Orientation Of Stiffeners Research Articles

Analysis of vibration characteristics of lattice-core sandwich annular spherical shells

This paper investigates the vibrational characteristics of lattice-core sandwich annular spherical shells. An effective analytical model, based on the Smeared Stiffener technique, is employed to integrate the stiffness contributions of the core with those of the shells. Helical stiffeners are modeled as beams capable of bearing axial forces and bending moments. The governing equations are derived from Donnell's classical thin shell theory. The Galerkin method is applied to extract the natural frequencies. To validate the analytical results and conduct a comprehensive parametric study, a 3D finite element model is developed using ABAQUS CAE software. Comparisons demonstrate a satisfactory agreement between the analytical and numerical results. Additionally, the effects of the spherical shell's geometric parameters, lamination angle, stiffener orientation angle, and various lattice core configurations are examined.

Optimization of Curvilinear Stiffener Beam Structures Simulated by Beam Finite Elements with Coupled Bending-Torsion Formulation.

This research presents the application of a beam finite element, specifically derived for simulating bending-torsion coupling in equivalent box-beam structures with curvilinear stiffeners. The stiffener path was simulated and optimized to obtain an expected coupling effect with respect to four typical static load cases, including geometric constraints related to the additive manufacturing production method. The selected load condition was applied to the centroid of the beam section, and the structure performance was consequently determined. A variation in load position up to one-fourth of the beam width was considered for investigating the stiffener path variation corresponding to a minimum bending-torsion coupling effect. The results demonstrated the capability of such a beam finite element to correctly represent the static behavior of beam structures with curvilinear stiffeners and show the possibility to uncouple its bending-torsion behavior using a specific stiffener orientation. The simulation of a laser powder bed fusion process showed new opportunities for the application of this technology to stiffened panel manufacturing.

Experimental and Numerical Dynamic Behavior of Bending-Torsion Coupled Box-Beam

Purpose Structural configurations related to new green aircraft design require high efficiency and low weight. As a consequence, moderate-to-large deformation under operating loads arise and aeroelastic instabilities different with respect to rigid counterpart are possible. Coupled structural configurations can provide the right mean to overcome such a critical situations selecting the right coupling parameters and structural performance. In this work, the dynamic behaviour of stiffened box-beam architecture with selected optimal stiffener orientation to emphasize the bending-torsion coupling characteristics has been investigated.MethodsAn extensive experimental activity has been performed for a validation and confirmation of the numerical results. Two cantilever beams produced with different technologies and materials have been tested. Modal performance has been determined by means of a laser Doppler vibrometer (LDV), while Finite-Element Method (FEM) numerical simulation based on solid elements and equivalent single layer approach have been applied and compared. Experimental/numerical comparison have been presented pointing out the specific coupling performance of this architecture with respect to natural frequencies and modal shapes.ResultsThe activity demonstrates a good correlation in natural frequencies that remains mostly under 4%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. Modal assurance criterion (MAC) has been considered in comparing experimental and numerical modal shapes.ConclusionThe proposed innovative configuration demonstrates its capability to be used in aeroelastic critical problem as a mean to reduce their influence in aircraft design. The numerical procedure used for equivalencing the stiffened parts of the box-beam has also been validated in dynamical response confirming the possibility to be used in design phase.

Damping analysis of stiffened laminated composite plates in thermal environment

High-strength and lightweight composites used in high-speed vehicles and aircraft experience increased temperature owing to aerodynamic friction. Because of the rise in temperature, the elastic moduli of the composites are degraded and inherent viscous damping is increased to the glass transition temperature. In this work, the damping performance of unstiffened and stiffened polyetheretherketone (PEEK) based intermediate modulus (IM7) carbon fiber laminated composite plates is evaluated at various temperatures using displacement- and energy-based approaches. In the displacement-based approach, the logarithmic decrement of the damped vibration is determined to investigate the effect of lamina sequences, stiffener orientation, and stiffener depth at different temperatures. A first-order shear deformation theory considering the viscoelastic property of the composite lamina is implemented to simulate the damped dynamic response of the laminated composite plates in a thermal environment. The best suitable damping model, among Rayleigh damping and modal expansion damping, has been identified to evaluate the damping matrix. Furthermore, the energy-based damping analysis appeared to be a robust approach to evaluate the damping performance as compared to the displacement-based analysis. It is concluded that stiffened plates effectively suppress the dynamic response at elevated temperature, whereas the unstiffened plates show relatively better damping performance at lower temperature.

External pressure buckling of composite sandwich conical shells with variable skin thickness

In this paper, an analytical model is developed to investigate the buckling analysis of the composite sandwich conical shell with variable skin thickness under lateral pressure loading. This problem involves composite shells, which are produced during the filament-winding process, where the skin thickness varies through the length of the shell. An effective smeared method is employed to reduce the reinforced lattice core into a layer. This is done by analyzing forces and moments on a unit cell. Therefore, equivalent stiffness parameters of reinforced lattice core are determined. By superimposing stiffness parameters due to the lattice core with those of the inner and outer skins, the equivalent stiffness of the sandwich panel will be obtained. Governing equations are established based on the first shear deformation theory. The power series method is used to extract the buckling load of the stiffened shell. To verify achieved results, a 3D finite element model is provided. Comparisons showed that the analytical solution is qualified enough to study the buckling behavior of the composite sandwich conical shell. Through this study, the effects of a set of important parameters like stiffener orientation angle, number of stiffeners, semi-vertex angle, and skin lamination are investigated.

Buckling behavior of grid stiffened composite conical shells subjected to the lateral pressure

This paper presents the buckling behavior of the grid stiffened composite conical shell subjected to the lateral pressure. A smeared method is employed to equivalent grid structure into a layer. For this purpose, a typical unit cell is chosen for analyzing forces and moments on it. Therefore equivalent stiffness parameters due to the grid structure are determined. By determining the stiffness parameters of the shell and superimposing with those of the stiffeners, equivalent stiffness of the whole structure is obtained. Governing equations are established based on the Donnell shell theory. The power series method is used to extract the buckling load of the stiffened shell. To validate obtained results, a 3 D finite element model is built using ABAQUS software. The comparison showed that the analytical solution is qualified enough to study the buckling behavior of the grid stiffened composite conical shell. Through this study, the effect of a set of important parameters due to stiffeners like stiffener orientation angle, the number of stiffeners, and due to due to shell like lamination angle and semi-vertex angle are investigated, and finally are presented based on this study results.

Parametric investigation of vibration of stiffened structural steel plates using finite element analysis and grey relational analysis

Thin plates with arbitrary shapes and stiffeners find wide usage in construction, aerospace, marine, etc. industries. In the present work a parametric investigation of thin structural steel plates has been carried out. The design parameters considered were the subtended angle and aspect ratio of plates to account for the different shapes of plates used for various applications. Another design parameter that was considered is the stiffener and its different orientation. The impact of varying parameters on the first five modal frequencies and in turn the stiffness was considered as the response. Finite element method (FEM) coupled with Taguchi’s L16 orthogonal array and grey relational analysis was used to maximize the first five natural frequencies simultaneously. The thin plate was subjected to modal analysis when all its sides are in simply supported boundary condition. The optimum combination of design variables predicted by grey relational analysis is a thin plate with 80° subtended angle, 1.75:1 aspect ratio and crossed stiffener orientation for simultaneous maximization of the frequencies. Analysis of variance revealed highest contribution of stiffener type which affects the first 5 natural frequencies simultaneously.

Buckling Characteristics of Sandwich Conical Shells with Variable Skin Thickness

In this paper, an analytical solution is presented to study the buckling analysis of the composite sandwich conical shells with variable skin thickness and reinforced with lattice cores. This problem involves the filament wound conical shells, where the skin thickness varies through the length of the shell. First, the reinforced core is converted to a layer by analyzing smeared moments and forces on a unit cell. Next, superimposing the stiffness contribution of the stiffeners with those of the inner and outer shells, the equivalent stiffness of the whole structure is achieved. The power series method based on the first-order shear deformation theory (FSDT) is employed to solve the buckling load of the laminated sandwich conical shell. Numerical solution is conducted to verify analytical results by preparing finite element models. Furthermore, using the analytical model, the impact of several design parameters like buckling load, specific buckling load, stiffener orientation, value of stiffeners angle, lamination angle and semi-vertex angle is investigated, and presented based on the results of this study.

Investigation on the free vibration behavior of sandwich conical shells with reinforced cores

The free vibration behavior of sandwich conical shells with reinforced cores is investigated in the present study using experimental, analytical, and numerical methods. A new effective smeared method is employed to superimpose the stiffness contribution of skins with those of the stiffener in order to achieve equivalent stiffness of the whole structure. The stiffeners are also considered as a beam to support shear forces and bending moments in addition to the axial forces. Using Donnell’s shell theory and Galerkin method, the natural frequencies of the sandwich shell are subsequently derived. To validate analytical results, experimental modal analysis (EMA) is further conducted on the conical sandwich shell. For this purpose, a method is designed for manufacturing specimens through the filament winding process. For more validation, a finite element model (FEM) is built. The results revealed that all the validations were in good agreement with each other. Based on these analyses, the influence of the cross-sectional area of the stiffeners, the semi-vertex angle of the cone, stiffener orientation angle, and the number of stiffeners are investigated as well. The results achieved are novel and can be thus employed as a benchmark for further studies.

On the buckling resistance of grid-stiffened composite conical shells under compression

In this paper, an analytical approach has been employed to investigate the global buckling behavior of grid-stiffened composite conical shells with cross stiffeners, on the basis of the first-order shear deformation theory (FSDT). First, the equivalent stiffness parameters of the stiffening structure have been derived through smearing the forces and moments on a typical unit cell taking the shear effects into consideration. Then, superimposing this stiffness contribution with those of the skin, the equivalent stiffness associated with the whole structure is determined. The power series method has been used to solve the equations governing the global buckling of the grid-stiffened composite conical shells. The obtained analytical results have been verified using a 3D finite element model built in ABAQUS software. Furthermore, the influences of some important design parameters such as the stiffener orientation, skin lamination and semi-vertex angles have been investigated on the buckling characteristics of the examined structure. The presented results are novel and can be used for further relevant investigations.

Forced vibration analysis of laminated composite stiffened plates

The extensive parametric study on the forced vibration characteristics of laminated composite stiffened plates using finite element method (FEM) is investigated in this paper. A nine noded isoparametric plate element with five degrees of freedom and a three noded isoparametric beam element with four degrees of freedom as stiffener element are appropriately combined together to obtain stiffened plate element. Newmark's method is applied to obtain the dynamic response of stiffened plates and is investigated for three different types of transient loads: uniformly distributed step load of infinite duration, uniformly distributed step load of finite duration (1 s) and uniformly distributed half sine load of finite duration (1 s). The dynamic response analysis of laminated stiffened plate is conducted with respect to boundary conditions of the plate, number, type and orientation of stiffeners, stiffener depth to plate thickness ratio and types of dynamic loading. Significant effects of the above parameters are observed on the dynamic responses of the laminated stiffened plates. Reduction of displacement response of the laminated composite plate is noticed to a large extent with introduction of stiffeners.

Global buckling analysis of laminated sandwich conical shells with reinforced lattice cores based on the first-order shear deformation theory

In this paper, a new effective smeared stiffener method is presented for investigating the global buckling behavior of the laminated sandwich conical shells with lattice cores. Superimposing the stiffness contributions of the skins with those of the stiffeners, the total stiffness of the whole sandwich structure is obtained. Theoretical formulation is derived based on the first-order shear deformation theory. Using Galerkin method, the buckling load of sandwich conical shell is calculated. A 3-D model of the structure has been numerically analyzed by the finite element method in order to validate the accuracy of the analytical solutions. Finally, the effects of several important design parameters such as stiffener orientation angle, lamination angle, lattice core dimensions, number of the stiffeners, semi-vertex cone angle and skin thickness, have been examined on both buckling and specific buckling loads. The results indicated that at higher semi-vertex angles, an increment in the stiffener paramters such as the number, orientation angle and dimension, although increases the buckling load but decreases specific one. Moreover, the analytical approach led to high-accuracy results for higher skin thicknesses. It was found that variations of the lamination, inner and outer skin thicknesses, significantly affect the buckling load of sandwich conical shells. Results can be considered as a benchmark for the design of these structures which are extensively used in the aerospace structures.

Free vibration characteristics of laminated composite stiffened plates: Experimental and numerical investigation

This investigation deals with the numerical and experimental study on the free vibration of woven glass fibre laminated composite stiffened plates. Thirty-four stiffened plates fabricated from woven glass fibre and binder (epoxy and hardener) by varying the parameters, such as numbers, types and orientation of stiffeners; depth of stiffener to thickness of plate ratio; and aspect ratio and boundary conditions of plates; are tested in FFT analyser to obtain their natural frequencies. A finite element model is used for vibration of laminated composite stiffened plates for validation of the experimental results. The experimental and numerical results are compared, which shows a very good agreement between them. From this study, it is observed that the above-mentioned parameters significantly influence the fundamental frequency. Since, the experimental investigation on laminated composite stiffened plates is scanty; this study can be considered as a reference for the future work.

Force generation and wing deformation characteristics of a flapping-wing micro air vehicle ‘DelFly II’ in hovering flight

The study investigates the aerodynamic performance and the relation between wing deformation and unsteady force generation of a flapping-wing micro air vehicle in hovering flight configuration. Different experiments were performed where fluid forces were acquired with a force sensor, while the three-dimensional wing deformation was measured with a stereo-vision system. In these measurements, time-resolved power consumption and flapping-wing kinematics were also obtained under both in-air and in-vacuum conditions. Comparison of the results for different flapping frequencies reveals different wing kinematics and deformation characteristics. The high flapping frequency case produces higher forces throughout the complete flapping cycle. Moreover, a phase difference occurs in the variation of the forces, such that the low flapping frequency case precedes the high frequency case. A similar phase lag is observed in the temporal evolution of the wing deformation characteristics, suggesting that there is a direct link between the two phenomena. A considerable camber formation occurs during stroke reversals, which is mainly determined by the stiffener orientation. The wing with the thinner surface membrane displays very similar characteristics to the baseline wing, which implies the dominance of the stiffeners in terms of providing rigidity to the wing. Wing span has a significant effect on the aerodynamic efficiency such that increasing the span length by 4 cm results in a 6% enhancement in the cycle-averaged X-force to power consumption ratio compared to the standard DelFly II wings with a span length of 28 cm.

FLEXURAL VIBRATION BAND GAPS IN PERIODIC STIFFENED PLATE STRUCTURES

Based on Mindlin plate theory, Timoshenko beam theory and Bloch’s theorem, an improved finite element model for periodic stiffened plate structures with any number or orientation of stiffeners is developed to describe the propagation of elastic waves in the periodic structures undergoing flexural vibration. Using the finite element model, the flexural vibration band gaps of a periodic grid structure and several periodic stiffened plate structures with different skin thicknesses are compared and analyzed. The results indicate that the vibration coupling between the skin and the stiffeners influences the formation of flexural vibration band gaps. DOI: http://dx.doi.org/10.5755/j01.mech.18.2.1557

Free Vibration Analysis of Laminated Stiffened Shells

The free vibration of the laminated composite anticlastic doubly curved stiffened shells is investigated using the finite element method. The stiffened shell element is obtained by appropriate combination of the nine-node doubly curved isoparametric thin shallow shell element with the three-node curved isoparametric beam element. The shell forms include the hyperbolic paraboloid, hypar, and conoidal shells. The accuracy of the formulation is validated by comparing the authors' results of specific problems with those available in the literature. The additional problems are taken up for parametric studies to include the effects of fiber orientation and lamina stacking sequence of shells and stiffeners. Moreover, the effects of number, types, and orientations of stiffeners, and stiffener depth to shell thickness ratio on the fundamental frequency are also included in the present study. Further, mode shapes corresponding to the fundamental frequency for typical cases are obtained to verify the parametric trend of the results of the fundamental frequency.

Estimation of Layerwise Elastic Parameters of Stiffened Composite Plates

For the first time, an investigation of stiffened and unstiffened multilayered composite plates has been conducted to determine the material property parameters of the plate as well as the stiffener from numerically simulated experimental modal data and finite element predictions, using model updating techniques. The problem is formulated as a global minimization of the error function, defined by the difference in undamped eigenvalues as well as mode shapes, as predicted from the finite element modeling compared to that obtained experimentally. The parameter estimation problem is solved using an iterative gradient-based minimization algorithm, which can start from any randomly selected set of initial parameters. The position, physical properties, and orientation of stiffeners create considerable variations in the modal properties as compared to the bare plates of similar construction. This makes each of the stiffened plate problems rather unique. A few simulated examples are presented, and the methodology is found to be robust, even in the presence of random noise.

ESTIMATION OF IN-PLANE ELASTIC PARAMETERS AND STIFFENER GEOMETRY OF STIFFENED PLATES

An investigation on stiffened plates has been conducted for the first time to determine the elastic parameters as well as the cross-sectional dimensions of rectangular stiffeners from experimental modal data and finite element predictions, using model-updating technique. The problem is formulated as a global minimization of the error function, defined by the difference in modal properties as predicted from the finite element modelling to that obtained “experimentally”. The parameter estimation problem is solved using an iterative-gradient-based minimization algorithm and can start from different randomly selected set of initial parameters. The Levenberg–Marquardt algorithm has been implemented to minimize the error function. Proper bounds are realistically chosen for the selection of the initial values of the parameters. The position, physical properties and orientation of stiffeners create considerable variations in the modal properties as compared with the bare plates of similar construction. This makes each of the stiffened plate identification problem rather unique. The position of stiffeners as well as its orientation makes certain measurement points more suitable for comparing analytical and experimental mode shapes. The optimum measurement set of co-ordinates, which can be used for the purpose of identification, is thus case specific. The geometrical properties of stiffener cross-section also affect the modes. Inclusion of different sets of modes in noisy environment and the differences in the estimated parameters are studied. A few simulated examples are presented to investigate the uniqueness and convergence of results. The methodology is found to be very accurate and robust.

Application of Genetic Algorithms to Stiffness Optimization of Laminated Composite Plates with Stress-Concentrated Open Holes

Recently, laminated composite plates have been applied to many aircraft structures because their mechanical properties are superior to those of conventional materials. Since the laminates have anisotropic elastic properties, an optimum design is needed to make advantageous use of composite laminates. The authors have proposed a successful object-oriented expert system to design laminated composites with actual constraints. A solution to optimize the fiber orientation of stiffeners around open holes, however, has not yet been developed because it is very difficult and requires stress redistribution analysis. In this study, therefore, genetic algorithms (GA) were applied to solve the optimization problem by the object-oriented finite-element stress analysis method. Results obtained were as follows. (1) The GA method is applicable to an open hole model. (2) The random search method is easily applicable to any model.

Application of Generic Algorithms to Stiffness Optimization of Laminated Composite Plates with Stress Concentrated Open Holes.

Recently, laminated composite plates have been applied to many aircraft structures because their mechanical properties are superior to the conventional materials. Since the laminates have anisotropic elastic properties, the optimum design is reqired to make the best use of the composite laminates. The authors have proposed a successful object-oriented expert system to design the laminated composites with actual constraints. A solution to optimize the fiber orientation of stiffeners around the open hole, however, has not been developed because it is very difficult and reqires stress redistribution analysis. In this study, therefore, the genetic algorithms were applied to solve the optimization problem with the object-oriented finite-element stress analysis method. Results obtained were as follows. (1) The GA method is applicable to an open hole model. (2) The random search method is applicable to any model.