Anisotropic Plate ◽  
Plate Theory ◽  
Coupling Effect ◽  
Strain Analysis ◽  
Coupled System ◽  
Lap Joints ◽  
Stress And Strain ◽  
Peel Stress

Based on the laminated anisotropic plate theory, an analytical model is proposed to determine the stress and strain distributions of adhesive-bonded composite single-lap joints under tension. The laminated anisotropic plate theory is applied in the derivation of the governing equations of the two bonded laminates. The entire coupled system is then obtained through assuming the peel stress between the two laminates. With the Fourier series and appropriate boundary conditions, the solutions of the system are obtained. Based on the proposed model, the stress and strain distributions of the adherends and the adhesive can be predicted. The coupling effect between the external tension and the induced bending due to the asymmetry of composite laminates are also included. The two adherends can also have different materials and properties. An existing FEA code, “ALGOR,” is used as a comparison with this proposed analytical model. Results from this developed model are also compared with Goland and Reissner’s as well as Hart-Smith’s papers.

Numerical and Experimental Studies on Cured Shape of Thin Unsymmetric Carbon/Epoxy Laminates

2007 ◽  
Vol 334-335 ◽  
pp. 137-140 ◽  
Author(s):  
Fu Hong Dai ◽  
Bo Ming Zhang ◽  
Xiao Dong He ◽  
Shan Yi Du
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Value Function ◽  
Ritz Method ◽  
Experimental Studies ◽  
Experimental Result ◽  
Multiple Value

An analytical model was established by means of Ritz method to calculate the cured shape of cross-ply unsymmetric composite laminates. A number of experiments of Carbon/Epoxy laminates were conducted. It was found in the experiment that the warped surface could be a multiple-value function, which should be studied further. The result of calculation correlates well with the experimental result except the regions very near the laminate edge. The conclusion is instructive to manufacture of composite laminates.

An Improved Reissner-Mindlin Plate Theory for Composite Laminates

Aerospace ◽  
2004 ◽  
Author(s):  
Wenbin Yu
Keyword(s):  
Exact Solution ◽  
Asymptotic Method ◽  
Composite Laminates ◽  
Plate Theory ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Two Dimensional ◽  
Previous Theory ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

An improved Reissner-Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner-Mindlin theory with an excellent accuracy comparable to that of higher-order, layerwise theories. The present work is extended from the previous theory developed by the writer and his co-workers with two sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner-Mindlin model; and (b) the semi-definite programming technique is used to seek the optimum Reissner-Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner-Mindlin model and the second order asymptotical energy can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and first-order shear-deformation, demonstrating that the present theory has an excellent agreement with the exact solution.

Sign in / Sign up

Export Citation Format

Share Document