Stress Stiffening Effect Research Articles

Optimizing Structural Integrity of Fighter Aircraft Wing Stations: a Finite Element Analysis Approach

Modern fighter aircraft are equipped with multiple stations on the fuselage and under the wings to accommodate various external stores, both jettisonable and non-jettisonable. Each configuration undergoes airworthiness certification, including structural analysis of individual stations within the carriage flight envelope. This study focuses on the structural analysis of a fighter aircraft wing station within this specified envelope. To perform this analysis, the wing station is extracted from the comprehensive global wing model, creating a sub-model with equivalent stiffness properties. Utilizing ANSYS Workbench®, Finite Element Analysis (FEA) is conducted for critical load cases to determine the Factor of Safety (FoS). The initial analysis reveals that the wing station has an FoS of 1.2 under the maximum design load. Prestressed modal and buckling analyses indicate a 10% increase in stiffness due to stress-stiffening effects. To further enhance load-carrying capacity, parametric design changes are introduced. Increasing the bolt diameter from 8 mm to 10 mm raises the FoS to 1.33, resulting in an 8% increase in the maximum load-carrying capacity of the wing station. This comprehensive approach, employing FEA, ensures the wing’s structural integrity under static load conditions within the carriage envelope. The study's findings support the wing station's enhanced performance and contribute to safer and more efficient aircraft operations.

Stress stiffening effects in flexible Earth observation satellites with spinning appendage

Modern satellites often adopt innovative configurations to meet the escalating requirements of space operations. This study specifically focuses on one such configuration, exemplified by an Earth observation spacecraft equipped with a large rotating payload connected to the main bus through a flexible boom. The rotational motion of the payload is designed to extend the scanned area, resulting in a substantial reduction in the time required to complete a set of measurements, thus enhancing the overall performance. However, this configuration introduces greater complexity both in the analysis of the dynamical behavior and in the design of the control architecture. When dealing with flexible structures subject to rotational motion, as in this scenario, the stiffening effect resulting from inertial loads—particularly the centrifugal action—becomes crucial. In this study, we derive the dynamic equations of the multibody flexible spacecraft using Kane's formulation, which provides a streamlined set of ordinary differential equations by simplifying their derivation. Treating the link as an elastic beam, flexibility is incorporated through a modal decomposition approach that considers nonlinear elastic dynamics, ensuring the inclusion of stress stiffening in the dynamical model. Stress stiffening emerges as a fundamental effect in spinning space structures, where the contribution of the centrifugal force is significant. Incorrect predictions and structural instability for high spinning rates are observed when this effect is neglected. Furthermore, the error associated with overlooking this physical phenomenon is found to be dependent on the spinning rate. We identify kinematical conditions that render this effect negligible in relation to the fundamental deformation frequencies of the space system. Several numerical results are presented and discussed.

Effect of GGBFS and fly ash proportions on fresh, tensile and cracking features of alkali activated concrete with low NaOH concentrations

This study mainly investigated the tensile and cracking features of ash alkali activated concrete with different slag-fly ash proportions and low NaOH concentrations cured at ambient temperature. High-molarity NaOH leads to risk and is costly, whereas, in field conditions, heat curing is difficult. Therefore, in this study three mixes (mix-A, B and C) were developed using 0/100, 20/80, 40/60, 60/40, 80/20, and 100/0 slag-fly ash proportions in this study. Sodium hydroxide (SH) and sodium silicate (SS) were used as activators and concentrations of sodium hydroxide were used as 1M, 2M and 4M in mixes A, B and C respectively, but alkaline ratio (SS/SH) was fixed as 1.5 in all the mixes. Slump, and strength aspects (compressive, split tensile, and flexural) were evaluated. The tensile (tensile strength, tension stiffening) and cracking characteristics (crack spacing, crack width) were evaluated under uniaxial tensile loading on reinforced prismatic members. From test outcomes, workability in terms of slump of the composites decreased with increased percentage of slag or granulated blast furnace slag (GGBFS) in the total binder, but the tensile (tensile stress and tension stiffening effect) and compressive strengths increased with increasing percentage of GGBFS. Better cracking properties (i.e., minimum crack widths and reduced crack spacings) were observed when the mixes contained higher percentages of GGBFS. The obtained crack spacings were correlated with CEB-FIP model code, and existing research studies. The crack spacings obtained in this study are consistent with CEB-FIP model code. Finally, this study demonstrated that when slag-fly ash alkali activated concretes were prepared with solutions containing low NaOH concentrations and cured at room temperature (ambient), there was an increase in the strength and cracking properties with higher percentages GGBFS.

Delamination Behavior of CFRP Laminated Plates under the Combination of Tensile Preloading and Impact Loading.

When subjected to impact loading, aircraft composite structures are usually in a specific preloading condition (such as tension and compression). In this study, ballistic tests were conducted using a high-speed gas gun system to investigate the effect of biaxial in-plane tensile preload on the delamination of CFRP laminates during high-speed impact. These tests covered central and near-edge locations for both unloaded and preloaded targets, with the test speeds including 50 m/s, 70 m/s, and 90 m/s. The delamination areas, when impacting the center location under 1000 με, show a 14.2~36.7% decrease. However, the cases when impacting the near-edge location show no more than a 19.3% decrease, and even more delamination areas were observed. In addition, in order to enhance the understanding of experimental phenomena, numerical simulations were conducted using the ABAQUS/Explicit solver, combined with the user subroutine VUMAT with modified Hou criteria. The experimental and simulation results were in good agreement, and the maximum error was approximately 12.9%. The results showed that not only the preloading value but also the impact velocity have significant influences on the delamination behavior of preloaded CFRP laminated plates. Combining detailed discussions, the biaxial tensile preload enhanced the resistance to out-of-plane displacement and caused laminate interface stiffness degradation. By analyzing the influence of the preloading value and impact velocity on competing mechanisms between the stress-stiffening effect and interface stiffness degradation effect, the complex delamination behaviors of laminates under various preloading degrees and impact velocities at different impact locations were reasonably explained.

Centrifugal forces enable band gaps that self-adapt to synchronous vibrations in rotating elastic metamaterial

The rotation of mechanical systems can greatly change their modal and wave propagation response. In the classic example of the Foucault pendulum, the Coriolis force from the Earth’s rotation causes the pendulum path to appear deflected to an observer on Earth. More recently, Coriolis forces and gyroscopic effects from rotation have been shown to break time-reversal symmetry, induce non-reciprocity, and change the band structure of phononic crystals. However, rotation also introduces centrifugal forces that can considerably affect the vibration response through stress stiffening and spin softening effects. Although this is well studied in the field of rotor dynamics, the effects of centrifugal forces on the dynamic behavior of acoustic metamaterials (AMs) are still unexplored. In this paper, we study the dependence of torsional band gaps on rotational speed in a rotating shaft with attached local resonances. Different from previous studies, we explicitly consider the effects of stress stiffening in local resonances by introducing a stress stiffening function in a reduced order model of the rotating AM. We then calculate the stress stiffening function for beam-tip-mass resonators and show that these resonators have a resonant frequency that scales linearly with the rotational speed in the asymptotic limit, which in turn causes the band gaps of the AM to depend linearly on the rotational speed. Motivated by the presence of synchronous vibrations in rotating machinery, in which frequency is also linearly dependent on rotational speed, we show that this rotating AM supports band gaps that self-adjust to the synchronous vibration frequency, resulting in attenuation over a wide range of frequencies and thus rotational speeds. Finally, we validate the reduced order model of the rotating AM using 3D finite element analysis. This work contributes a foundational understanding of the effects of rotation in AMs and builds a connection between the AM and rotor dynamics communities, with the potential to introduce novel vibration control in rotor dynamics problems.

Compliant assembly variation analysis of composite structures using the Monte Carlo method with consideration of stress-stiffening effects

Compliant assembly variation analysis of composite structures using the Monte Carlo method with consideration of stress-stiffening effects

Large-amplitude vibration of rotating functionally graded blades including geometrical nonlinearity and stress stiffening effects

The nonlinear frequency responses of functionally graded (ceramic/metal/ceramic) straight/curved blade-type structures are examined under rotation and thermal environment. Here, the geometrical nonlinearity is introduced using Green-Lagrange’s strain via the higher-order shear deformation theory. The constituent materials, i.e. ceramic and metal-alloy, are considered to be temperature-dependent, whereas, the overall blade material properties are evaluated using Voigt’s homogenization scheme via a modified power-law function. The equations of motion are obtained using Hamilton’s principle by including the geometrical nonlinearity and stress stiffening effects. The linear and the nonlinear frequency responses are computed through the developed nonlinear finite element method and Picard’s successive iteration scheme. An exhaustive computation is carried out to report the linear and the nonlinear vibrational behavior of the proposed composite straight/curved blade model at small-to-large amplitudes for various sets of combinations of geometric and material parameters, such as blade span, blade thickness, volume fractions, rotational speed, and temperature.

Size-Dependent Rigid–Flexible Coupling Dynamics of Functionally Graded Rotating Moderately Thick Microplates

Micro air vehicles, which are typical small-sized rotating-motion systems, have seen major advancements in recent years. To provide some theoretical basis for developing and producing micro air vehicles, this study establishes a novel rigid–flexible coupling dynamic model for functionally graded (FG) moderately thick rectangular microplates attached to a central rotating rigid hub based on the modified couple stress theory and first-order shear deformation theory. The proposed model incorporates nonlinear coupling term of in-plane deformation to reflect the dynamic stiffening effect caused by rotational motion. Material characteristics of the FG microplate have a linear power-law distribution along the thickness axis. Further, the discrete form dimensionless coupling dynamic equations and their numerical solutions are obtained by combining the Euler–Lagrange equation and the Chebyshev–Ritz method. Convergence and comparative studies are carried out to demonstrate the accuracy and validity of the proposed model. Thereafter, the influence of material length scale parameter, rotational speed, gradient index, and aspect ratio on the frequency of the microplates is investigated. Numerical results reveal that couple stress and dynamic stiffening effects both enhance the rigidity of the microplates, whereas the gradient index decreases the rigidity. Nonlinear coupling term which leads to significant differences in frequency value and trace line can’t be ignored for rotative structure. In-plane motion and its coupling terms play a significant function for the moderately thick or thick microplates. The increase of rotational speed and gradient index will reduce the size dependency of the microplate. Furthermore, the frequency trajectory steering and corresponding mode transition phenomenon are graphically represented.

Research on 3D Modeling and Dynamic characteristics of wind turbine blade

In order to prevent blade resonance, reduce blade deflection, improve wind turbine power generation efficiency and wind energy utilization rate, the blade model of 3 kW wind turbine is established, and the natural frequency of wind turbine blade is analyzed. Based on the vibration theory, the effects of dynamic stiffening and rotational softening on the natural frequencies of blades are analyzed. Study the change rule of blade vibration mode under rotating speed of 0~300rpm, and analyze the influence of two effects on blade frequency. The results show that at low speed, the rotating softening effect of the blade is obvious, and the vibration frequency decreases; At high speed, the stress stiffening effect is more obvious, the vibration frequency increases, and the coupling vibration has greater destructiveness.

Self-adapting band gaps in rotating elastic metamaterials

Rotation in mechanical systems can drastically change their vibrational response. For example, it can enable new properties, such as break time-reversal symmetry and induce non-reciprocity in acoustic metamaterials, due to Coriolis forces and gyroscopic effects. Rotation can also be highly detrimental: for example, synchronous vibrations occur in rotating mechanical components and can be extremely damaging when they coincide with system resonances. In addition, centrifugal forces from rotation significantly affect the dynamics of rotating systems, through stress stiffening and spin softening, however their effects on acoustic and elastic metamaterials have rarely been explored. Here, we demonstrate that centrifugal forces in rotating elastic metamaterials enable band gaps that “self-adapt” to synchronous vibrations, attenuating these vibrations over a broadband frequency range. Specifically, this talk presents a reduced order model that captures stress stiffening effects on the band gaps of a rotating elastic metamaterial. The resonators are beams with tip masses oriented perpendicular to the rotational axis, such that stress stiffening causes their resonant frequency to be linearly proportional to the rotational speed. The reduced order models are validated by full finite element simulations of a 3D elastic metamaterial whose band gap self-adapts to synchronous vibrations that are linearly proportional to rotational speed.

Similarity design method for dynamic characteristics of rotating composite blades in thermal environment

A similarity method for rotating composite blades in thermal environment is developed for the problems of difficulty, time consumption, high cost, and risk in the dynamic test under a high-temperature environment. Within this study, a set of scaling laws are derived for thin-walled composite plates based on their dynamic models and the applicability of the scaling laws is demonstrated in the similitude design of composite blades. The present dynamic model takes into account thermal stress and centrifugal stiffening effect. Analytical calculations show that the scaled models at relatively low temperatures can well reproduce the dynamic characteristics of their corresponding prototypes at high temperatures when taking into account the scaling of temperature change and rotational speed.

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

While flexure time bases have gained significant traction in the watchmaking industry thanks to their high quality factor and monolithic design, maintaining a stable frequency in varying orientations of wrist watches with respect to gravity remains a significant challenge. This results from the fact that the flexures play two roles simultaneously: guiding the oscillating mass along a one-degree-of-freedom pivotal motion, and providing the oscillator’s elastic restoring force. Indeed, varying stress-stiffening effects induced by the varying direction of the weight of the oscillating mass affect the pivot angular stiffness, which impacts its oscillating frequency. In order to address this issue, two design approaches are presented which, when combined, allow to reach the strict chronometric standards of mechanical watches. Firstly, the frequency differences for all vertical positions (i.e., gravity orthogonal to the rotation axis) are mitigated by designing architectures with reduced parasitic center shift, or by offsetting the center of mass (COM) along their axis of symmetry, or both. Secondly, the frequency differences between vertical and horizontal positions (i.e., gravity parallel to the rotation axis) are reduced by offsetting the COM along the rotation axis. The implementation and effectiveness of these approaches are demonstrated by numeric simulations, as well as by experimental measurements performed on watch-scale silicon etched prototypes.

Thermally-induced transitions of multi-frequency defect wave localization and energy harvesting of phononic crystal plate

Defect mode of phononic crystals has presented superiority in vibration energy harvesting with its ability in wave localization. For defect-based harvesters, harvesting performance is directly determined by the wave manipulation behavior of the defect structure which is affected by design parameters and thermal environment. In this paper, multi-frequency wave localization and harvesting characters are studied for heated binary phononic crystal plates with a single defect. Considering the stress stiffening effect of thermal load, variations in the multiple defect modes are investigated for varying defect dimensions at different heating levels. From the perspective of stiffness and mass matrices of the PC plate, the transition of defect modes is explained with considering the driving effects of both changes in the defect configuration and structural temperature. Thermally-induced local non-periodic perturbation of stiffness is the essential factor that prompts the transition of defect wave manipulation behavior. Discrepancy in sensitivity to the perturbation results in different thermal responses of defect modes. It leads to the variation in multi-frequency wave localization of the defect PC plate. Accordingly, thermal load shifts the harvesting band of the defect-based harvester toward the lower frequency range, and may convert the discrete harvesting points into a continuous band. Temperature could be a potential means to tune the multi-frequency wave localization behavior and the defect-based harvesting performance.

Vibration Response of Steam Turbine Healthy and Cracked Blade under the Stress Stiffening and Spin Softening Effects

In the present paper, vibration responses of the healthy and cracked blade under the influence of stress-stiffening and spin-softening have been studied. The three-dimensional finite element-based numerical analysis is carried out to study the blade's mode shape and natural frequencies and are validated with the experimental modal analysis test results. In the case of spin softening, for healthy blade at the turbine’s speed over 1000 RPM, natural frequencies increase significantly in both first flap-wise and chordwise bending modes. In both cases of STF and SOF, for the cracked blade, the deviation from the healthy blade in the natural frequency increases with increasing crack size, maximal in a crack size of 90%. It is also observed that irrespective of crack size, deviation in natural frequencies as compared to healthy blade increases as spin speed increases in the cases of chordwise bending mode (Mode II) and higher-order overlapped mode IV, and in the case of fundamental torsion mode (Mode III), higher-order overlapped mode V and VI natural frequencies decrease in both STF and SOF cases.

Static and dynamic NURBS-based isogeometric analysis of composite plates under hygrothermal environment

In this paper, a computationally efficient isogeometric plate model, employing nonpolynomial shear deformation theory (NPSDT), for static and dynamic analysis of laminated and sandwich composite plates under hygrothermal environment is presented. Transient and steady-state response using Rayleigh damping model and fast Fourier transformation of transient response have also been obtained for the hygrothermal environment. The non-uniform rational B-splines (NURBS) based formulation has been considered, which attribute only five-degree of freedom and satisfies the stringent continuity requirement of the NPSDT model (C1-continuity) without any additional variables. A total Lagrangian approach in conjunction with Hamilton’s principle is utilized to formulate the governing equations for thermal bending and subsequent dynamic analysis of multilayered composite plates. To model stress stiffening effect due to hygrothermal load, both von Kármán and Green–Lagrange strain displacement relations are incorporated and obtained solutions are compared. It has been shown that at higher temperature (around one fourth of the critical buckling temperature), the consideration of Green–Lagrange strain relationship for modeling stiffening effect due to hygrothermal load is important for better accuracy. Further, it has been shown that bending strip is essential in case of higher-order shear deformation theory (HSDT) to get more accurate solution. In addition, the obtained transient damped/undamped solutions may be used to get the natural frequency from their FFT solution.

An Analytical Model of a Rotating Radial Cantilever Beam Considering the Coupling Between Bending, Stretching, and Torsion

Abstract In this paper, the mode coupling between bending, stretching, and torsional deformations is mainly studied by presenting an analytical model of a rotating cantilever beam with pre-twist angle and arbitrary cross section. Equations of motion of the beam are derived using Hamilton's principle. The Coriolis effect due to the coupling of the bending deformation and stretching deformation, the eccentricity caused by inconsistency between elastic center and centroid, spin softening effect, stress stiffening effect, shear deformation, and rotary inertia are included in the model. Equations of motion are solved by the Rayleigh-Ritz method. The natural frequencies obtained by the proposed analytical modal are in good agreement with those obtained by finite element method (FEM) which proved the accuracy of the analytical model. Finally, the coupling between different mode components is studied in detail based on a quantitative method. The transformation/conversion between different mode components is revealed, the influence of rotational speed, setting angle, and pre-twist angle on this conversion mode is studied. Results show that a specific mode shape is usually composed of multiple mode components. The essence of mode coupling is the coupling between different mode components. The influence of rotational speed, setting angle, and pre-twist angle on the mode coupling is that they cause the transformation/conversion between different mode components.

Interference fit estimation through stress-stiffening effect on dynamics

This paper proposes a method to estimate applied fitting force and interference between two press-fitted components by exploiting the stress stiffening effect on the dynamics of components before and after press-fit.Differently from specific solutions in literature, the proposed approach is independent of component dimensional characteristics, geometrical complexity and uncertainties, and is based on experimental data only. Moreover, it is non-destructive and easily embeddable in an industrial quality control workflow.The core of the activity is the development of a ranking strategy of the natural frequencies most affected by stress stiffening effect based on modal assurance criterion.To prove the effectiveness of the selection approach, interference polynomial chaos expansion meta-models based on best ranked natural frequencies are developed and compared to established analytical models and finite element solutions. Also, the reliability of the methodology is tested against an industrial case study i.e. press-fitted automotive steel wheel samples.

Numerical Modeling of Initial Stress Stiffening Effect on the Dynamic Behavior of Axisymmetric Shells

AbstractThis paper presents a numerical model to simulate the initial stress stiffening effect, induced by radial pressure and/or axial load on the dynamic behavior of axisymmetric shells. This effect is particularly important for thin shells since their bending stiffness is very small compared to membrane stiffness. The theoretical formulation is based on a combination of the finite element method and classical shell theory. For a perfect geometrical consistency, two semi-analytical finite elements, conical and cylindrical, are used to model axisymmetric shells. The displacement functions are derived from exact solutions of Sanders' shell equilibrium equations. The results obtained using this approach are remarkably accurate. The potential energy is calculated to estimate the initial stiffening effect using direct membrane forces per unit width and rotations about the orthogonal axes. The final stiffness matrix of each finite element is composed of the regular stiffness matrix and the added stiffness matrix generated by membrane loads. The frequencies of vibration are compared with those obtained in other experimental and theoretical research works and very good agreement is observed.

Finite element model updating of composite with adhesive jointed structure under built-up internal stress

Highly complex engineering structures such as the body-in-white of a car consist of hundreds of different parts that are assembled using various types of joints such as welded and adhesive joints. The finite element method has been used extensively in various engineering fields to predict and analyze the dynamic behavior of assembled structures. However, despite the use of well-characterized individual subcomponent models, the predicted results frequently differ from measured results. This is believed to be because of the invalid assumptions of the joint model such as the material properties and other uncertainties associated with the assembly. This study investigated the use of a model updating method (MSC Nastran SOL 200) to identify the invalid assumptions and uncertainties in adhesive jointed composite structures and to minimize the difference between predicted and measured results. Results revealed that the stresses built-up in a structure during the assembly process are permanently retained in the structure after the adhesive is completely cured and that they cause a local stress stiffening effect, which is believed to affect the resonance frequencies of the structure. Introducing the effect of the stresses as an updating parameter in the model updating process increases the prediction accuracy.

Stochastic eigenfrequency and buckling analyses of plates subjected to random temperature distributions

Many studies previously reported in the literature have demonstrated, both theoretically and experimentally, the influence of thermally-induced stresses on the static and dynamic behavior of structures, due to the so-called stress-stiffening effect. In most cases of practical interest, temperature variations associated to environmental and operational conditions are governed by rather complex combinations of conduction, convection and radiation mechanisms. As a result, the temperature values at different points of a structure are very difficult to control and can rationally be considered as random quantities. In this context, the present paper addresses the stochastic modeling and characterization of the influence of thermal stresses on the natural frequencies of thin rectangular plates, assuming space-dependent temperature fluctuations modeled as stationary two-dimensional Gaussian random fields. For this purpose, based on the hypotheses of the classical Kirchhoff plate theory, a Rayleigh-Ritz-based dynamic model is first derived for the bending vibrations of plates, accounting for the presence of thermal stresses. This model is combined with the Karhunen-Loève expansion (KL), which is used to discretize the temperature random field, after which the statistics of the random natural frequencies are estimated by Monte Carlo sampling. Numerical simulations are performed for plates under free boundary conditions. Simulation results, which encompass sampling-based statistics for the thermal stresses and the first six natural frequencies of the plate, are presented and discussed. In addition, since thermal stresses can induce buckling, reliability has also been estimated considering this type of failure. Results enable to conclude that space-dependent temperature uncertainty can be significant upon the vibration and buckling behavior of plates, which justifies its consideration.