Mechanics Research Communications最新文献

The buckling of a thin film deposited on an infinitely rigid substrate and delaminated over a finite length is studied in the framework of the Föppl-von Kàrmàn theory of thin plates. Assuming the two edges of the ductile film can fold, an energy-based analysis of the different morphologies of the film has been carried out. Depending on the delamination length, the film can either be unfolded, partially folded at one edge or symmetrically folded at its two edges.

The bifurcation behavior of deployable structures has received significant attention from different fields. Apart from pin-jointed structures, origami, as a thriving inspiration for valuable and practical deployable structures, develops singular configurations along its kinematic paths. The kinematic behaviors of single vertex origami patterns are studied in this work. General four-crease patterns and symmetric six-crease patterns are thoroughly investigated based on the analytical solutions obtained by constraint equations. Moreover, the corresponding motion paths are described to discuss the bifurcation behavior. A comparative analysis of kinematic behaviors with the different actuating coordinates is performed. Three types of bifurcation are analyzed, concluding that three different motion paths cannot occur at the same time. The research findings of the present work can contribute to the development of novel deployable structures and mechanical systems.

An innovative composite bistable system (CBs) coupled of prestressed linear and buckled beams with fixed ends has been designed to enhance the damping and suppress the dynamic response. The dynamic equations of the system are derived by applying Hamilton's principle. When the amplitude of the harmonic excitation exceeds the critical value, the buckling beam of the bistable system enters a state of inter- and in-well combined oscillations. Chaotic motion is present. This motion disperses the vibrational energy over a wide frequency band. The vibration in the high-frequency range significantly enhances the dissipation of the viscoelastic layer, leading to an effective suppression of the system's vibration. Approximate analytical solutions and numerical validation of the chaotic and non-chaotic boundaries of the steady state vibration of the bistable system are carried out based on the harmonic balance method (HBM) and the Melnikov method. The Particle Swarm Optimisation (PSO)  algorithm is used to optimise system parameters for specific operating conditions. This optimisation process provides guidance for the design and improvement of CBs systems.

3D-printed composite structures employed in applications such as soft robotics, actuators, and artificial muscles typically experience different loading and deformation modes throughout their life cycle. Tailoring the mechanical properties and responses to those modes in an independent manner can significantly enhance performance. In this work, we propose a helical fiber embedded cylindrical matrix as a platform to independently tune the behavior under two loading modes — uniaxial extension without twist and torsion at a constant length. Using finite elements (FE), we study the influence of the helical geometry, the volume fraction, and the moduli of the matrix and the fiber on the stiffness and the constitutive behavior. Our findings reveal that the responses to tension and torsion can be programmed by an appropriate choice of geometrical and material parameters. For example, we show that one can achieve composites with the same stiffness and behavior under uniaxial extension but a wide range of responses to torsion. As a design guide, the wide range of properties and potential strengths that can be obtained in these composites are mapped. To demonstrate the validity of this design, composites embedded with a helical fiber were 3D-printed and tested under tension and torsion. The experimentally observed trends agree with the FE simulations. The design and the insights from this work can be used to enhance and optimize the performance of structures in various applications. For example, this composite design can be used in lattice structures to tune the local response.

The theory of layerwise beam, which considers both microstructure and flexoelectric effects, is used in the curvature-based flexoelectricity theory. The displacement field function of the layerwise beam model is given. The governing equations and boundary conditions are obtained using a variational formulation based on Hamilton's principle. Analytical solutions for static bending and free vibration of a simply supported layerwise beam are derived. Isogeometric analysis (IGA) with higher-order continuity considering the flexoelectric effect is presented to numerically solve the static bending and free vibration problems. The results obtained from the analytical and IGA approaches are compared through several examples in which the microstructure and flexoelectric effects on the mechanical responses of layerwise nanobeams are analyzed.

In this paper, an efficient topology optimization approach is developed for maximizing the fundamental natural frequency of extruded beams. Mass fraction and static compliance bounds are defined using inequality-type constraints in the optimization problem. An XFEM approach, previously proposed by the authors for analyzing beam elements, is extended herein to compute the natural frequencies of the beam. The method allows for 3D modeling of beams with a significant reduction in the number of degrees of freedom and therefore also yields efficient optimization procedure. This reduction is made possible by incorporating global enrichment functions in the longitudinal direction, which enables a significant reduction in the number of elements in that direction without loss of accuracy. A nonlinear optimization problem is formulated using continuous density-based design variables that represent the material distribution in the beam’s cross-section. The optimization problem is then solved using a gradient-based approach with analytical sensitivities. The well-known Solid Isotropic Material with Penalization (SIMP) method is used to acquire discrete solutions. We study the optimal design of short and long beams. It is shown that for short beams, localized vibration modes appear within the cross-section, leading to a significant distortion deformation mode of the cross-section. The optimized design of the long beam shows global deformation modes with an increase of 15% in the fundamental frequency compared with a non-optimized design consisting of a hollow rectangular cross-section with the same mass.

In this study, a Kelvin–Voigt fractional viscoelastic model is developed based on the two-variable refined plate theory (TV-RPT) to investigate the dynamic behavior of rectangular viscoelastic plates under support movement. The TV-RPT is a novel, simple, and efficient plate theory that provides accurate results for both thin and thick plates. The steady-state condition is governed by assuming the lower limit of the integral in the Riemann-Liouville fractional derivative to be negative infinity. After deriving the governing equation, an analytical solution based on the Navier method is employed for fully simply-supported viscoelastic plates. The proposed approach is validated by comparing the natural frequencies of viscoelastic and elastic plates with existing results in the literature. Additionally, the results obtained from TV-RPT and the classical plate theory (CPT) are compared. It is observed that both theories provide similar results for thin plates. However, for thicker plates, the amplitude and frequency of vibrations for TV-RPT are smaller and larger than those for CPT, respectively. The study also investigates the effects of fractional derivative order and damping coefficient on the frequency and amplitude of vibration.

Fluid flow through fractures is intimately linked to the fracture surfaces that define the void geometry through which fluids flow. Thus, an understanding of what controls fracture surface roughness is essential to the development of models for predicting fluid transport through fractured rock. The difficulty in predicting surface roughness arises from the complexity of rock which is inherently heterogeneous and nonuniform in composition, fabric, and structural components, even when samples are acquired from the same rock mass. Here, a benchmarked-simulation approach motivated from geo-architected 3D printed synthetic gypsum rocks is used to provide insight into the competing contributions from fabric and layering on fracture roughness formation. Simulation results from a discrete element model (Particle Flow Code, Itasca Consulting Group, Inc.) clearly indicate that the relative orientation between mineral layers and in-layer mineral fabric, and the variability in mineral bonding strengths determine whether anisotropic corrugated surfaces or isotropic surfaces are formed. Weak mineral layers oriented perpendicular to the applied load resulted in strong roughness anisotropy. Peak failure loads were found to vary up to 30% depending on the strength of the mineral fabric at the location of fracture initiation, which provides insight into the observed high variability in strength values of natural rock. The uniqueness of induced fracture roughness and peak failure load is intimately linked to layering, mineral fabric, and their distribution in the rock. These findings have important implications for any architected material fabricated through serial printing of layers with local compositional heterogeneity.

Continuum-like nonlocal deformation gradients have been constructed based on discrete simulation results. In this paper, the accuracy of the nonlocal deformation gradient based on different influence functions is examined for both representing material point deformation and mapping bonds. A new class of parameterized influence functions that accounts for both bond relative length and angle (with respect to a target bond) is proposed. Numerical example shows great accuracy of the nonlocal deformation gradient using the proposed influence functions in both representing material point deformation and mapping bonds. It is concluded that the proposed influence functions can be used to accurately capture bond-level continuum-like measures.