Archive of Applied Mechanics最新文献

Rotor stability analysis is essential to ensure rotating composite structures' safe and efficient operation. In this paper, the stability analysis of a hybrid composite shaft with two disks placed on elastic supports is investigated by the three-node finite element method. The strain potential energy of the hybrid composite shaft is calculated by considering the Timoshenko beam theory and using shape functions and the ABD matrix's effective components. The governing equations of the composite rotor are derived by replacing the kinetic energy of the shaft and disks, the strain potential energy, and the force of the bearings in the Lagrange equation. The equations of motion obtained from the finite element method are coded in the state space using MATLAB script. Their eigenvalues are calculated as a function of the rotor rotation speed, and the instability threshold of the composite rotor is evaluated. To validate the simulation results of the composite shaft in the free–free state in the ANSYS software, a hybrid composite shaft is made using the filament winding method, and its natural frequencies are extracted by performing the experimental modal analysis test. The instability threshold of the non-hybrid composite rotor of the presented model in different stacking sequences is compared with the results of the previous studies, and the validity of the three-node finite element method is confirmed. Finally, the effect of the fiber angle and the arrangement of the layers in the usage of carbon/epoxy and glass/epoxy in a specific stacking sequence on the stability of the hybrid composite rotor is studied.

In this work, a novel quadrilateral four-node element capable of simulating the axisymmetric-torsion deformation of small-scale solids of revolution is developed based on the consistent couple stress theory (CCST). To establish the element formulation, the C¹ requirement for displacement in the CCST is enforced in weak sense by using the penalty function method and the independent nodal rotation degrees of freedom are introduced into element construction to approximate the mechanical rotation fields. Besides, the stress functions that can satisfy the relevant equilibrium equation of the axisymmetric-torsion deformation are adopted as the basic functions for designing the element’s stress trial function. Several numerical tests are carried out and the results are compared to the solutions obtained using the analytical method or hexahedral solid element from the literature. It is shown that the new element exhibits good accuracy and captures the size dependences efficiently in prediction of the axisymmetric-torsion behavior of small-scale solids.

The present paper investigates the accuracy of the finite element method (FEM) in stochastic setting. The performance of the FEM for solving the transversal vibration eigenvalue problem of a uniform, homogeneous beam in presence of uncertainties is considered aiming to establish how accurate the method is in predicting the beam’s reliability as well as its probability of failure. An explicit solution is first provided for the approximate fundamental frequency of the beam as a function of the number of elements, for different boundary conditions when the mesh is uniform along the length of the beam allowing an analytical evaluation of the structural reliability and the probability of failure when, e.g., the random uncertainty in the Young modulus of the beam is considered. The exact solution of the vibration problem derived within Bernoulli-Euler beam theory is exploited to evaluate the actual reliability as well as the actual probability of failure which, being compared with required reliability or allowed probability of failure thresholds, permits to verify the accuracy of the FEM in the probabilistic context and to warn about “unreliability of reliability conclusions”.

The free vibration and traveling wave stability of a rotating ferromagnetic functionally graded cylindrical shell in magnetic and temperature fields are explored. The geometric and physical equations are determined within the framework of the Love’s theory. The expressions of kinetic energy and strain energy are obtained by considering temperature and rotation effects. The magnetoelastic theory is employed to establish a model of magnetic force. By using Hamilton’s principle and Galerkin truncation, the governing equations are obtained. The effects of different parameters on the natural frequencies of forward and backward waves are determined. It is found that the natural frequency undergoes separation of forward and backward waves due to the Coriolis force; with increase in the circumferential wave number, the frequency shows a trend of first decreasing and then increasing. The coupling effect of the magnetic induction intensity, rotational speed, power–law index, and thickness-to-diameter ratio leads to the nonlinear trend of frequencies. In addition, the influence of different parameter variations on the traveling wave stability is discussed.

Damage growth phenomenon in sheet metal forming processes is one of the most important issues in the manufacturing industries. Predicting the onset and location of crack can help engineers to postpone the failure as well as to produce safe parts. In this research, first, six different calibration methods are employed for the Bao-Wierzbicki damage criterion. Then, to evaluate the accuracy of the calibration approaches, a few conventional sheet metal forming processes with the positive stress triaxiality are numerically simulated. Finally, the numerical predicted results are compared with the empirical tests. The comparisons reveal that the hyperbolic quadratic hyperbolic 3 (HQH3) method is the best calibration approach, due to its accuracy and the fewer number of required experimental tests for the calibration.

This research adopted a micromechanical modeling approach to elaborate the debonded layered structure behavior under the combined mechanical and hygro-thermal loading. The structural distortion under the combined loadings has been modeled through Green’s strain and Lagrangian reference frame. In addition, the structural deformation has been modeled using two types of kinematic models with and without stretching term effect. Moreover, the corrugated composite properties are evaluated with the help of a micromechanical model due to the hygro-thermal effect considering the individual volume fractions and moisture retention ratio. The final form of governing equations is obtained using variational technique and solved numerically (finite element steps and direct iterative method). The model validity and its repeatability are verified through the comparison study. The predicted numerical response differs from the literature data by a minimum of − 1.39% and a maximum of − 16.08%. Finally, a set of numerical examples has been solved to elaborate on the model’s adequacy and investigate the influence of delamination, environmental effects, and other input parameters related to the geometrical details of the composite components. Delamination in the curved panel affects linear and nonlinear dynamic responses regardless of size, position, or location. An increase in fiber volume fraction and aspect ratio (a/b) reduces both higher-order models dynamic linear and nonlinear responses.

It is necessary to accurately and efficiently calculate the wrinkling stresses of sandwich panels under in-plane compression. However, the simple equations used in engineering may obtain inaccurate results, whereas finite element methods with higher accuracy may be computationally expensive. This study proposes a new method for solving the wrinkling problem of sandwich panels using structural optimization theory at a low computational cost. A sandwich panel was divided into several virtual plies, which were assigned design variables to describe the vertical displacement during wrinkling. The wrinkling stress was obtained by minimizing the admissible in-plane compressive stress. The method was verified using finite element and experimental methods, as good agreement was found. The differences were less than 5% and 20% with the finite element and experimental results, respectively. Moreover, this method can easily compute the wrinkling stress of sandwich panels with functionally graded material cores with a little increase in computational cost. This method allows engineers to compute the wrinkling stress effectively and efficiently without the need for complex numerical models.

Self-actuated oscillation systems possess the unique ability to extract energy from their surroundings to sustain oscillation autonomously, which makes them ideal for applications in soft robotics, active actuators and smart devices. In contrast to conventional materials, mechanical metamaterials, known for their negative Poisson's ratio and volume expansion properties, can boost the functionality and performance of self-actuated systems. This theoretical study proposes an electrothermally-induced self-actuated oscillation system in liquid crystal elasomter (LCE) mechanical metamaterials under steady-state circuits and investigates its self-actuated mechanism and behavior. The electrothermal effect caused by the external electrical circuit enables LCE fibers to do net positive work. When the net positive work done by LCE fibers exactly compensates for the damping dissipation of the system, self-actuated oscillation can be triggered and maintained. The results indicate that self-actuated oscillation can be modulated and controlled by system parameters. The procedure can pave the path for designing active micromachine, energy harvester, medical devices and monitoring sensors.

This research presents an in-depth exploration of the vibrational performance exhibited by sandwich beams with variable thickness profiles. These beams undergo a gradual reduction in thickness along their length. The core material of these sandwich beams is constructed from FG cellular materials, while the facesheets are reinforced with carbon nanotubes. Due to the varying distribution patterns of these reinforcements concerning the beam’s height, it becomes essential to apply stress transformations at specific angles to accurately compute the equivalent material properties. The study employs both Hamilton’s principle and variational approach to derive the governing equations for motion, as well as the associated boundary conditions. To comprehensively assess the effects of various parameters such as geometry, porosity coefficient, diverse distribution patterns of porosity and carbon nanotubes, as well as the transformation angle on the natural frequencies, a robust numerical technique known as the differential quadrature method is employed to solve the derived equations. It is found that compared to beams with a constant thickness, tapered beams typically display lower frequencies. Also, if the reinforcements are not arranged in the upper and lower layers in the direction of changing the thickness, the results will have noticeable changes.

This study investigates the two-dimensional deformations within the framework of the two-temperature thermoelasticity theory, focusing on the interplay between laser pulse heating, acoustic pressure, and the resultant elastic material response. Our exploration is centered on the understanding of how acoustic waves, generated by laser pulses, influence the thermoelastic and mechanical behavior of materials. The role of acoustic pressure in modulating the thermoelastic response during laser pulse heating is investigated. Theoretical formulations are developed to describe the coupled evolution of temperature and deformation fields in the two-dimensional (2D) space. Employing normal mode analysis, the exact solutions of the main variations (wave propagation) of physical fields are obtained. Some boundary conditions are utilized for more accurate numerical simulations. The numerical results are discussed theoretically and the wave propagation of the physical quantities under study is represented graphically. The results obtained from this study have significant implications for various applications, including laser material processing, biomedical procedures, and non-destructive testing.