Search Results (20)

Fiber-reinforced and laminated composite materials, widely used in engineering applications, may develop periodic curvature during manufacturing due to technological requirements. Given such curvatures in widely used composites, static and dynamic analyses of plates and shells under loads, along with related stability issues, have been extensively investigated. However, studies focusing specifically on the static analysis of such materials remain limited. Composite materials with structural curvature exhibit complex mechanical behavior, making their analysis particularly challenging. Predicting their mechanical response is crucial in engineering. In response to this need, the present study conducts a static analysis of plates made of periodically curved composite materials using the Navier method. The plate equations were derived based on the Kirchhoff–Love plate theory within the framework of the Continuum Theory proposed by Akbarov and Guz’. Using the Navier method, deflection, stress, and moment distributions were obtained at every point of the plate. Numerical results were computed using MATLAB. After verifying the convergence and accuracy of the developed MATLAB code by comparing it with existing solutions for rectangular homogeneous isotropic and laminated composite plates, results were obtained for periodically curved plates. This study offers valuable insights that may guide future research, as it employs the Navier method to provide an analytical solution framework. This study contributes to the limited literature with a novel evaluation of the static analysis of composite plates with periodic curvature. Full article

Nano-structures play a crucial role in advancing technology due to their unique properties and applications in various fields. This study examines the forced vibration behavior of an orthotropic nano-system consisting of an elastically connected nanoplate and a doubly curved shallow nano-shell. Both nano-elements are simply supported and embedded in a Winkler-type elastic medium. Utilizing the Eringen constitutive elastic relation, Kirchhoff–Love plate theory, and Novozhilov’s linear shallow shell theory, we derive a system of four coupled nonhomogeneous partial differential equations (PDEs) describing the forced transverse vibrations of the system. We perform forced vibration analysis using modal analysis. The developed model is a novel approach that has not been extensively researched by other authors. Therefore, we provide insights into the nano-system of an elastically connected nanoplate and a doubly curved shallow nano-shell, offering a detailed analytical and numerical analysis of the PDEs describing transverse oscillations. This includes a clear insight into natural frequency analysis and the effects of the nonlocal parameter. Additionally, damping proportional coefficients and external excitation significantly influence the transverse displacements of both the nanoplate and nano-shell. The proposed mathematical model of the ECSNPS aids in developing new nano-sensors that respond to transverse vibrations based on the geometry of the nano-shell element. These sensors are often used to adapt to curved surfaces in medical practice and gas sensing. Full article

Flywheels have been largely used in rotating machine engines to save inertial energy and to limit speed fluctuations. A stress distribution problem is created due to the centrifugal forces that are formed when the flywheel is spinning around, which leads to different levels of pressure and decompression inside its structure. Lack of balance leads to high energy losses through various mechanisms, which deteriorate both the flywheel’s expectancy and their ability to rotate at high speeds. Deviation in the design of flywheels from their optimum performance can cause instability issues and even a catastrophic failure during operation. This paper aims to analytically examine the stress distribution of radial and tangential directions along the flywheel structure within a linear elastic range. The eigenvalues and eigenvectors, which are representative of free vibrational features, were extracted by applying finite element analysis (FEA). Natural frequencies and their corresponding vibrating mode shapes and mass participation factors were identified. Furthermore, Kirchhoff–Love plate theory was employed to model the transverse vibration of the system. A general solution for the radial component of the equation of flywheel motion was derived with the help of the Bessel function. The results show certain modes of vibration identified as particularly influential in specific directions. Advanced time-frequency analysis techniques, including but not limited to continuous wavelet transform (CWT) and Hilbert–Huang transform (HHT), were applied to extract transverse vibration features of the flywheel system. It was also found that using CWT, low-frequency vibrations contribute to the majority of the energy in the extracted signal spectrum, while HHT exposes the high-frequency components of vibration that may cause significant structural damage if not addressed in time. Full article

In this study, the resonant characteristics of the off-center-driven Chladni plates were systematically investigated for the square and equilateral triangle shapes. Experimental results reveal that the number of the resonant modes is considerably increased for the plates under the off-center-driving in comparison to the on-center-driving. The Green’s functions derived from the nonhomogeneous Helmholtz equation are exploited to numerically analyze the information entropy distribution and the resonant nodal-line patterns. The experimental resonant modes are clearly confirmed to be in good agreement with the maximum entropy states in the Green’s functions. Furthermore, the information entropy distribution of the Green’s functions can be used to reveal that more eigenmodes can be triggered in the plate under the off-center-driving than the on-center-driving. By using the multiplication of the resonant modes in the off-center-driving, the dispersion relation between the experimental frequency and the theoretical wave number can be deduced with more accuracy. It is found that the deduced dispersion relations agree quite well with the Kirchhoff–Love plate theory. Full article

In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the smart materials. The plate structure is rigorously modeled based on the Kirchhoff–Love plate theory, while the piezoelectric actuators are formulated in accordance with the Prandtl–Ishlinskii model. This research proposed a control system that addresses the interference effects arising during vibration control by dividing multiple piezoelectric elements into two groups and implementing MIMO control. The efficacy of the proposed control method was validated through simulations and experiments. Full article

The simulation of elastic slender objects like cables is essential for industrial applications in predicting elastic behaviors and life cycles. The Cosserat model and its variants are the dominant approaches due to their high efficiency and accuracy. However, these assume cables with homogeneous interiors and thus cannot simulate hybrid cables containing different materials. We address this by developing a novel coarsened-shell-based Cosserat (CSC) model. The CSC model constructs a material-aware elastic energy function along the cable’s cross-section to describe the global elastic behavior. The CSC model is specifically developed by carefully leveraging the strengths of three approaches: the Cosserat theory to model slender cables, the Kirchhoff–Love shell theory to model the cable’s cross-sectional energy, and numerical coarsening to reduce the degrees of freedom in the shell simulation via constructing a set of new types of material-aware shape/base functions. This allows the more accurate computation of the local and global deformations of hybrid cables, surpassing the classical Cosserat models in accuracy. Full article

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. Full article

The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff–Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method (SFDM) implemented using three different probabilistic approaches. The BEM, FEM, and FDM were used equally to describe plate deformation, and the BEM was applied to describe the dynamic interaction of water on a plate surface. The plate’s inertial forces were expressed using a diagonal or consistent mass matrix. The inertial forces of water were described using the mass matrix, which was fully populated and derived using the theory of double-layer potential. The main aspect of this work is the simultaneous application of the BEM, FEM, and FDM to describe and model the problem of natural vibrations in a coupled problem in solid–liquid mechanics. The second very important novelty of this work is the application of the Bhattacharyya relative entropy apparatus to test the safety of such a system in terms of potential resonance. The presented concept is part of a solution to engineering problems in the field of structure and fluid dynamics and can also be successfully applied to the analysis of the dynamics of the control surfaces of ships or aircraft. Full article

It was recently proved that the knowledge of the transverse displacement of a nanoplate in an open subset of its mid-plane, measured for any interval of time, allows for the unique determination of the spatial components ${\left\{f_m(x,y)\right\}}_{m=1}^M$ of the transverse load ${\sum }_{m=1}^M{g}_m\left(t\right)f_m(x,y)$, where $M\ge 1$ and ${\left\{g_m\left(t\right)\right\}}_{m=1}^M$ is a known set of linearly independent functions of the time variable. The nanoplate mechanical model is built within the strain gradient linear elasticity theory, according to the Kirchhoff–Love kinematic assumptions. In this paper, we derive a reconstruction algorithm for the above inverse source problem, and we implement a numerical procedure based on a finite element spatial discretization to approximate the loads ${\left\{f_m(x,y)\right\}}_{m=1}^M$. The computations are developed for a uniform rectangular nanoplate clamped at the boundary. The sensitivity of the results with respect to the main parameters that influence the identification is analyzed in detail. The adoption of a regularization scheme based on the singular value decomposition turns out to be decisive for the accuracy and stability of the reconstruction. Full article

The aeroelastic characteristics of the panel under the action of coolant are obviously different from the flutter characteristics of the traditional panel. In order to solve this problem, the dynamics model of the panel flutter was established in this paper based on von Karman’s large deformation theory and the Kirchhoff–Love hypothesis. The panel dynamics equations were discretized into constant differential equations with finite degrees of freedom by Galerkin’s method, and solved by the fourth Runge–Kutta method in the time domain. The nonlinear modified piston theory was used to predict the unsteady aerodynamic loads, and the accuracy of the flutter analysis model was verified. On this basis, the effects of the head-panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively. The results showed that reducing the pressure drop ratio, and reducing or increasing the head-panel pressure (valuing away from the freestream pressure) can improve the critical dynamic pressure when bifurcation occurs. At $M_{\infty }=5.0$, the pressure drop ratio causes a 22.1% increment in the critical dynamic pressure. The influence of the coolant injection direction on the panel bifurcation is mainly influenced by the head-panel pressure. The inertial resistance slows down the convergence process of the panel response, increases the limit cycle amplitude, and reduces the critical dynamic pressure of the panel, while the viscous resistance plays the opposite role. Based on these conclusions, this paper finally proposes the suppression method of panel fluttering from head-panel pressure, inertial resistance, viscous resistance, etc. Full article

In this paper, we develop a T-spline-based isogeometric method for the large deformation of Kirchhoff–Love shells considering highly nonlinear elastoplastic materials. The adaptive refinement is implemented, and some relatively complex models are considered by utilizing the superiorities of T-splines. A classical finite strain plastic model combining von Mises yield criteria and the principle of maximum plastic dissipation is carefully explored in the derivation of discrete isogeometric formulations under the total Lagrangian framework. The Bézier extraction scheme is embedded into a unified framework converting T-spline or NURBS models into Bézier meshes for isogeometric analysis. An a posteriori error estimator is established and used to guide the local refinement of T-spline models. Both standard T-splines with T-junctions and unstructured T-splines with extraordinary points are investigated in the examples. The obtained results are compared with existing solutions and those of ABAQUS. The numerical results confirm that the adaptive refinement strategy with T-splines could improve the convergence behaviors when compared with the uniform refinement strategy. Full article

This study analyzes the composite laminated T-beams using the composite beam and laminated composite plate theories. The theoretical formula was derived assuming that the composite T-beam has one- and two-dimensional (1D and 2D) structures. The 1D analysis was performed according to the Kirchhoff-Love hypothesis, thereby considering only the axial strain to derive a relationship between the strain and displacement. The 2D analysis was performed considering the T-beam as a combination of two composite sheets. The effective stiffness of the beam was derived from the stress-strain and moment-curvature relationships. Furthermore, the deflection of the beam and the stress of each laminate were calculated. A simple support beam, made of AS4/3501-6 carbon/epoxy, was used as a composite laminated T-beam. MSC/NASTRAN finite element software was used for analysis. The accuracy of the theoretical formula and limitations of its use was verified using the finite element analysis. Higher accuracy of the theoretical formula was obtained at a composite beam aspect ratio greater than 15. The formula derived in this study is suitable for thin and long beams. Full article

The main objective of this study is to conveniently and rapidly develop a new dimensionless number to characterize and predict the deflection of square plates subjected to fully confined blast loading. Firstly, based on the Kirchhoff–Love theory and dimension analysis, a set of dimensionless parameters was obtained from the governing equation representing the response of a thin plate subjected to impact load. A new dimensionless number with a definite physical meaning was then proposed based on dimensional analysis, in which the influence of bending, torsion moment and membrane forces on the dynamic response of the blast-loaded plate were considered along with the related parameters of the blast' energy, the yield strength of the material, the plate thickness and dimensions of the confined space. By analyzing the experimental data of plates subjected to confined blast loading, an approximately linear relationship between the midpoint deflection–thickness ratio of the target plate and the new dimensionless number was derived. On this basis, an empirical formula to predict the deflection of square plates subjected to fully confined blast loading was subsequently regressed, and its calculated results agree well with the experimental data. Furthermore, numerical simulations of square plates subjected to blast loading in a cuboid chamber with different lengths were performed. The numerical results were compared with the calculated data to verify the applicability of the present empirical formula in different scenarios of blast loading from explosions in a cuboid space. It is indicated that the new dimensionless number and corresponding empirical formula presented in this paper have good applicability and reliability for the deflection prediction of plates subjected to fully confined explosions in a cuboid chamber with different lengths, especially when the plates experience a large deflection–thickness ratio. Full article

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated. Full article

Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage. Full article