Acta Mechanica最新文献

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.

This paper investigates the nonlinear dynamic response of auxetic thin plates subjected to a combination of resonance while resting on a viscoelastic Pasternak foundation. Auxetic materials, known for their unique negative Poisson’s ratio, exhibit superior mechanical properties. It makes them ideal for applications requiring enhanced energy absorption and vibration resistance, such as soft robotic systems. The study derives the governing equation of motion using classical plate theory, nonlocal elasticity, and external influences, including magnetic fields. To solve these nonlinear equations, analytical methods such as the Galerkin method and the multiple time scale perturbation method are employed. While the primary focus is on combination harmonic excitation, the effects of plate thickness, auxetic and small-scale factors on the nonlinear dynamic response are also examined. Furthermore, advanced nonlinear dynamic analysis tools such as Poincaré sections, phase portraits, and Lyapunov exponent evolution are used to evaluate the system’s stability and chaotic behavior. These methods facilitate an understanding of periodic, quasi-periodic, and chaotic responses. Unlike previous studies, this work focuses on the combined effect of harmonic excitations and magnetic fields on auxetic plates. It analyzes how parameters like plate thickness, auxetic ratio, and small-scale effects influence system behavior. Advanced tools, such as phase portraits and Lyapunov exponents, are used to evaluate stability and chaos. The findings offer new insights into designing auxetic structures for vibration control and stability in smart systems and soft robotic applications.

Under plane strain conditions, the leading two terms of the asymptotic stress field near the interface corner of two dissimilar nonlinear elastic–plastic materials with differing hardening behavior were formulated. Assuming that the second material has a higher hardening coefficient (n₂ > n₁), two limiting cases were considered: (1) a rigid case with zero secondary displacement in the second material and (2) a non-rigid case where it equals the first material’s primary displacement. The associated eigenvalues and mixed-mode parameters were then computed for varying angle and hardening levels of the second material. The obtained results exhibited a distinctive characteristic at the angle of 130°, where the mode-mix parameter remains unchanged with varying hardening coefficients. Coefficients for the first two stress terms were determined by minimizing the RMS difference between asymptotic and finite element (FE) stresses under tensile loading. Agreement was assessed across various angles and hardening coefficients. Higher n₁ values improved correlation in the first material by reducing mode-mix contrast in two materials. Larger notch angles and greater hardening in the second material increased deviations, requiring additional asymptotic terms for accuracy.

This paper discusses axisymmetric contact problems of pressing absolutely rigid stamps in the form of bodies of revolution into a homogeneous elastic half-space with static friction. It is assumed that the contact zone is circular with a radius that is not known in advance. Using rotation operators, the problem solution is reduced to a singular integral equation of the second kind with variable coefficients. Based on the theory of the analytic functions, a closed solution in quadratures is constructed. Some important special cases of the problem are considered. Using numerical calculations, the patterns of change in the radius of the contact zone, contact stresses and rigid displacement of the stamp are determined depending on the maximum value of the friction coefficient.