This paper investigates the effects of radiation pressure, albedo, and oblateness within the framework of the Circular Restricted Three-Body Problem (CR3BP). We have considered the smaller primary produces the albedo effect, while the larger primary is treated as a radiating body. Moreover, the smaller primary is assumed to be oblate, characterized by the zonal harmonic coefficient J_2 , while higher-order terms are neglected due to their weaker influence on the dynamical system. The novelty of this work lies in the development of a generalized CR3BP model that simultaneously incorporates radiation pressure, albedo, and oblateness, enabling a comprehensive investigation of their combined influence on the system dynamics. Within this framework, we determine the equilibrium points, analyze their linear stability, investigate the zero-velocity curves (ZVCs), and compute Lyapunov periodic orbits around the collinear equilibrium points L_1 and L_2 , together with their corresponding Lyapunov characteristic exponents. Radiation pressure was found to have the dominant influence on the displacement of the equilibrium points, whereas albedo and the oblateness parameter J_2 exert comparatively weaker but still observable effects. The combined perturbations significantly modify the Jacobi constant, reshape the topology of ZVC, and alter the geometry and stability characteristics of the Lyapunov orbits. The corresponding Lyapunov characteristic exponents reveal chaotic behavior in the vicinity of the L_1 and L_2 equilibrium points. These results provide a more realistic description of perturbed three-body dynamics and contribute to design of efficient trajectory planning to trajectory design, station-keeping, and low-energy transfer missions involving libration-point orbits.
A novel formulation to determine the incremental crystallographic slip in a rate-independent elastoplastic single crystal subjected to mixed traction and velocity boundary conditions is proposed. Slip is governed by Schmid’s law. The present formulation is based on a theorem due to Maier [Meccanica [49], 3;121–130], which amounts to a statement of the principle of maximum dissipation. It reduces the present problem to one of non-negative quadratic programming. The quadratic program is solved using the non-negative least squares algorithm due to Lawson and Hanson, which has mathematically guaranteed convergence properties. The incremental elastoplastic formulation is used to simulate tensile, and simple shear deformation of copper crystals symmetrically oriented for multislip. The predicted mechanical and microstructural responses compare well with the experimental measurements, and computational results reported in the literature. A computer implementation of the present method is found to be about an order of magnitude faster than a previous formulation based on the unregularised Schmid’s law.
This study presents an analytical investigation into the nonlinear free vibrations of viscoelastic porous cylinders, accounting for the critical effects of geometrical nonlinearity. The nonlinear governing equations of motion are derived for an arbitrary porosity distribution using Hamilton’s principle, integrated with the first-order shear deformation theory and von Kármán nonlinear relations. The material’s viscoelasticity is modeled via the three-parameter Zener model, while the porosity effect is incorporated through Biot’s assumption. To resolve the complex nonlinear equations, the multiple-scale method is employed. A comprehensive parametric study is conducted to elucidate the influence of various porosity distributions, viscoelastic parameters, and geometric configurations on the natural frequencies. A significant advantage of the proposed analytical framework is its versatility in accommodating any continuous porosity distribution. The accuracy and reliability of the analytical results are rigorously validated through comparisons with existing literature and finite element analysis benchmarks.
Magnetic brakes are devices used in rotating systems to apply a resisting torque to the machine. The most common configuration relies on electromagnetic induction, which generates eddy currents in a rotating component, typically a disk. The torque can be adjusted by controlling the electric current in the electromagnet coils. In contrast, brakes that use permanent magnets produce a constant torque, which depends solely on the distance between the magnets and the rotating part. Although electromagnetic brakes have been extensively studied, permanent magnet brakes are less explored. There are relatively few studies that provide mathematical models capable of accurately predicting the braking torque in line with experimental results. This work contributes to the field by bringing a different approach to model the system. The NdFeB (Neodymium–Iron–Boron) magnets are modeled using an equivalent coil circuit, and the generation of eddy currents is described based on electromagnetic theory to calculate the induced magnetic field in the disk. The model also incorporates the effect of torque saturation at high rotational speeds. The numerical predictions of the braking torque are compared with experimental measurements obtained from a test bench. Tests were conducted at various rotational speeds and with different gaps between the magnets and the rotating element. The results show a strong correlation between the model and the experimental data, confirming the accuracy of the model.
In functional composite waveguide configurations, viscoelastic coatings serve as protective encapsulants and provide tunable dissipation that significantly affects energy transmission and transference profiles. The interactions between stress waves and viscoelastic coatings depend intensively on the coating’s rheological behavior, which necessitates accurate modeling through appropriate constitutive frameworks. In this article, axisymmetric torsional wave propagation is analyzed in a two-layer hollow cylindrical structure consisting of a non-piezoelectric semiconductor tube internally coated with a viscoelastic polymer. The hollow semiconductor tube is subjected to an external voltage source and coated with a metal electrode. The rheological influence of the viscoelastic layer is modeled with two distinct standard-linear-solid configurations, namely, the Zener and Poynting–Thomson models, to capture the material’s frequency-dependent relaxation behavior. The governing equations for the electrically active semiconductor and the electrically inactive viscoelastic phases are formulated in a cylindrical coordinate system and solved analytically through rigorous application of Bessel functions, including an imperfect interface modeled by a linear spring model. The resulting frequency equation is used to compute the multimodal frequency, phase velocity, and attenuation spectra of torsional waves against wave number, relaxation time, coating thickness, and depicted through graphical plotting for separately Zener and Poynting-Thomson rehologies. Also, comparative analyses between the two SLS formulations and the simpler Kelvin–Voigt and Maxwell models reveal distinct rheological influences on torsional wave propagation. The findings portray high sensitivity of torsional wave characteristics toward viscoelastic relaxation parameters, offering valuable insight into the design and optimization of tubular ultrasonic waveguides and semiconductor-based acoustic devices where precise damping control is essential.
Random defects in rock masses introduce uncertainties in their mechanical responses and failure behaviors. To explore this, a finite element cohesive zone model (FEM-CZM) is developed, incorporating random hole and mineral distributions, alongside a split Hopkinson pressure bar system and dynamic Brazilian splitting simulations. This approach systematically analyzes the impact of hole ratio (HR) on the dynamic mechanical behavior and crack evolution of sandstone. Results indicate that as HR increases, strain rate (SR) and the proportion of tensile cracks rise monotonically, while dynamic Brazilian tensile strength (D-BTS), damage dissipation energy of cohesive elements (ALLDMD), number of cracks (NC), and proportion of shear cracks decline. Specifically, SR and NC show a linear relationship with HR, while D-BTS and ALLDMD follow a quadratic relationship. Furthermore, the results demonstrate that the effect of increasing SR on D-BTS, ALLDMD, and NC mirrors the effect of increasing HR. As HR increases, the failure mode transitions from multi-path to single-dominant crack propagation, with significant changes in the distribution of tensile and shear cracks. Analysis of the maximum principal stress and displacement fields reveals the full process of crack nucleation, growth, and coalescence.
Identifying multi-defect is a challenging problem in structural health monitoring. An inverse algorithm that cooperates with the numerical manifold method (NMM) and a whale algorithm optimized-back propagation (WA-BP) neural network is developed to detect the multi-defect in heat conduction problems. Leveraging its distinctive dual-cover system, the NMM provides a convenient and accurate solution for forward modeling of multi-defect scenarios. The WA, serving as a global optimization technique, synergizes with the BP neural network to form a mutually beneficial algorithm, enhancing the convergence performance of the WA and preventing BP from falling into a local trap. To train the WA-BP neural network, a database is first constructed using NMM-based boundary temperatures of sampling points, along with corresponding predefined defect configurations, after which the task of defect prediction is executed. Validation through representative cases, a single-edge crack, double cracks, and crack-hole coexistence, demonstrates that the proposed method achieves superior accuracy and robustness compared to standalone BP networks. This streamlined approach holds significant potential for addressing multi-defect identification challenges in engineering applications.
The purpose of this study is to examine the out-of-plane free and forced vibration responses of axially functionally graded (AFG) curved beams resting on the Pasternak foundation. The dynamic analysis of beams with circular, parabolic, and sinusoidal shapes is carried out within the framework of Timoshenko beam theory. The curved-axis kinematics are defined using the Frenet–Serret frame, and the system’s differential equations are obtained from the equilibrium, compatibility, and constitutive equations. A unified method based on the combination of the Laplace transform and the complementary functions method (CFM) is used to analyze the damped and undamped vibration response of AFG curved beams. The viscoelastic behavior has been included in the formulation via the Kelvin damping model. Unlike previous isolated models, the primary novelty of this work lies in the simultaneous integration of out-of-plane spatial kinematics, arbitrary variable curvatures, and foundation interactions into a single, discretization-free state-space framework for continuous AFG beams. The results indicate that curvature distribution, material gradient index, radius-to-thickness ratio, boundary conditions, foundation parameters, and damping effects play a significant role in natural frequencies and transient dynamic response for curved beams resting on a Pasternak foundation.
In this paper, a finite element (FE) solution based on the modified strain gradient theory (MSGT) for size-dependent nonlinear bending analysis of ideal functionally graded graphene platelet-reinforced nanocomposite (FG-GPLRC) circular/annular microplates with smooth and continuous distributions of GPLs is compared with the modified couple stress theory (MCST). The effective Young’s modulus and Poisson’s ratio of the FG-GPLRC microplates are computed by the Halpin–Tsai (H–T) model and rule of mixtures (ROM), respectively. The strain–displacement relation and stress resultants are determined according to the surface fundamental form. The energy functional of the FG-GPLRC microplate is formulated based on the principle of virtual work and then solved numerically using the nonlinear FE method (FEM). Numerical results are examined to evaluate the influences of length scale parameters on the nonlinear bending response of FG-GPLRC microplates with different GPL patterns, weight fractions, and geometries. For l/h = 1.0, the nonlinear displacement results calculated using MSGT are consistently lower than those calculated using MCST, by approximately 2.7–3.0 times for clamped circular microplates and 3.8–4.1 times for clamped-pinned annular microplates. The results from these two theories diverge significantly under conditions with a small thickness-to-length scale ratio.
Conventional finite element methods face significant challenges in the lower bound limit analysis of thin plates, primarily due to the strict C1 continuity requirement and high sensitivity to mesh distortion. To overcome these issues, this study proposes a novel lower bound limit analysis method for thin plates based on a generalized conforming element developed using the quadrilateral area coordinate (QAC) method. Because the consistently linear transformation between the area and Cartesian coordinates, the proposed element maintains high numerical accuracy even under severely distorted meshes. The principle of virtual work is then employed to weakly enforce the equilibrium conditions for the self-equilibrated moment field. On this basis, a lower bound analysis framework is established following the lower bound theorem of plastic limit analysis, which maximizes the limit load multiplier subject to two essential constraints, namely the equilibrium conditions of a self-equilibrated moment field and the von Mises yield criterion. The von Mises yield criterion is reformulated into second-order cone constraints, thereby leading to a standard second-order cone programming (SOCP) problem that is efficiently solved using the primal-dual interior-point method as implemented in MOSEK. Numerical results validate the rationality and effectiveness of the proposed method, demonstrating superior accuracy and robustness even for severely distorted meshes.
The rotating sandwich cylindrical shell with bolt connection is a common substructure in aerospace. Due to the complexity of actual working conditions, bolts tend to loosen, resulting in connection detuning. To explore the failure mechanism and variation law of bolt connection detuning, a general semi-analytical dynamic model for the bolted composite sandwich cylindrical–cylindrical shell structure under rotational conditions is established. The model is constructed with a functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) core and fiber-reinforced composite (FRC) face sheets, which combines the advantages of lightweight, high specific strength, and high stiffness. With the aim of fully investigating the detuning behaviors of the bolt connection, a discontinuous artificial spring method is utilized. Then, the displacement continuity assumption of the layerwise theory and the first-order shear deformation theory (FSTD) are used to establish the equation of motion. According to the Rayleigh–Ritz method, the traveling wave vibration characteristics of the bolted shell structure are solved by the state-space method. Through extensive comparisons with experimental results in the literature, the accuracy and rationality of the model are fully verified. The modeling and solution methods proposed in this paper provide valuable theoretical references and engineering guidance for the application of FGP-GPLRC-FRC cylindrical–cylindrical sandwich shell structures in aerospace.
Large floating rafts with variable cross-sections and perforated sandwich layers are extensively used for mechanical noise control, yet simplified modeling methods that preserve the intrinsic mechanical properties of the sandwich structure for marine applications have received limited attention. This study proposes a novel semi-analytical method that establishes a simplified computational model (3D-MHM) for large floating rafts using a multilevel homogenization model, enabling efficient and highly accurate static and vibrational predictions of static and vibrational characteristics. This approach addresses the computational challenges of traditional numerical methods while accurately capturing key structural responses including structural displacement, strain, and natural frequency. A comparative analysis with 3D-FEM and 2D-traditional equivalent model (2D-FSDT) shows that 3D-MHM is superior to 2D-FSDT in terms of accuracy and superior to 3D-FEM in terms of computational efficiency. The perforation geometry of the wall is described parametrically using Bézier curves, enabling more efficient analysis of the effects of perforation geometry and quantity on vibration performance and mechanical properties. Further comprehensive bending and natural frequency analyses were performed on variable-section floating rafts featuring typical openings. The results show that when the sandwich parameters are consistent, the proposed method remains well adapted to floating rafts with variable cross-sections and typical openings. The 3D-MHM achieves high accuracy (errors < 5
Biofilms are complex structures which are inhabited by numerous amount of different species of microorganisms. Due to their ubiquity, they influence human life on an everyday basis. It is therefore important to understand the interactions between different bacterial populations within a biofilm and their reactions to outside conditions. For this purpose, mathematical models and in silico experiments have proven themselves to be fundamental. In combination with in vitro and in vivo experiments, they can give more insights and focus researchers’ attention, reducing costs in the process. In this work, a comprehensive multi-species continuum-based model for the development of bacterial populations is presented. This model is capable of replicating a variety of different bacteria interactions with an arbitrary number of species, while still being comprehensive to encourage usage by researchers less familiar with mathematical modeling. In addition to a nutrient source, antibiotic agents and their effect on the biofilm can also be depicted. The model is derived using Hamilton’s principle of stationary action, ensuring thermodynamic consistency automatically. The numerical examples demonstrate the model’s capability to qualitatively reproduce complex interaction patterns.
The static and dynamic analysis of beams and plates resting on or embedded within an elastic half-space has attracted increasing attention due to their widespread applications in civil, mechanical, and geotechnical engineering. Achieving reliable and accurate designs requires either improving existing calculation methods or developing new approaches capable of more effectively capturing their static and dynamic behavior. This study investigates the dynamic behavior of rectangular plates resting on the surface of an elastic half-space with inertial properties according to Lamb’s model. A semi-analytical approach based on the Zhemochkin method is employed. This method combines the Ritz technique, used to evaluate plate deflections, and Green’s function for computing the surface displacements of the elastic half-space. The plate–foundation system is discretized into identical rectangular elements, whereby the continuous contact is replaced by partial contacts established at the centers of the elements while ensuring continuity of contact between them. The canonical equations incorporate all relevant parameters, including the mechanical and geometric properties of the plate and the foundation, reactive forces, inertial effects, plate deflections, and vertical surface displacements of the elastic half-space. After incorporating the relevant formulas, the mathematical transformations yield a matrix formulation enabling the determination of the reactive forces in the contact zone. Using the principles of elasticity theory, further quantities such as eigenfrequencies, natural modes, and dynamic responses under various external excitations are obtained. The accuracy and applicability of the proposed approach are demonstrated through validation against the modal superposition method and comparison with results obtained from Boussinesq’s model and the finite element method. The proposed methodology provides a versatile and efficient framework for the dynamic analysis of plate–foundation systems.
This study proposes an energy-based method for vibro-acoustic properties of functionally graded carbon nanotube-reinforced composite submerged cabins integrated with double-layer floating isolating system. In this method, a unified variational principle is developed not only to address mechanical coupling between isolating system and the cabin, but also to consider acoustic-structure coupling between the cabin and surrounding fluid. Arbitrary boundary conditions and various distributions for the composite material can also be considered. Based on the moderately thick plate or shell theory and Helmholtz equation, energy equations for the structural and acoustic domains are obtained, respectively. Fluid–structure coupling is effectively introduced using the work done by the acoustic pressure at the fluid–structure interface. Since the proposed unified variational principle has naturally taken the interface couplings into account, semi-analytical solutions can then be achieved by expanding the displacement and acoustic pressure components analytically in the circumferential direction and numerically in the axial direction. The vibro-acoustic control metrics are also obtained for the isolating system. The efficiency and accuracy of the presented method are validated through comparisons with published results and finite element analysis. The effects of material properties and key parameters of the isolating system on vibro-acoustic properties and control outcome are then studied.
This paper derives closed-form solutions for the static analysis of coupled shear walls with an arbitrary number of stiffening beams at arbitrary locations and with arbitrary properties, explicitly incorporating local wall shear deformation, for single- and multiple-bay configurations. Coupled shear walls derive their lateral efficiency from the interaction among four deformation mechanisms: Global bending and global shear of the system, and local bending and local shear of the walls, whose relative contribution governs both the total response and the effectiveness of the stiffening beams employed in tall buildings. Existing analytical formulations model the walls as Euler–Bernoulli beams, suppressing local shear; this assumption introduces systematic errors that grow with the cross sectional depth of both the walls and the coupling beams, while simultaneously restricting closed-form solutions to the single stiffening beam case, with no possibility of systematic extension to the general case. This work demonstrates that both limitations share a common root and are resolved simultaneously. By modeling the walls as Timoshenko beams through a physics-based derivation, the resulting governing equation is fourth-order, structurally consistent with the classical sandwich beam model, from which it recovers as a particular case upon suppression of the local shear stiffness. This equation admits an exact decomposition into three independent subsystems: A pure bending beam, a pure shear beam, and a bending–shear beam, whose linear combination exactly reproduces the total response under any static load profile, and which allows the lateral displacement and story drift to be decomposed into their three physical components: bending, shear, and interaction. The decomposition establishes two results that had not been analytically demonstrated: The stiffening beams act exclusively on the interaction component, leaving the bending and shear components strictly invariant regardless of their number, location, or stiffness; and local shear acts exclusively on the shear component, without affecting the interaction component. Since only the bending–shear subsystem carries the discontinuities introduced by the stiffening beams, the general problem reduces to a linear algebraic system of four equations per stiffening beam, from which closed-form solutions are derived for lateral displacement, interstory drift, additional axial force, shear flow, and degree of coupling under uniform, triangular, and concentrated loads. Validation against finite element models confirms errors below 1.2
A comprehensive numerical framework is presented to study the geometrically nonlinear free vibration behavior of functionally graded (FG) microplates with arbitrary shapes, considering size-dependent effects within Mindlin’s strain-gradient elasticity theory. The proposed formulation employs the first-order shear deformation plate theory in conjunction with Hamilton’s principle to derive the general nonlinear governing equations. The strain-gradient tensors and their conjugate higher-order stresses are represented in an efficient vector–matrix form, enabling a computationally tractable implementation of the variational differential quadrature (VDQ) method for domains of irregular geometry. By assigning appropriate gradient-based material parameters, the developed model can seamlessly degenerate to simplified size-dependent continuum theories or recover the predictions of the classical theory. The free vibration response is determined by solving the resulting nonlinear eigenvalue problem using a reduced-order Galerkin approach followed by a time-periodic discretization and the pseudo arc-length method. Parametric studies are carried out to examine the influence of key factors, including geometrical shape, boundary conditions, FG index, and length scale parameters, on the fundamental frequencies and nonlinear frequency–amplitude relations. The results highlight significant sensitivity of the nonlinear vibration response to both the material gradation and the microscale length parameters, underscoring the necessity of using higher-order strain-gradient models for accurate prediction of FG microplate dynamics.
This paper presents a fracture mechanics analysis of a composite plate subjected to transient hygrothermal loading. The plate is subjected to sudden reductions in surface moisture content and temperature, resulting in transient hygrothermal stresses. The coupled moisture and heat diffusion through the plate thickness is solved analytically, and the resulting stress field in the uncracked plate is determined. Using superposition, the transient mode I stress intensity factor is evaluated via a weight function method. The peak stress intensity factor is systematically investigated as a function of crack length and plate thickness. Based on these results, fracture-mechanics-based design criteria are established, yielding simple empirical formulas for the critical moisture and temperature drops that can be sustained without crack propagation. These formulas provide a practical tool for the rapid assessment of the structural integrity of composites exposed to transient hygrothermal environments. The analytical results can also serve as benchmark solutions for validating other numerical methods, such as finite element analysis, or for comparison with experimental results.
In this paper, the problem of delaminated doubly-curved composite shells is taken into consideration including variable radii of curvature. The mechanical model was built-up based on the method of four equivalent single layers using the first- and second-order shear deformation shell theories. The governing equations were derived through the principle of virtual work for the delaminated and intact parts. The differential quadrature method was applied to solve the equations for three different delamination scenarios. Besides, the geometry of the shells was varied, too. In this respect, the parabola and ellipse profiles were utilized. In the first stage the deflections and their convergence were taken into account and the comparison with finite element model results was brought to the stage. The second stage was dedicated to the calculation of the J-integral and its mode-II and mode-III components over the four delamination fronts of the embedded rectangular delamination. Based on the fracture mechanical analysis and the maxima of the J-integral distributions, the location of delamination initiation points and the order of initiation were determined. The maximum value of the total energy release rate of the shells with ellipse profile varies between 7.3 and 98.6
Hydrogen gas flowing through pipes permeates through the pipe wall and induces compressive stress within the pipe material. This phenomenon, together with hydrogen embrittlement, reduces the pipe strength. This article examined the flow-induced buckling vibration response of a functionally graded pipe conveying hydrogen gas on a Pasternak foundation. The hydrogenation stress in the pipe material was derived by modifying Stashchuk and Dorosh's hydrogen stress model of a cylindrical metal block. The dynamic model of the hydrogen conveying pipe was developed using the Reddy–Bickford third-order beam theory, incorporating the hydrogenation stress. A comparison study was undertaken, and the results indicate that the present derivation is consistent with the model based on Timoshenko theory when a small-bore, thin-walled pipeline is considered. However, further comparison using a large-bore, thick-wall pipeline, the present model predicts higher values of the critical velocity and the initial compression. This study also examines the effect of hydrogenation, temperature, and Pasternak parameter on the buckling characteristics of the pipelines. The results show that hydrogenation and thermal load lower the pipeline's resistance to buckling. Also, hydrogen pressure and fluid velocity raised the likelihood of buckling in the pipe. Comparing the buckling of FGM and steel, the values of the critical buckling parameters were observed to be higher in FGM than in steel. The presence of ceramics reduces the chances of buckling in the FGM pipe.
