Acta Mechanica最新文献

Wave propagation through a saturated frozen soil layer sandwiched by two elastic soil half-spaces is investigated in this paper. The saturated frozen soil layer in the middle consists of a saturated three-phase medium of solid, liquid and ice, which is considered isotropic. Due to the presence of the three-phase medium, three types of longitudinal waves and two types of shear waves exist in saturated frozen soil. The concept of state vector is introduced. The state transition differential equation is derived based on the reduction of order of the motion equations, and the state transfer matrix is obtained by solving the state transition differential equation. By introducing the interface conditions between saturated frozen soil and elastic soil, the state transition matrix is simplified, and redundant state vectors are eliminated to establish the relationship between the incident wave, reflection wave and transmission wave. Two cases (incident P wave and incident SV wave) are considered, and the reflection and transmission amplitude ratios varying with the incident angle are calculated. The results indicate that the incident wave frequency, porosity, saturation and cementation parameters have a substantial influence on the reflection and transmission. This study provides a new research perspective for controlling the propagation of elastic waves in saturated frozen soils.

The same axis of rotation can be defined in different coordinate systems, leading to different form and different interpretation of the rotation matrix. This definition is particularly important in case of successive rotations due to the wide use of finite orientation parameters to define rigid- and flexible-body kinematics as well as deformation measures. As discussed in this paper, in case of successive rotations, the rotation axes can be defined using a single frame or multiple intermediate frames. As it is known, the single-frame method (SFM) and multi-frame method (MFM) lead to different order of multiplication of the rotation matrices. It is demonstrated that the coordinate system in which the rotation axis is defined determines the physical interpretation of the rotation matrix and deformation measures. In the SFM approach, the single frame can be global, cross section, or body frame. Nonetheless, the SFM sequence does not allow easy interpretation of the rotations as torsion and/or bending measures. In the MFM approach, on the other hand, the rotations are defined relative to intermediate frames; and such relative rotations can only be given physical interpretation as deformation measures in case of infinitesimal rotations. Such a physical interpretation is not valid in case of using noncommutative finite rotations. Regardless of which method (SFM or MFM) is used, the sequence of rotations cannot, in general, be reversed. Using Rodrigues formula with the analysis and results of this study, it is demonstrated that the noncommutativity problem is not attributed to the choice of the spatial orientation parameters but to the noncommutativity of the rotation matrices.

Based on the strong form of three-dimensional (3D) consistent couple stress theory (CCST), we develop a meshless differential reproducing kernel (DRK) point method for the static instability and free vibration behavior analyses of a one-directional nonhomogeneous microplate under simply supported conditions and subjected to uni- and bi-axial compression. By selecting the transverse stress and displacement components as primary variables and employing the double Fourier series expansion method, we obtain a set of Fundamental equations expressed in the thickness coordinate to address this issue. By incorporating the DRK interpolants into the Fundamental equations, we develop a meshless point method for analyzing the 3D size-dependent static instability and free vibration behaviors of the microplate. The accuracy and convergence rate of the meshless DRK point method are validated by comparing the solutions it produced with those obtained using a 3D approach documented in the Literature. The results demonstrate that the solutions obtained using our meshless DRK point method align excellently with the corresponding 3D solutions and converge rapidly. The effects of the aspect ratio, material length-scale parameter, length-to-thickness ratio, and inhomogeneity index are demonstrated to have a significant impact on the microplate’s natural frequency and critical load. Furthermore, the applicable range of the structure size for the CCST is recommended to be between 1× 10^–7 and 1 × 10^–3 m.

The backward-facing step (BFS) is an appropriate model for studying flow separation. In this study, controlling separation bubbles behind a curved edge BFS with plasma actuators was investigated experimentally in Reynolds numbers ranging from 17 × 10³ to 51 × 10³ (depending on step height). Smoke flow visualization experiments were conducted to analyze the flow pattern around a BFS in the presence of a plasma actuator. Pressure distributions were measured under a variety of situations and analyzed. Seven curved edges were created, with a radius of curvature ranging from 0 (a sharp edge) to 50 mm. The results reveal that the length of the separation bubble decreases as the radius of curvature increases. Another series of experiments were carried out for bigger radius of curvature, studying the location of the placed plasma. The location varies when the angle with respect to the center of curvature changes. Plasma actuators were mounted on the curvature at two different angles (0 and 20 degrees). Both plasma actuators were utilized simultaneously at angles of 0 and 20 degrees. The best results were obtained by putting two plasma actuators on curvature at the same moment, which results in lowering reattachment length. The separation bubble's length was also lowered by using a plasma actuator at a 20-degree angle according to the center of the radius of curvature.

This work aims to generalize the method of conditional moments (MCM), a statistical approach developed for classical elasticity, to the case of strain gradient elasticity and to evaluate the effective properties of random particulate composites within the simplified strain gradient elasticity theory. The problem of finding the effective constants is reduced to a system of stochastic differential equations based on the fundamental equations of linear elasticity, which are solved by the method of conditional moment functions. Closed-form expressions for the effective moduli of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities are derived. The effective properties obtained within strain gradient elasticity depend not only on the properties of constituents, their volume fraction, shape, and distribution of inhomogeneities, but also on their size, which is impossible in the frame of usual classical elasticity. As a numerical example, it is considered a special case of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities, where the materials of the matrix and the inhomogeneities are second gradient media. Variation of the normalized bulk and shear moduli of the particulate composite material as a function of volume fraction of inhomogeneity and as a function of inhomogeneity size is evaluated, analyzed, and compared in the context of other theoretical predictions.

An analytical-based methodology is developed for elastic analysis of a graphene origami enriched composite cylindrical sport equipment shell as pommel horse subjected to thermal and mechanical loads with clamped constraints. The shear deformable model is used as kinematic relation for deformation analysis of the graphene origami enriched composite shell. The novel proposed material can be used in the sport equipment and accessories with improved characteristics. The virtual work principle is developed to derive governing equations of elastic deformation with computation of strain energy and external work. The novel analytical solution is developed to derive a general solution method for clamped–clamped boundary conditions. The material characteristics are extracted from the Halpin–Tsai micromechanical model and rule of mixture. The mathematical method based on Eigenvalue–Eigenvector-based solution approach is developed to obtain the numerical results. The longitudinal and radial variation of the displacements, strains and stresses are presented. An investigation on the effect of folding and volume fraction is presented. An investigation on the effect of folding and volume fraction is presented. Comparison between the numerical values of the various stress components indicates that the circumferential stress is a dominant one among all stress components.

Based on the three-dimensional elasticity theory, the isogeometric analysis method was employed to investigate the thermal buckling behavior of composite laminated plates with irregular delaminations. The shape of the delamination was generated by rational cubic Bézier curves. By altering the control points and weights, delaminations of various shapes could be represented. Based on isogeometric analysis, three-dimensional non-uniform rational B-splines basis functions were used to describe the displacement field of the laminated plate. The eigenvalue equation of the laminated plate was derived using the principle of minimum potential energy. A multi-patch modeling approach was adopted to construct the delamination model, and the strong coupling method was used to connect the delaminated region and the intact region. This paper also considered the contact effect between the upper and lower interfaces of the delamination. The augmented Lagrangian method was employed to address the penetration problem between the upper and lower interfaces at the delamination during buckling. The results of this paper were compared with existing research results to verify the validity of the proposed method. Through a parametric study, the influence of the control points and weights of the delamination shape on the critical buckling temperature and buckling mode of the delaminated laminated plate was analyzed in detail.

Although some third-order shear deformation plate theories, including Levinson plate theory (LPT) and Reddy plate theory (RPT), are available, their computational complexity limits their application. Based on LPT, a single-variable third-order shear deformation theory, named the simplified LPT, is proposed by requiring vanishing torsional deformation along the thickness direction. The LPT is described by a sixth-order partial differential equation (PDE), whereas the simplified LPT is described by a fourth-order PDE, similar to that of classical plate theory (CPT). Following the CPT, the twisting moments are converted into shear forces in the boundary conditions of the simplified LPT. To further demonstrate the effectiveness of the simplified LPT, the free vibration analysis of Lévy-type plates is conducted, where two opposite edges are simply supported (or guided) while the remaining two edges are subject to arbitrary boundary conditions. Using the Lévy approach, the natural frequencies based on the CPT, Mindlin plate theory, LPT, RPT, and simplified LPT are compared. The numerical results indicate that the simplified LPT is effective and can be applied to thin, moderately thick, and thick plates. Consideration of shear deformation brings the results of the simplified LPT closer to those of LPT and RPT.

This article deals with the modeling and buckling analysis for two different types of toroidal sandwich shells made of a metal-based nanocomposite foam core and titanium alloy face sheets. The sandwich shell is analyzed with two different shapes including the convex shell (positive curvature) and concave shell (negative curvature). The convex/concave sandwich shells are subjected to three different kinds of mechanical loadings including the lateral pressure, axial compressive, and hydrostatic pressure. The core of sandwich shells consists of six aluminum layers with different values of porosity reinforced by graphene nanoplatelets. Five different patterns are provided to model the porosity distribution through the thickness of the nanocomposite foam core. The nonlinear equilibrium equations of the convex/concave sandwich shell are extracted utilizing the principle of virtual displacement and considering the von Karman type of geometrical nonlinearities. The linear stability equations are also extracted for the toroidal sandwich shells by implementing the adjacent equilibrium criterion. An analytical approach based on the Airy stress function is implemented to solve the system of partial differential equations with simply supported boundary conditions. Several numerical examples are generated and presented to explore the effect of material/geometrical parameters on the shell’s critical buckling load.