Archive of Applied Mechanics最新文献

In the present study, a series of lattice structures with Gyroid minimal surfaces were meticulously designed to incorporate linear density gradients and two distinct trigonometric function-based density gradients. These advanced architectures were subsequently compared and contrasted with a uniform lattice sandwich structure. The mechanical behavior and energy absorption characteristics of the four lattice sandwich structures were rigorously investigated through a combination of experimental testing and finite element analysis (FEA). The results of this comprehensive analysis revealed that during compression, all four gradient lattice structures exhibited varying degrees of shear slip, which manifested as discernible discrepancies in their respective stress–strain curves. Relative to the uniform lattice structure, the linear gradient lattice sandwich structure exhibited an enhancement in elastic modulus by 1.69%, while the square sine function gradient lattice sandwich structure showed a significant increase of 14.45% in elastic modulus. Conversely, the square cosine function gradient lattice sandwich structure experienced a reduction in elastic modulus by 9.61%. Employing either a linear gradient or a square sine function density gradient design was found to augment the load-bearing capacity of the uniform lattice structure. Notably, when the strain in the uniform structure reached densification strain, it absorbed energy exceeding 5.842 MJ/m³, indicating superior energy absorption capabilities among the four structures examined, thus rendering it particularly suitable for applications where high energy absorption is imperative. Furthermore, finite element simulations were conducted to validate the experimental findings, and the simulation results demonstrated a high degree of correlation with the experimental data, with discrepancies less than 6%, thereby confirming the reliability of the FEA model in predicting the performance of these intricate lattice structures.

The reduced multibody system transfer matrix method is a completely recursive method utilizing joint coordinates and applicable for evaluating the generalized accelerations of a multibody system at any given moment, provided that the generalized coordinates and velocities are known. For an open-loop multi-rigid-body system, the generalized coordinates of the system are composed of the generalized relative coordinates of the joint elements. Typically, for each joint element, the dimension of the generalized relative coordinates is equal to its relative motion degrees of freedom, leading to minimum dimension of the generalized coordinates of the system, which is equal to the degrees of freedom of the system. However, this may result in singularity for a ball-and-socket joint element when evaluating its generalized accelerations if any triad of Euler angles is utilized as its generalized relative coordinates. The tetrad Euler parameters are an alternative to Euler angles to resolve such a singular problem, which is a common practice in the dynamics approaches using body coordinates as generalized coordinates; nevertheless, it has not been observed in the completely recursive methods with joint coordinates. In this paper, the self-constraint equations of Euler parameters are taken into account to establish the corresponding reduced transfer equations characterized by a symmetric generalized inertial matrix, which are in completely recursive form. Fundamental numerical stability analyses are conducted via condition numbers of corresponding matrices, demonstrating that employing Euler parameters to describe the relative kinematics of a ball-and-socket joint element enhances numerical stability compared to Euler angles.

The aim of the present work is to discuss the fractional mass-spring system with damping and driving force, considering a simple modification to the fractional derivatives with a non-singular kernel of the Atangana–Baleanu and Caputo–Fabrizio types. We introduce two novel modified fractional derivatives that offer advantages when the fractional differential equations involve higher-order fractional derivatives of order (1+alpha ) or (alpha +1), with (0<alpha <1). Previous definitions of fractional derivatives with non-singular kernel do not have a unique definition, leading to significant inconsistencies. One of the main results of the present work is that the proposed modifications provide a unique result for the fractional-order derivatives (1+alpha ) and (alpha +1). Additionally, we apply these two novel fractional derivatives to the fractional mass-spring system with damping and driving force. In the case of the modified Caputo–Fabrizio fractional derivative, novel analytical solutions have been constructed, showing interesting oscillating time evolution with a transient term not previously reported. This transient term features an initial nonzero oscillating return away from the equilibrium position. For the modified Atangana–Baleanu fractional derivative, the numerical solutions also exhibit this nonzero oscillating return away from the equilibrium position. These results are not present when using the Caputo singular kernel derivative, as demonstrated in the comparison figures reported here.

The control of the drag, noise, and vibration of underwater vehicles has always been a hot topic, causing the study of skin with multiple functions to become a development trend. In the present paper the vibration isolation and sound radiation reduction characteristic of a multiple functions skin, micro-floating raft array skin (MFRAS), are assessed by a mathematical model. The mathematical model is developed based on the thin plate theory and the effective medium theory and validated by the finite element model and reference. The structural parameters of MFRAS have been discussed and optimized by orthogonal experiment design with the evaluation index, the average value of the mean square velocity level. The results show that the MFRAS can isolate the vibration transmission of internal equipment by mismatched impedance between MFRAS and plate, and then reduce the sound radiation. The optimized MFRAS can reduce the mean square velocity level by 1.35 dB and the sound radiation power level by 2.47 dB within the frequency range of 10–2000 Hz compared with the equal weight free damping layer.

In this paper, a formulation of reduced-order finite element (FE) model is presented for geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation and harmonic balance method. The main focus is to formulate the nonlinear reduced-order models (ROMs) in the time and frequency domain without involving the corresponding full-order FE models, and it is carried out by means of a special factorization of the nonlinear strain–displacement matrix. Furthermore, a methodology for the enrichment of reduction basis (RB) over that obtained from conventional approaches is presented where the proper orthogonal decomposition method is utilized by comprising the correlation matrix as the union of stiffness-normalized reduction basis vectors and the corresponding static derivatives. The results reveal a significantly reduced computational time due to the formulation of the nonlinear ROMs without involving the full-order FE model. A good accuracy of the nonlinear ROMs of viscoelastic structures is also achieved through the present method of enrichment of RB.

The mechanic-electro coupling overlapping finite element method (OFEM) is proposed to improve the accuracy in solving the mechanical characteristics of piezoelectric structures. Based on the basic equations and boundary conditions of piezoelectric materials, overlapping triangle elements are used to discretize the solution domain of piezoelectric structures, and the displacement function and potential function of the mechanic-electro coupling OFEM are constructed through local interpolation. The control equation of the mechanic-electro coupling OFEM is derived using the variation principle. The accuracy and validity of this method are verified by comparing with the reference solution and analytical solution in patch test and piezoelectric patch bending test. The static characteristics of the cantilever-typed piezoelectric sensor model, the rectangular plate with one-sided piezoelectric patch configuration, and the hole-containing piezoelectric energy harvester model are analyzed. The mechanic-electro coupling OFEM has high engineering value and broad application prospects in analyzing the structural mechanical properties of intelligent piezoelectric components.

This paper dealt with the vibration characteristics of an auxetic rectangular plate under in-plane compression. Firstly, the equivalent bending stiffness matrix of a star-shaped auxetic plate was obtained using Castigliano's theorem and the homogenization technique. Then, employing the classical plate theory (CPT) in conjunction with the Rayleigh–Ritz method, the natural frequencies of auxetic plate were extracted. The chebyshev polynomial series has been selected to define the assumed displacement fields of the plate. Convergence study for the Rayleigh–Ritz method was conducted. The accuracy of the proposed mathematical model for the star-shaped auxetic plate was validated using the results from a finite element analysis (FEA). Effects of unit cell geometric parameters on the natural frequencies of the plate were examined. The auxeticity angle of star-shaped pattern had a significant effect on the natural frequencies. The present approach can be extended into other auxetic patterns, such as re-entrant bowtie auxetics.

Based on the surface elasticity theory combined with the theories of Kirchhoff plate and Mindlin plate, the influences of surface effects on the buckling and post-buckling behaviors of nano-laminates are studied. Analytical solutions for critical buckling loads under uniaxial and biaxial compressions are obtained. Furthermore, approximate solutions for critical post-buckling loads under moveable and immoveable edge conditions are provided by using the Galerkin’s method. Numerical examples are given to study the influences of thickness, number of layers, surface parameters and the length of the nano-laminates on buckling and post-buckling critical loads. Results obtained indicate that the surface/interface energy is connected with the number of layers. In addition, the effects of the surface/interface energy on the critical loads enhance through increasing the length of the laminates but reduce by increasing the thickness. Mechanical model, analytical method and conclusions of this work are helpful for designing and examining the stability of the nano-laminates and nanoscale devices.

A theoretical model was established to investigate the interaction between hydrogen clusters and edge dislocations emitted from a semi-elliptical surface crack tip in deformed nanometallic materials. The model’s solution was obtained by using the complex method, and the influence of the concentration and location of hydrogen clusters, temperature, crack shape, material constants, and the dislocation emission angle on the critical stress intensity factor (SIFs) corresponding to the first dislocation emission from crack tips was investigated through numerical analysis. The results show that dislocations are easily emitted from the crack tip at high hydrogen concentration, and hydrogen clusters close to the crack tip will hinder the emission of dislocations from its crack tip. When considering the influence of hydrogen cluster, an increase in temperature, an extension of crack length or an increase in crack tip curvature radius can all make the emission of dislocations at the crack tip difficult, thereby reducing the toughness of the material caused by dislocation emission.

In computational fluid dynamics, controlling grid scale is efficiently managed using the Advancing Front Technique (AFT). However, achieving grid generation convergence within a three-dimensional (3D) computational domain remains challenging, primarily due to excessive intersection judgments that significantly reduce efficiency. This paper addresses the non-convergence issues inherent in the 3D AFT and proposes preliminary solutions to enhance algorithm robustness while reducing intersection judgments. We introduce two neural networks trained on the backpropagation (BP) algorithms, Line-ANN and Plane-ANN, specifically designed for integration with AFT. These networks are individually combined with traditional 3D AFT to develop two enhanced methods. We assess these methods by comparing grid quality and time consumption against traditional AFT approaches. The results demonstrate that integrating Plane-ANN and Line-ANN with AFT improves overall efficiency by approximately 55% and 36%, respectively, thereby significantly enhancing grid generation efficiency.