Archive of Applied Mechanics最新文献

Rayleigh-type surface waves propagating in a magneto-elastic half-space containing voids are studied. Dispersion equation is derived under suitably constructed boundary conditions, which involves elastic, electro-magnetic, void parameters and angular frequency, but contains radicals, making it difficult to solve analytically. However, under limiting frequencies, the dispersion equation is analyzed and discussed. The effect of various parameters on phase velocity of propagating Rayleigh-type surface waves is investigated and shown graphically for a particular model. The effect of induced electric field on considered surface waves is also studied and explained. It is shown that the particles near the boundary surface move in an elliptic manner. However, if there is no phase difference between the displacement components, then we have a degenerate case. Some special cases of dispersion relation are also deduced from the present formulation.

In this paper, the static and dynamic analysis of the higher-order shear deformation nanobeam is investigated within the framework of the two-phase local/nonlocal integral model, in which, the stress is described as the integral convolution form between the strain field and a decay kernel function to address the long-range force interactions in the domain. Based on the principle of minimum potential energy, the finite element formulation of the nonlocal higher-order shear deformation theory nanobeams is derived in a general sense through finite element method (FEM). The explicit expressions of the stiffness, geometric stiffness and mass stiffness matrix of the higher-order shear deformation theory nanobeams are derived directly. The efficiency and accuracy of the developed finite element model of higher-order shear deformation nanobeam are validated by conducting a comparation with the existing analysis results in the researches. Furthermore, under different loading and supported conditions, the effect of nonlocal parameter, nonlocal phase parameter and slenderness ratio on the bending, buckling and free vibration responses of higher-order shear deformation theory nanobeams is investigated in detail.

A nonlinear phenomenological model of flexoelectricity in thermoelastic solids is presented within the frame of continuum mechanics and extended thermodynamics, incorporating the quasi-electrostatic approximation where the time derivative of the electric displacement vector can be neglected in Maxwell–Ampère’s law. An expression for the energy flux is proposed, including many internal variables. An advantage of the proposed model is that it presents a unified approach to study several thermo-electromechanical couplings, including electrostriction, piezoelectricity, dependence of entropy and spontaneous polarization on flexoelectricity, among others. The model may be of interest in revealing the effects of such couplings on the properties of polarizable media, in particular ferroelectrics, when simple boundary conditions prevail. For a fully dynamic description of flexoelectricity, Hamilton’s principle and the variational principle for external forces should be used instead.

Abstract

The cortical bone is a hierarchical composite material that, at the microscale, is segmented in an interstitial matrix, cement line, osteons, and Haversian canals. The cracking of the structure at this scale directly influences the macro behavior, and, in this context, the cement line has a protagonist role. In this sense, this work aims to simulate the crack initiation and propagation processes via cortical bone microstructure modeling with a two-dimensional mesh fragmentation technique that captures the mechanical relevance of its constituents. In this approach, high aspect ratio elements are inserted between the regular constant strain triangle finite elements to define potential crack paths a priori. The crack behavior is described using a composed damage model with two scalar damage variables, which is integrated by an implicit-explicit (Impl-Ex) scheme to avoid convergence problems usually found in numerical simulations involving multiple cracks. The approach’s capability of modeling the failure process in cortical bone microstructure is investigated by simulating four conceptual problems and one example based on a digital image of an experimental test. The results obtained in terms of crack pattern and failure mechanisms agree with those described in the literature, demonstrating that the numerical tool is promising to simulate the complex failure mechanisms in cortical bone, considering the properties of its distinct phases.

For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments.

By using carbon nanotubes (CNTs) to reinforce face sheets, mechanical performance of sandwich structures can be significantly improved. However, thermal expansion behaviors of sandwich structures reinforced by the CNTs are rarely studied in published literature. For a sandwich structure under uniform temperature rise, this is a typical three-dimensional (3D) issue as transverse normal deformation plays an important role. To study such issue, a novel higher-order model for the functionally graded (FG) sandwich plates has been developed, in which continuity conditions of transverse shear stresses at interfaces have been enhanced by considering the functionally graded alteration of material properties in the face sheets. After performance of the proposed model is verified by the 3D elasticity solutions and the 3D-FEM results, present model is extended to predict thermal response of sandwich plates reinforced by the CNTs. Moreover, the influence law of the CNTs on thermal behaviors has been investigated, in which volume fractions of the CNTs have a significant impact on thermal behaviors, and stiffness of sandwich structures can be obviously improved by changing the distributing profiles of the CNTs along thickness. However, the stresses display the sudden change along thickness direction of face sheets, which are harmful to structural safety. Therefore, before the CNTs are utilized to improve stiffness of sandwich structure, it is very necessary to predict thermal behaviors of sandwich structures by using an accurate and efficient model. This work can provide an effective model to design distributing profiles of the CNTs according to engineering requirements.

Composite corrugated plates have a great potential in the application to morphing wings. However, it takes high computational cost to conduct flutter analysis with detailed 3D finite element models due to its structural complexity. In this study, an analytical method is proposed for flutter stability analysis of composite corrugated plates in supersonic flow. The trapezoidal and sinusoidal composite corrugated plate is homogenized as an equivalent anisotropic plate based on an energy approach. The flutter model for the composite corrugated plate is derived based on Kirchhoff plate theory and the equivalent stiffness properties. The unsteady aerodynamic pressure is evaluated by using the supersonic piston theory in which the corrugated section is taken into account. Hamilton's principle with the assumed mode method is applied to formulate the aeroelastic equation of the composite corrugated plate. The eigenvalue criterion is utilized to reveal the flutter mechanism and evaluate the stability of composite corrugated plates in supersonic flow. The accuracy and reliability of the present method are verified by comparing aeroelastic responses with those obtained from commercial software. Parametric studies concerning different parametric variables are also conducted. It is shown that the proposed method has sufficient accuracy and requires less computational effort, providing a theoretical basis for the utilization of trapezoidal and sinusoidal composite corrugated plates in morphing wings.

Abstract

This manuscript introduces a novel mathematical formulation employing fractional-order principles to analyze the response of skin tissue exposed to ramp-type heating within the framework of the refined Lord–Shulman generalized thermoelasticity model. The classical, simple Lord–Shulman, and refined Lord–Shulman models are each examined. The governing equations for these three models are derived, and a general solution for the initial and boundary condition problem is obtained using the Laplace transform approach and its inverse. Numerical results are illustrated through figures, providing a comparative analysis across various theories and fractional-order values to elucidate the impact on temperature, displacement, and dilatation distributions. The numerical and graphical exploration of the influence of ramp-type heat on temperature, displacement, and dilatation distributions is conducted, considering different theoretical frameworks. The reduction in the conductivity caused by the fractional parameter and its ensuing effects on temperature, displacement, and stress are determined.

The analysis of the mathematical and mechanical properties of thermoelastic coupling tensors in anisotropic laminates is the topic of this paper. Some theoretical results concerning the compliance tensors are shown and their mechanical consequences analyzed. Moreover, the case of thermally stable laminates, important for practical applications, is also considered. The study is carried out in the framework of the polar method, a mathematical formalism particularly well-suited for the analysis of planar anisotropic problems, introduced by Prof. G. Verchery in 1979.

Abstract

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations.