Equivalent Stiffness Properties 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.

Pseudo-equivalent model for sandwich panels with egg-shaped honeycomb-grid core

The novel sandwich panel with egg-shaped honeycomb-grid core (SP-EHC), formed by chamfering the grid walls, can achieve a balance between lightweight and high-strength, as well as promote effective ventilation and drainage due to the semi-closed honeycomb design. To determine the panel’s equivalent stiffness properties, an asymptotic analysis of the energy functional stored within the periodic unit cell is conducted. On this base, a 2D pseudo-equivalent model (2D-PEM) in the form of the Reissner–Mindlin model was formulated. The pseudo-excitation method was employed to analyze the self-power spectral density function and root mean square response of the 2D-PEM under random vibration. The accuracy and effectiveness of the model were validated through comparisons of the three-point bending experimental results of the 3D-printed specimen, exhibiting relative errors of 2.95%. In addition, free and random vibration analyses were conducted on the hybrid SP-EHC to further validate the model. Furthermore, the influence of material and structural parameters on specific stiffness, natural frequencies and first velocity RMS was systematically investigated. The findings reveal that enhancing the grid wall’s chamfering ratio is beneficial in achieving the desired objectives of lightweight and high-strength. In addition, compared to sandwich panels with orthogonal and pyramid grid cores, this improvement positively impacts the vibration characteristics of the sandwich panel. These findings offer valuable insights for the future design and optimization of such sandwich panels.

Equivalent-oriented model for sandwich panels with ZPR accordion honeycomb

The core layer of accordion honeycomb sandwich panel (accordion HSP) exhibits exceptional affinity for one-dimensional curvature deformations due to its special zero Poisson’s ratio effect. This study thoroughly examines its static and dynamic characteristics by decomposing the analysis into unit-cell constitutive modeling and a two-dimensional equivalent-oriented model (2D-EOM) through the variational asymptotic method. The unit-cell constitutive modeling enables determining equivalent stiffness properties for the 2D-EOM. To validate the accuracy and efficiency of the proposed 2D-EOM, its results are compared against those obtained from a detailed 3D finite element model, including in-plane and out-of-plane behaviors of the core layer and sandwich panel, as well as free and random vibration under diverse excitation conditions. The comparison results demonstrate a significant three-fold increase in the equivalent stiffness of the accordion honeycomb in the direction of the added ligaments, as compared to the re-entrant honeycomb. Simultaneously, the acceleration amplitude of the accordion HSP is effectively reduced by 4% due to the involvement of lower high-order frequencies, rendering it exceptionally suited for shockproof meta-structural applications. This equivalent model not only fulfills accuracy requirements but also improves computational efficiency by 15 times, providing an effective approach for preliminary design of honeycomb sandwich panels.

Temperature- and Frequency-Dependent Nonlinearities of an Integrated Hydro-Pneumatic Suspension with Mixed Gas-Oil Emulsion Flow

Hydro-pneumatic suspension (HPS) systems are increasingly being implemented in commercial vehicles and various industrial equipment, which is mainly attributed to the integration of adaptable nonlinear pneumatic stiffness and hydraulic damping properties. The integrated HPS design with a shared gas-oil chamber, however, leads to gas-oil emulsion flow within the suspension chambers, which intricately affects the internal and external properties of the HPS, especially under variations in temperature and excitation frequency. This study experimentally and analytically investigated the temperature- and frequency-dependent properties of the hydro-pneumatic suspension with the gas-oil emulsion. Laboratory experiments were performed under three different near-constant temperatures (30, 40, and 50 °C) in the 0.5–8 Hz frequency range. An analytical model of the HPS was formulated considering the effects of temperature on internal fluid properties, gas-oil emulsion flow between the coupled chambers, the dynamic seal friction, and polytropic change in the gas state. The internal parameters, including the gas volume fraction, the discharge coefficient of the emulsion, and the dynamic friction components, as well as the external stiffness and damping characteristics, were determined. The relationships between these properties and the system temperature, velocity, and excitation frequency were further investigated. The simulated responses obtained under different excitations showed reasonably good agreement with the experimental results of the HPS. The results suggested that increased temperature yielded greater equivalent stiffness and comparable damping properties of the system. The gas volume fraction, discharge coefficient, and magnitude of seal friction generally tended to increase with increasing temperature. Increased excitation frequency led to greater hysteresis in hydraulic damping force and seal friction, and reduced seal friction magnitude and Stribeck effect.

Single-ply elastic properties determination in CFRP laminates using a combined ultrasonic method

Estimation of the elastic properties in composite laminates is very important. Researchers usually consider the laminate as a whole and identify its equivalent stiffness properties. However, determining the elastic properties of each layer within a laminate can provide more comprehensive information to the users. In this paper, an ultrasonic method is proposed to reconstruct the single-ply elastic properties by combing bulk and guided waves. Herein, a novel double-side-transmitted bulk wave method is developed to identify the stacking sequences, providing the necessary information for further evaluation of the single-ply elastic properties. The double-side-transmitted bulk wave method is demonstrated under various layup scenarios, allowing the detection of more layers than conventional techniques. The laser-generated guided wave velocities are then inverted by genetic algorithms (GAs) to reconstruct the single-ply elastic properties. An effective indicator, the coefficient of variation, is designed to represent the accuracy of the identified single-ply material properties. And the experimental dispersion curves are in good agreement with the theoretical dispersion curves under the identified material properties.

Stiffness and strength evaluation of lattice-based mechanical metamaterials by decoupled two-scale analysis

There is an emerging class of artificial materials, so-called mechanical metamaterials. By deliberately designing microscopic internal mechanisms, these materials exhibit exotic properties, which distinguish the mechanical metamaterials from natural materials. As additive manufacturing technology has been rapidly developed and its manufacturing quality has been improved, those conceptual artificial materials are ready to fabricate. This paper presents a decoupled two-scale analysis framework to efficiently evaluate the stiffness and strength characteristics of lattice-based mechanical metamaterials. Structural characteristics of lattice-based mechanical metamaterials are effectively captured by accommodating a computational homogenization method to lattice-based structures. In the computational homogenization procedure, a unit cell of the periodically distributed structure is modeled as representative finite elements. Equivalent stiffness properties of the unit cell are calculated based on the computational homogenization procedure. The equivalent structural properties are then used to perform macroscopic structural analysis of lattice-based structures in an effective manner. Similarly, a local/microscopic stress distribution within the periodic lattice unit cell is recovered by transforming macroscopic sectional loads, which are obtained from the macroscopic structural analysis, through a stress amplification matrix. The microscopic stress distribution obtained with the two-scale analysis can be used for strength evaluation. Subsequently, numerical results are validated by comparing them with experimental results providing actual behaviors of lattice-based mechanical metamaterials. This work presents the novel use of the multi-scale analysis scheme combining the computational homogenization method and the stress field transformation method enabling structural evaluations to design mechanical metamaterials with structural integrity. This study also demonstrates the feasibility and capability of the presented approach to effectively predict stiffness and strength characteristics of lattice-based structures.

Assessment of equivalent substrate stiffness and mechanical properties of sustainable alkali-activated concrete containing recycled concrete aggregate

The effects of using recycled concrete aggregate (RCA) as coarse aggregate on the equivalent substrate stiffness and mechanical properties of sustainable alkali-activated concrete were investigated in this paper. High-calcium fly ash (HFA) and commercial silica fume (SF) were used as the precursors for producing the alkali-activated high-calcium fly ash concrete (AAHFAC). Sodium hydroxide (SH) and sodium silicate (SS) solutions were used as alkaline activator solutions with the constant SS/SH ratio of 1.0 and liquid-binder (L/B) ratio of 0.50. The natural coarse aggregate (NCA) used in this study was crushed limestone and replaced with RCA at the rates of 0%, 20%, 40%, 60%, 80%, and 100% by volume. The setting time, compressive strength, elastic modulus, Poisson’s ratio, and bond strength obtained by pull-out tests of AAHFAC and Portland cement concrete (NC) were investigated. Experimental results showed that the use of RCA to replace NCA resulted in reducing the setting time of concrete. Also, the setting time of the AAHFAC with and without SF were shorter than that of NC mixes for all of RCA replacement level. The use of RCA had a positive effect on the mechanical properties of alkali-activated binder; however, they declined at NC mixes. Therefore, the use of RCA in alkali-activated binder concrete is an excellent alternative for sustainable concrete since it allows for the substitution of natural resource components while somehow producing low CO2 emissions.

Post-processing of additive manufactured parts: a numerical strategy applied in maxillary implantology

To obtain a functional part from additive manufacturing (AM) technologies, some surfaces require post-processing by machining. An approach is developed using additive manufacturing supports as a clamping device for the milling operation. A model combining an analytical approach to determine the cutting forces with a finite element model (FEM) to predict the dynamical response of the workpiece-supports system is proposed. The complex structure of the supports is homogenized with a simplified geometry with equivalent stiffness and mechanical properties. A case study from the biomedical field is proposed: the finishing operation of a custom-made maxillary reconstruction plate is simulated. A parametric study is proposed with: (1) two different lattice geometries used as support structures; (2) up and down milling; (3) different depths of cut.

A semi-active variable equivalent stiffness and inertance device implemented by an electrical network

Semi-active devices have been widely investigated and applied due to their advantages in control systems. However, for satisfying complicated applications, some semi-active devices need to be capable of controlling multiple mechanical properties, which is hard to implement with a mechanical network considering the space limitation. In this paper, a semi-active variable equivalent stiffness and inertance (VESI) device is developed by an electrical network and an electromagnetic device instead of a mechanical system. Due to that the inerter and spring can store energy, the dynamic control of their mechanical properties without the external power to compensate the stored energy will cause the system discontinuity, which will affect the control performance. Therefore, the variable damping (VD) device is applied to connect with spring or inerter in series to obtain variable equivalent stiffness or inertance properties. Then, according to the force-current analogy, an electrical “VESI” network is designed to simulate the mechanical VESI network. An electromagnetic device equips with the variable electrical system can achieve the VESI mechanical properties, which is validated with experiments. The imaginary part of the admittance of the proposed device can vary to the positive phase and also the negative phase by controlling two resistors. The application of VESI device in the vehicle is investigated and analysed. A semi-active control strategy is designed for vibration control and rollover prevention of vehicles with VESI suspensions. According to the simulation result, the proposed semi-active system can significantly improve the vibration reduction performance at both vertical and roll directions; also, it can decrease the roll angel when vehicles in the cornering maneuver. Besides, the semi-active VESI device with an electrical network has the advantages in installation and maintenance. It has great potential in practical applications.

Experimental methodology to assess the dynamic equivalent stiffness properties of elliptical orthotropic plates

This paper deals with the dynamic characterisation of plate structures with elliptical orthotropic stiffness properties, using an equivalent thin plate theory using a wave fitting approach. The method consists in projecting the experimentally determined transverse displacement field of a plate on an analytical Green’s function of an elliptical orthotropic plate based on Hankel’s functions. The error between the projected and measured fields is then minimized, varying the characteristics of the function until an optimal fit is reached. The thus obtained characteristics are the two flexural rigidities defining the elliptical orthotropy of the plate, and the orthotropy angle. This fitting procedure is applied at each frequency, enabling the determination of frequency dependent dynamic material properties. The method is applied to a honeycomb sandwich panel to validate the proposed fitting approach. The identified flexural rigidities are compared to the estimations obtained by means of an analytical model and the IWC (Inhomogeneous Wave Correlation) method assuming three different type of plate characteristics (anisotropic, orthotropic and elliptical orthotropic). For the elliptical orthotropic assumption, consistent results are observed between the methods and the model over a large frequency range (from 1 to 50 kHz).

Novel Building Diaphragm Layouts Generated through Topology Optimization

ABSTRACTThe objective of this paper is to explore the layout of floor diaphragms in steel buildings subject to demands generated from lateral loads, such as those from wind and earthquakes, optimized for shear stiffness and minimum weight. The design of floors is typically dominated by considerations for gravity loads. In some classical cases, e.g. the works of Nervi, optimized floor topologies have been expressed in non‐grid patterns, such as through ribs oriented in principal stress directions. Floor designs employing steel deck generally express only one‐way action spanning between joists. Layouts of floor diaphragms are investigated here for improved lateral stiffness through topology optimization. To handle the widely different equivalent stiffness properties of steel deck the classic topology optimization algorithm is augmented to allow for orthotropic material in the formulation and material orientation as a design variable. A range of possible orthotropic stiffness properties are developed from a database of existing designs for bare steel deck and composite steel‐concrete deck diaphragms. The floor designs are generally found to follow the principal stress trajectories developed in the model under the considered shear loading. This work is the first step in an effort to develop optimized floor layouts under combined gravity and lateral (seismic) load and is part of a larger initiative (www.steeli.org) that aims to better understand and optimize the role of diaphragms in the seismic response of steel buildings.

Conceptual design and simulation validation based finite element optimisation for tubercle leading edge composite wing of an unmanned aerial vehicle

A finite element model is developed to determine deformation and stresses on a composite wing of unmanned aerial vehicle (UAV) with a tubercle design at the leading edge of the wing. Tubercles, commonly known as protuberances found on the leading edge of a whale pectoral flipper, offering great performance from an aerodynamic perspective. This paper deals with a first order shear deformation theory (FSDT) approach to discover the UAV laminates composite wing model of tubercle leading edge (TLE) with rib-reinforced so that the equivalent stiffness and material properties are obtained from the simulation of finite element analysis using ANSYS. Another structural configuration of design replicating the idea of monocoque concept, whereby foam is used at the leading and trailing edges of the wing. Styrene acrylonitrile (SAN) core foam is used representing high strength-to-weight ratio with its superiority in the mechanical properties of polymeric sandwich composites. The updated static structural analysis from rib-reinforced can be applied to update the wing stiffness distribution of monocoque-foam. The optimum design is concluded from the tabulated deformation and stresses of both wings, where monocoque-foam showed better performance with a reduction in 50.72% of deformation and 35.88% of stress, compared to rib-reinforced design.

3D truss structures with coreless 3D filament winding technology

A coreless manufacturing process for generic 3D rigid frame topologies will be introduced in this paper. The aim is to extend the field of filament winding from mainly 2D-shells and some exceptional cases of 3D rigid frames. This manufacturing process employs a coreless translation cross-winding method in order to continuously deposit a roving around deflection points in space. On this basis, a design methodology is being created and deductively verified by designing a beam for a three-point bending load case. The composite beam is designed on a macro level simulation approach to match the stiffness of a reference aluminum profile, which is commonly employed as structural component for robotic gripper systems in automotive assemblies. The performance of the beams is subsequently compared by three-point bending experiments. This demonstrates that the composite beam offers equivalent stiffness and strength properties with a weight-reduction potential of nearly 50% for bending loads.

Seismic reliability-based design of inelastic base-isolated structures with lead-rubber bearing systems

In this paper, a seismic reliability-based approach is proposed to design inelastic steel moment frame structures isolated by lead-rubber bearing (LRB) systems. An equivalent two-degree-of-freedom system is assumed in which a bilinear behaviour is assigned to both the superstructure and the base. Furthermore, uncertainties associated with the equivalent superstructure mass, stiffness, and yield properties are taken into account by employing proper probability density functions. The proposed design approach is twofold: 1) Reliability curves that return the key design parameters of the inelastic base-isolated structure including: the period of the superstructure, the target base displacement, and the ductility-dependent strength reduction factor for a given target reliability. 2) Regression equations, which estimate the displacement ductility demand of the inelastic superstructure and the optimal design properties of the lead-rubber bearing system including: the total initial stiffness and the total yield force. These regression equations are calibrated against a large set of optimally-designed base-isolated buildings using Genetic Algorithm.

Topology optimization for microstructural design under stress constraints

This work aims at introducing stress responses within a topology optimization framework applied to the design of periodic microstructures. The emergence of novel additive manufacturing techniques fosters research towards new approaches to tailor materials properties. This paper derives a formulation to prevent the occurrence of high stress concentrations, often present in optimized microstructures. Applying macroscopic test strain fields to the material, microstructural layouts, reducing the stress level while exhibiting the best overall stiffness properties, are sought for. Equivalent stiffness properties of the designed material are predicted by numerical homogenization and considering a metallic base material for the microstructure, it is assumed that the classical Von Mises stress criterion remains valid to predict the material elastic allowable stress at the microscale. Stress constraints with arbitrary bounds are considered, assuming that a sizing optimization step could be applied to match the actual stress limits under realistic service loads. Density–based topology optimization, relying on the SIMP model, is used and the qp–approach is exploited to overcome the singularity phenomenon arising from the introduction of stress constraints with vanishing material. Optimization problems are solved using mathematical programming schemes, in particular MMA, so that a sensitivity analysis of stress responses at the microstructural level is required and performed considering the adjoint approach. Finally, the developed method is first validated with classical academic benchmarks and then illustrated with an original application: tailoring metamaterials for a museum anti–seismic stand.

Bending and free vibration analysis of foam-filled truss core sandwich panel

This paper presents the studies carried out on bending and free vibration behavior of truss core sandwich panel filled with foam typically used in aerospace applications. Equivalent stiffness properties for foam-filled truss core sandwich panel are derived by idealizing 3D foam-filled sandwich panel to an equivalent 2D orthotropic thick plate continuum. The accuracy of the derived elastic property is ensured by the numerical comparison of free vibration response of 3D and its equivalent 2D finite element model. The derived stiffness constants were used in closed form solution to evaluate the maximum deflection of the continuum. The results show that the free vibration and static behavior of the sandwich panel can be enhanced in due consideration to the space constraint by filling foam in the empty space of core. The results also reveal that triangular core foam-filled sandwich panel deflects less compared to other cores. From the free vibration analysis, effect of filling foam is effective in cellular and trapezoidal core.

A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis

A one-dimensional finite element method for generally layered smart beams is presented in this paper. The model implements the first-order shear deformation beam theory and is based on the preliminary analytical condensation of the electric state to the mechanical state. This allows us to establish an effective mechanical beam kinematically equivalent to the original smart beam including the effects of electro-elastic couplings. The contributions of the external electric loads are included in both the equivalent stiffness properties and the equivalent mechanical boundary conditions. Hermite shape functions, which depend on parameters representative of the staking sequence through the equivalent electro-elastic stiffness coefficients, are used to formulate the finite element method. The state space representation is then invoked for the assembled smart beam finite element model to favor its implementation in a block diagram environment for multi-domain simulation. Validation results and solutions for passive and active vibrations damping system are presented last.

Probabilistic micromechanical analysis of composite material stiffness properties for a wind turbine blade

This work presents a coupled approach for stiffness property prediction of composite materials used in wind turbine blades using an advanced micromechanics and reliability-based methodologies. This approach demonstrates how to map the uncertainties in the fiber and matrix properties onto the equivalent stiffness properties of composite laminates. Square and hexagonal unit cells were employed for the estimation of the composite equivalent properties. The finite element formulation of the unit cells were performed in the ANSYS Multiphysics. The results from numerical experimentation conform well with the available test data and to the results from the Modified Rule of Mixture (MROM). A probabilistic analysis using Monte Carlo Simulation with Latin Hypercube Sampling was used to assess the uncertainties in the equivalent properties according to the variability in the basic properties of the constituents. Furthermore, a sensitivity analysis based on the Spearman Rank Order correlation coefficients was carried out to highlight the influence of important properties of the constituents. As an illustration, the above approach is applied to analyze a 5MW wind turbine blade section under static loading. Results demonstrate the possibility of the coupled approach at macro level (structure) from micro level (unit cell) with the aim to design robust structures.

Stiffness properties of certain oscillatory systems: quantification and possibilities for corrections

This study is concerned with the use of energy methods to find the equivalent stiffness properties of certain vibration models. The first class of models are one-degree-of-freedom oscillatory systems that include several combinations of a main spring and an additional spring. The stiffness properties of the equivalent system as well as the condition for different types of the resulting oscillatory motion are determined. Then, two-degree-of-freedom systems comprising two pairs of mutually orthogonal or symmetrically attached springs are examined. The corresponding equivalent stiffness properties are obtained and the possibilities for corrections are also discussed.

Equivalent mechanical properties for cylindrical cell honeycomb core structure

Structural members made up of two stiff, strong skins separated by a lightweight core are known as sandwich panels. The separation of the skins by the core increases the moment of inertia of the panel with little increase in weight, producing an efficient structure against in-plane and out-of-plane loadings. In general, the mechanical behavior of cellular structures is given by the effective elastic modules, which are also dependent on the structure topology and different geometric parameters. This paper presents analytical equations for equivalent stiffness properties of a cylindrical cell honeycomb core. The cylindrical cells are obtained by connecting bended plate strips using adhesion or laser-welding. The stiffness properties and effective elastic modules for in-plane and out-of-plane compression and shear loadings are derived using an energy based approach. The analytical models are validated by 3D finite element method based on solid elements. The obtained mechanical properties are used to assess the stress and strain state of a sandwich beam in three-point bending. The present investigation shows that the analytical equations can predict the stiffness coefficients and respectively the effective elastic modules with very good accuracy.