Concept Of Stiffness Research Articles

Multivariable optimization design method of composite stiffener based on critical stiffness

Based on the optimization design of ship structure, in view of the current situation that the structural safety margin is too high and the stiffener of stiffened plate is over matched, the concept of the critical stiffness of the stiffener matching was proposed, and the relationship between the stiffness ratio of plate and stiffener was derived. The optimization model of T-type composite stiffener was established. Based on Isight software platform, sensitivity analysis of design variables was carried out to simplify design variables. The Multi-Island genetic algorithm was used to carry out the multivariable optimization design of stiffener. Then, combined with the engineering practice, the design scheme was determined on the basis of the stiffener optimization results. The feasibility of the multivariable optimization design method was verified by the experimental study on the mechanical properties of composite stiffened plates. Research shows that the stiffness ratio formula of the stiffened plate can be used to guide the design of stiffener stiffness matching. In the optimization design of T-type composite reinforcement, the effect of web height on the optimization target is the most obvious. Under the condition of equal stiffness constraint, the optimal design scheme of T-type stiffener can achieve the optimization goal and ensure the better economy.

A Novel Pressure-Controlled Revolute Joint with Variable Stiffness.

The compliance and deformability of soft robotics allow human-machine interactions in a safe manner without the need of sophisticated control systems inherent in rigid-body robotic devices. However, these advantages introduce controllability and predictability challenges. In this study, we propose a novel fluidic-driven variable stiffness revolute joint (VSRJ) based on hybrid soft-rigid approach to achieve adjustable compliance while addressing the abovementioned challenges. The VSRJ is composed of a silicone rubber cylinder as a pressure chamber and two identical rigid links. The soft cylinder is positioned in a fully closed compartment created by the assembly of the two rigid links, thus constraining its expansion when pressure is applied. By applying pressure, the stiffness of the joint increases accordingly for the following reasons: (1) increasing the friction force between the cylinder and the compartment walls and (2) creating a locking mechanism through the expansion of the cylinder into space between rigid links in a "bump" formation. Experimental results show that the VSRJ can achieve up to 8-fold rotational stiffness enhancement from 0 to 5 bar input pressure within -30° to +30° rotation angle. The modular design of the rigid link allows the assembly of multiple VSRJs to build a variable stiffness structure in which each VSRJ has an independent stiffness and relative position. The VSRJ was characterized in terms of repeatability, torque, and stiffness. The experimental results were validated by finite element analysis. This approach can provide opportunities for the use of this new variable stiffness concept as an efficient alternative to traditional variable-stiffness linkages.

Use of electromechanical analogies in the construction and calculation of a simulation model of the process of torsional oscillations of the shaft line of an internal combustion engine

The purpose of the article is to substantiate the possibility of using electromechanical analogies in the construction and calculation of parameters of the simulation model of the process of torsional oscillations of the internal combustion engine shaft, which will allow to move from mechanical models of shafts to their electrical counterparts. Results of the research. The article clarifies the relationship between phenomena occurring in mechanical and electrical systems, mechanical and electrical analogues are established, namely force is considered as electromotive force or voltage, velocity as current, moment of inertia as inductance, spring flexibility as capacitance, coefficient friction as electrical resistance, and the kinematic scheme of the shaft line is presented in the form of a diagram of a reactive bipolar, the parameters of which are determined during analytical calculations of the kinematic scheme of the elastic system. The concept of dynamic stiffness is introduced, which is similar to the concept of reactive resistance of a bipolar. The initial data for the calculation of a linear system in which it is assumed that the pliability of the shock absorber is zero. Conclusions. According to the results of the analogies, the parameters of the simulation model were obtained. The calculation of the elastic system using the method of electromechanical analogies allowed to build a simulation model of the shaft line of an internal combustion engine.

Eigenfrequencies of prestressed variable stiffness composite shells

The introduction of the variable stiffness concept has broadened the design space for high-performance lightweight composite structures. In particular, when considering prestressed dynamically excited aerospace components, a wider design space allows designers to find more effective solutions with higher overall stiffness and fundamental frequency. In this context, an efficient and versatile Ritz method for the eigenfrequency analysis of prestressed variable stiffness laminated doubly-curved shells is presented. First-order shear deformation theory is considered without further assumptions on the shallowness or on the thinness of the structure. A rational Bézier surface representation is adopted for the description of the shell, allowing general orthogonal surfaces to be represented. The proposed approach is validated by comparison with published benchmark results and finite element solutions, showing great accuracy with 65% to an order of magnitude fewer variables. Due to the reliability and efficiency of the Ritz method for eigenfrequency analysis, original parametric studies are carried out, showing the flexibility given by the variable stiffness concept for finding trade-off solutions for prestressed shell components.

Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach

Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a set of regular terms, built using orthogonal polynomials, augmented with special functions able to describe the crack opening and the singular behaviour at the crack tips; boundary functions are used to ensure the required homogeneous essential boundary conditions. Governing equations are inferred via the stationarity of the energy functional an solved to carry out an extensive study on the buckling behaviour of variable angle tow homogeneous and layered composite plates. The results obtained for homogeneous plates evidence that the crack presence strongly influences the buckling behaviour depending on its length and inclination and plate boundary conditions with a meaningful variability with respect to the fibre paths configuration, which can arrange for better performances with respect to the straight fibre case. Also for cracked laminates the results show that there are several fibre path able to provide higher buckling loads and higher overall axial stiffness with respect to the straight fibre case. In the framework of damage tolerant engineering applications, this allows to select fibre paths that guarantee predefined design levels of buckling load and axial stiffness even in presence of cracks. Finally, this study highlights the potential of the proposed approach for the analysis of the buckling behaviour of cracked composite variable stiffness plates, which provides an efficient analysis tool for the damage tolerant design and optimization of advanced variable stiffness structures.

Theory of dipole insulators

Insulating systems are characterized by their insensitivity to twisted boundary conditions as quantified by the charge stiffness and charge localization length. The latter quantity was shown to be related to the expectation value of the many-body position operator and serves as a universal criterion to distinguish between metals and insulators. In this work we extend these concepts to a new class of quantum systems having conserved charge and dipole moments. We refine the concept of a charge insulator by introducing notions of multipolar insulators, e.g., a charge insulator could be a dipole insulator or dipole metal. We develop a universal criterion to distinguish between these phases by extending the concept of charge stiffness and localization to analogous versions for multipole moments but with our focus on dipoles. We are able to relate the dipole localization scale to the expectation value of a recently introduced many-body quadrupole operator. This refined structure allows for the identification of phase transitions where charge remains localized but, e.g., dipoles delocalize. We illustrate the proposed criterion using several exactly solvable models that exemplify these concepts and discuss a possible realization in cold-atom systems.

Improvement of structural characteristics of composite thin-walled beams using variable stiffness concept via curvilinear fiber placement

This study presents the use of variable stiffness concept via curvilinear fiber placement to achieve improved structural characteristics in composite thin-walled beams (TWBs). The TWB used in the study is constructed in circumferentially asymmetric stiffness (CAS) configuration. The variation of fiber angles along the span and the width of the TWB is included by defining two fiber path functions. A parametric study is performed to investigate the effects of different fiber paths on the structural performance metrics including frequency spacing, unit twist, and critical buckling load. For this purpose, a semi-analytical solution method is developed to conduct free vibration, deformation, and buckling analyses of the TWB with curvilinear fibers. The semi-analytical method is validated with several finite element (FE) analyses performed using ABAQUS. Elastic stress analyses of TWBs with selected fiber paths subjected to simplified distributed loading are also conducted using the FE method, and a ply failure criterion is applied to evaluate the strength of these TWBs. Overall results show that curvilinear fiber placement varied along the span leads to greater structural performance for a composite TWB than the straight fiber configuration.

Modified Stiffness-Based Soft Optical Waveguide Integrated Pneumatic Artificial Muscle (PAM) Actuators for Contraction and Force Sensing

This article presents design, fabrication, characterization, and experimental verification of a new sensing method (soft optical sensing) for pneumatic artificial muscle (PAM) actuators. Soft optical waveguides are designed and fabricated using the proposed modified stiffness concept for soft sensors. The design of the sensor allows us to measure both contraction and force of a PAM actuator under loaded conditions. This proposed method makes it possible to have a highly sensitive actuator system with linear contraction sensing. The sensorized PAMs are supposed to work in high-pressure applications with the ability to be used repeatedly without significant degradation in signal quality. To characterize and validate the proposed method, two PAM actuators make use of two separately designed test systems to plot and model the characteristic curves. Finally, the validation for control is provided using measured sensor data as feedback to the controller.

Determination of Effective Elastic Properties of a Composite Material in Simple Stress States, Based on the Concept of Stiffness

Determination of Effective Elastic Properties of a Composite Material in Simple Stress States, Based on the Concept of Stiffness

Research on lateral vibration coupling mechanism of high-speed train based on singular coefficients

The lateral vibration coupling mechanism is the basic law of the current vibration behavior of high-speed train. The main reason is that there are design defects in the prototype of ICE3 bogie. Therefore, the passenger dedicated line is not a necessary and sufficient technical condition for ensuring the stability and safety of high-speed railway operation. Based on the previous research, this article further develops the theoretical demonstration and experimental verification of the lateral vibration coupling mechanism of high-speed train. According to the concept of system stiffness and the statistical characteristics of Gaussian process, a new concept of singular coefficient is proposed to describe non-stationary and non-Gaussian processes. Combined with the quality vibration tracking test of a high-altitude vehicle, the conclusions are in good agreement through the experimental testing and the dynamic simulation. The application of the singular coefficient further gives three conditions for determining the lateral vibration coupling mechanism of high-speed train, namely sufficient excitation energy, vibration transmission medium and coupling resonance possibility. Aiming at the influence of high-order modal interception and residual force of flexible body, the new concept of singular coefficient is applied. The rigid-flexible coupling simulation reflects the main statistical characteristics of non-stationary and non-Gaussian processes, and reveals the current lateral vibration coupling mechanism of high-speed train.

A preliminary analysis on mechanical characteristics of transmission conductors in the vicinity of suspension clamps

Overhead transmission conductors are prone to wire strands breaking under the conditions of breeze vibration, and many broken strands occur in the vicinity of suspension clamps. In order to research the stress distribution characteristics of the conductor in the vicinity of suspension clamps, a relatively effective Finite Element (FE) model was proposed. Preliminary verification of model rationality through comparative analysis of theoretical calculation and simulation, and use this model to study the mechanical characteristics of the cross-section of the conductor in the key position of the conductor-clamp system. The research conclusions are as follows: a new concept of equivalent bending stiffness and equivalent diameter is proposed, which is used to calculate the alternating bending stress of conductors under breeze vibration conditions. The alternating bending stress of the wire strands follow the bending amplitude (Y b) increases with increasing. Under the complex load, the Equivalent (Von-Mises) stress of the aluminum wire strands at the Last Point of Contact (LPC) of the conductor and the clamp shows a decreasing trend from the outside to the inside, and the maximum Von-Mises stress occurs at the contact position between the outermost wire strands and the clamp.

An Investigation of Effects and Safety of Pipelines due to Twin Tunneling

To efficiently and accurately predict the effects of twin tunneling on adjacent buried pipelines, the effects of upward and downward relative pipeline‐soil interactions were considered. A series of numerical parametric studies encompassing 8640 conditions were performed to investigate the responses of a pipeline to twin tunneling. Based on the dimensionless analysis and normalized calculation results, the concept of equivalent relative pipeline‐soil stiffness was proposed. Additionally, expressions for the relative pipeline‐soil stiffness and relative pipeline curvature and for the relative pipeline‐soil stiffness and relative pipeline settlement were established, along with the related calculation plots. Relying on a comparison of prediction results, centrifuge model test results, and field measured results, the accuracy and reliability of the obtained expressions for predicting the bending strain and settlement of adjacent buried pipelines caused by twin tunneling were validated. Based on the calculation method, the maximum bending strain and maximum settlement of pipelines can be calculated precisely when the pipeline parameters, burial depth, soil parameters, and curve parameters of ground settlement due to tunneling are provided. The proposed expressions can be used not only to predict the maximum bending strain and maximum settlement of pipelines caused by single and twin tunneling but also to evaluate the effects of single and twin tunneling on the safety of existing buried pipelines. The relevant conclusions of this article can also provide a theoretical basis for the normal service of buried pipelines adjacent to subway tunnels.

Fundamental Frequency Optimization of Doubly Curved Aerospace Structural Panels via Variable Stiffness Concept

In the present study, the fundamental natural frequencies of curvilinear fiber composite doubly curved panel are optimized. Doubly curved panels are used in various components of the structural frames of the aerospace vehicles. The variable stiffness behavior is obtained by altering the fiber angles continuously according to curvilinear fiber path function in the composite laminates. Structural model is utilized based on the virtual work principle. The aim is to achieve the best fiber paths with maximized fundamental frequencies or in-plane strengths for a composite panels. An eight-layer composite doubly curved panel with two types of boundary conditions are considered as a case study in this research. The boundary conditions include; CCCC, FCFC where C stands for clamped, and F for free edges. Von-Karman kinematic strain relations are used and the first order shear deformation theory (FSDT) is employed to generalize the formulation for the moderately thick doubly curved panel including transverse shear effects. Generalized Differential Quadrature (GDQ) method of solution is employed to solve the governing equations of motion. Numerical results demonstrate the effectiveness fiber angle path and boundary conditions on the natural frequencies of the composite panel. The optimal fiber angle paths of each layer are presented for the above cases in free vibration analysis.

Experimental and numerical evaluation of the damping properties of a foil bearing structure taking into account the static and kinetic dry friction

Over the past decades, experimental and theoretical studies on gas foil bearings have been conducted extensively. The essence of the operation of these bearings lies in the use of a unique underlying support mechanism, whose properties adapt to current operating conditions. The static and dynamic characteristics of the foil bearing structure depend not only on the geometry of the supporting structure but also on foil material, surface topology, the velocity of contact surfaces, load, etc. While the concept of stiffness is more intuitive and well described in the literature, the evaluation of the damping in foil bearings is not as obvious. The goal of this paper is to improve the understanding of the damping mechanism of the bump-type foil bearing structure under dynamic loads. At the beginning of the paper, the experimental studies of the foil bearing structure in a wide frequency range are discussed. Then, the experimental conditions were reproduced using an advanced numerical model that took into account the geometry of the top and bump foil, contact phenomena and dry friction. A new solution, unprecedented in the existing literature, is the inclusion of static and kinetic friction in the numerical model of the foil bearing structure. The developed numerical model made it possible to determine the system characteristics, including the evaluation of stiffness and damping. An important contribution of this work is the comparison of the results of calculations obtained with the use of an advanced numerical model with the results of experimental research. The paper gives clear guidelines for the experimental and numerical determination of dynamic characteristics for the bump-type foil bearing structure. The presented results of the experimental research can also be used to verify other numerical models.

Enhancement of Static and Dynamic Performance of Composite Tapered Pretwisted Rotating Blade With Variable Stiffness

AbstractComposite pretwisted tapered rotating thin-walled beams (TWB) can be used as a load-carrying structural part of a composite helicopter, wind turbine, fan, and turbomachinery blades. In the present study, the variable stiffness concept with curvilinear fiber path is used to achieve improved structural statics and dynamics performance of uniform and asymmetric composite thin-walled rotating beams. A parametric study is performed to investigate the effect of different fiber paths on the structural performance metrics including frequency spacing, coupling factor, and critical buckling load. For this purpose, The Euler–Lagrange governing equations of the dynamic system are derived via Hamilton's principle. To solve the governing set of equations, the extended Galerkin’s method (EGM) is employed. To validate the TWB model with curvilinear fibers, commercial finite element analysis tools abaqus is used. The author believes that the results presented here are likely to provide valuable information to the engineers involved in the design of advanced turbomachinery rotating blades using a variable stiffness concept with curvilinear fiber placement.

Разработка и обоснование пространственной механической модели основания сооружений с приведенными расчетными характеристиками грунтов с учетом конечной жесткости фундаментных конструкций

Предложена и обоснована новая пространственная ме­ханическая динамическая модель оснований сооружений атомных станций.
 В настоящее время при выполнении практических расчётов широко применяется модель оснований соору­жений атомных станций, приведённая в [1]. В этой модели мгновенные жёсткости основания при вращательных движениях жёсткого невесомого штампа функционально зависят от массы сооружения и от моментов инерции масс сооружения относительно координатных осей, что противоречит физической сути понятия мгновенных жёст­костей основания при вращательных движениях жёсткого невесомого штампа на поверхности инерционного полу­пространства.
 В свете вышеизложенного разработка динамической механической модели основания, устраняющей упомянутые несоответствия, представляется важной задачей, имеющей несомненную научную и практическую ценность
 Для обоснования проектных решений фундаментных конструкций сооружений необходимо определить величи­ны внутренних усилий, возникающих в их сечениях. При учёте конечной жёсткости фундаментных конструкций с применением метода конечных элементов необходимо установить закон распределения квазистатических и мгновенных жёстокостей грунтов основания по подошве фундаментной плиты.
 Известно, что параметры модели основания по существу должны имитировать параметры реакции основания жёст­кого невесомого штампа при его единичных смещениях и скоростях (линейных и угловых) по и относительно коор­динатных осей.
 В работе определены и обоснованы параметры модели основания, закон распределения интегральных жёсткостей по поверхности контакта. На примере сопоставления расчётов систем реакторного отделения совместно с основаниями, параметры которых были установлены по [1; 2], обоснована достоверность предлагаемой модели.

Stiffness vs flexibility based triangular spring cell – analysis of performance

PurposeThe purpose of the present study is to explore the incomplete substitution of the simplex triangular finite element by either of two models: one evolving out as part of the element flexibility, and the other as part of the element stiffness.Design/methodology/approachThe elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration.FindingsDespite a superiority of the flexibility cell concept observed in computations, the study reveals constellations of shape and stressing of the triangle that favour the stiffness concept. The latter is seen to behave stiffer than its flexibility counterpart and produces results more distant to the finite element in most cases.Research limitations/implicationsThe difference between the stiffness and the flexibility approach to spring cells is investigated for triangular elements in dependence of the geometrical configuration under specific conditions of stressing. This suffices to refute an exclusive superiority of the flexibility concept although largely true.Practical implicationsThe results of the investigation appear useful in deciding between the spring cell models depending on the case of a spring lattice application.Originality/valueThe flexibility approach to the spring cell is not widely known yet. This cell model deserves a study on performance and comparison to the different, more common stiffness cell model.

The equivalent dynamic stiffness of a visco-elastic half-space in interaction with a periodically supported beam under a moving load

A periodically supported beam on a visco-elastic half-space is considered to model the vibration of railway tracks. The viscosity of the half-space is assumed to be of the Kelvin-Voigt type. Making use of the concept of equivalent dynamic stiffness, the reaction of the half-space to the sleepers is replaced by a system of identical spring located under each sleeper. The frequency-dependent equivalent stiffness of the springs is a function of the phase shift of vibrations of neighbouring supports. The equivalent stiffness is derived analytically employing the contour integration technique, resulting in a comprehensive expression for different phase velocities of the waves in the beam with respect to the wave speeds of the half-space. Apart from the Rayleigh type surface wave (quasi-elastic wave), an extra visco-elastic surface wave may exist in a visco-elastic half-space depending on the parameters of the half-space and the frequency range. The existence of this second surface wave has not been addressed within the field of train-induced ground vibration. The importance of this wave for the equivalent stiffness is analysed. An effective method to determine the frequency range for the visco-elastic surface wave to exist is proposed.

Optimal finite locally resonant metafoundations enhanced with nonlinear negative stiffness elements for seismic protection of large storage tanks

Metamaterials represent a new trend in the field of seismic engineering. Their capacity to attenuate waves at the superstructure level is highly desirable and sought after in recent years. One of their main drawbacks to date, is the excessive size of the necessary resonators and, consequently, the uneconomic design they require. In order to tackle this problem, we apply the concept of negative stiffness to a metamaterial-based foundation system and analyse the potential improvements such a mechanism may have on the metamaterial as well as the coupled structural behaviour. Since negative stiffness is a property that cannot be achieved through conventional measures, a novel mechanism, designed for the implementation in periodic metamaterial-based structures, is proposed herein. The inevitable nonlinearity of the mechanism will be discussed and taken into account, while the advantages of the negative stiffness element (NSE) will be treated analytically and verified numerically. Additionally, through an optimization in the frequency domain and nonlinear time history analyses (THAs), the performance of the system coupled with a fuel storage tank is elaborated. With only 50% of the theoretically allowable NSE value, the foundation system could be reduced to 1/3 of its size. Furthermore, the nonlinear effect of the device has proven to diminish the band gap of the periodic system, which led us to introduce nonlinearity parameters that can help avoid the strongly nonlinear range. In sum, this article tackles three problems that are intertwined: (i) reducing the size of metamaterial-based structures; (ii) the design of a mechanism that exerts a negative stiffness in a periodic structure; and (iii) the study of the inevitable nonlinearity of NSEs and the subsequent effect on the metamaterial behaviour.

Investigation of the thermal stiffness and thermal tooth profile modification of spur gears

This paper first proposed the concept of thermal stiffness of gears and then calculated thermal stiffness using the finite element method and the analytical method, respectively. After that, based on the thermal stiffness, the thermal tooth profile modification of gears was studied. The results showed that the meshing thermal stiffness of tooth pair under the thermo-elastic coupling is a serial connection of elastic stiffness and modified thermal expansion stiffness. In addition, the meshing thermal stiffness of tooth pair decreases compared with the meshing elastic stiffness in the entire meshing region. There is only one intersection point of the distribution curves of the single tooth thermal stiffness and elastic stiffness along the meshing line. In the tooth root side of the intersection point, the thermal stiffness is larger than the elastic stiffness, and it is opposite in the tip side of the intersection point. It can be concluded from the thermal tooth profile modification parameters that the maximum amount of profile modification is the thermo-elastic coupling deformation of point B or D, with the modification index being 1.33.