Archive of Applied Mechanics最新文献

The tension–compression asymmetry is a basic mechanical property of materials themselves, which results in differences in elastic constant, yield strength, creep and fatigue. Among them, bimodular elastic effect and strength differential (SD) effect in plastic yielding will influence the whole elastic–plastic response. Existing studies have focused either on bimodular elastic effect of structures or on SD effect of materials, and few of them have combined the two effects. In this study, we theoretically analyze, for the first time, the elastic–plastic bending behavior of beams with the bimodular and SD effects, including loading and unloading process. The comparisons with our numerical simulation results and others’ experimental results validate the analytical solution obtained. The results indicate that during loading, the ratio of plastic limit bending moment to elastic limit bending moment is greater than known 3/2 and during unloading, the bending moment required by reverse yielding is greater than twice of elastic limit bending moment. The modulus ratio and yield strength ratio play an important role in elastic–plastic analysis and their relative magnitude determines whether the tensile edge yields first or the compressive edge. These results may help design optimal structural components in engineering.

Nonlinear vibration of axially moving systems has been a hot research topic. In the present paper, the influence of nonhomogeneous boundaries caused by wheel curvature on the dynamics of axially moving beams is explored. The equilibrium deformation of axially moving beams with nonhomogeneous boundaries is solved by using the iterative scheme developed by the differential quadrature method (DQM). Moreover, the forced vibration response of the system is evaluated by using the multi-scale method. The stability of the solutions for given parameters was determined. The results of the multi-scale method are verified by using the Galerkin truncation method (GTM). Numerical examples disclose that nonhomogeneous boundary conditions exhibit specific phenomena, namely an increase in the amplitude of the steady-state response, a decrease in the nonlinear characteristics, and an upward shift of the instability boundary. The discovery of this phenomenon is of great significance for the analysis of the dynamic response of axially moving beams under nonhomogeneous boundary conditions caused by wheel curvature. It is helpful for structural optimization and performance improvement in corresponding engineering fields.

Loading–unloading is a ubiquitous phenomenon in engineering applications and an enduring topic in contact mechanics. Yield plateau and strain hardening are essential for material behaviors, but they have not been well considered in contact mechanics. This work developed a three-phase constitutive model to accurately describe the elastoplastic contact behaviors considering both yield plateau and strain hardening, merging the elastic-perfectly plastic and power-law hardening behaviors. The significance of the yield plateau and strain hardening was emphasized, and new empirical formulations of dimensionless contact load, area, and residual interference were presented, expanding the present knowledge of the elastoplastic contact problem.

The paper further develops the method of matched sections as a new universal numerical technique. Like the finite element method, FEM, it supposes that: a) the domain is represented as a mesh of simple elements; b) algebraic relations between the main parameters are established from the governing differential equations; c) relationships from all elements are assembled into one global matrix. The relations between the main parameters are established similarly to those for the corresponding 1D task, so any 2D problem is considered a combination of two 1D problems—one is x-dependent, and the other is y-dependent. In all technical aspects, this paper resembles our previous one, which was devoted to the static analysis of plate bending. It operates by the same governing parameters, the same structure of the dependencies between them as well as the organization of the calculation scheme. The only difference consists in connection equations (analogy of element interpolation functions), which establish the relationship between inlet parameters (about the left and lower sides of the element) and outlet parameters (the left and upper sides). They are derived as the frequency-dependent ones (frequency is explicitly used in them) and in the liming case of very long (narrow) plates coincide with the known beam frequency-dependent solution. Several practical examples demonstrate the efficiency of the proposed method.

This paper identifies a null-Lagrangian in the reduced relaxed micromorphic model. We show that the introduction of a micro-inertia depending on the skew-symmetric part of (nabla dot{u}) with the macroscopic displacement field u does not enrich the dispersion relations of the reduced relaxed micromorphic model. Reciprocally, we show that one can switch from the full micro-inertia (with both sym(nabla dot{u}) and skew(nabla dot{u}) terms) to the reduced micro-inertia (only sym(nabla dot{u})) without any additional fitting. This is related to the fact that the introduction of such a skew-symmetric term is equivalent to a null-Lagrangian that leaves the bulk response unchanged while modifying the Neumann boundary conditions at the boundaries. Thus, the introduction of the skew-symmetric part of the micro-inertia, while redundant for wave dispersion, may potentially be used to improve the response of finite-size mechanical metamaterials at the homogenized macroscale due to boundary effects.

Soil is a multi-scale granular material and has dramatic particulate and structural characteristics. Soil particles are divided into matrix and reinforcing particles to establish a multi-scale soil cell model according to the mechanical effect generated by the interaction between soil particles at various scales and the physical mechanism at different structural levels of soil. A multi-scale Mohr–Coulomb strength criterion (MCSC) that accounts for the particle size of soil is proposed by using the soil cell model. A series of soil cell samples are prepared to conduct consolidated and undrained tri-axial compression test to determine the model parameters. The yield locus of the multi-scale MCSC is drawn on the deviatoric plan based on the theoretical analysis and test results. Results show that the yield locus of the multi-scale MCSC is also hexagonal and expands with the decrease in the size of the reinforcing particle and the increase in the volume fraction of these particles. In this regard, the multi-scale MCSC can relate the microscopic physical details of soil to its macroscopic shear strength.

In deep rock medium excavation, the unloading waves due to the blasting excavation can bring great damage to the neighboring structures. In this paper, the visco-elastic interface model is introduced to study the dynamic strength around an existing lined tunnel subjected to blasting and unloading waves. Three unloading paths because of tunnel blasting excavation are considered, and the dynamic interface stresses of existing lined tunnel resulting from these unloading paths are derived. To describe the wave fields around the existing tunnel and in the tunnel lining, the wave function expansion method is used, and the elastic and viscosity coefficients of interface is used to describe the interfacial characters. The analytical solutions of displacement and stress fields in the rock mass are obtained. An approximate numerical integration method is introduced to calculate the displacements and stresses around the existing tunnel. In numerical examples, the circumferential stress around the existing tunnel under different interface parameters, unloading paths and geometrical and physical parameters of tunnels is analyzed. Comparison with the existing numerical results validates this model.

During the assembly process, deformation occurs in composite thin-walled parts, leading to damage at the hole connections of their single-longitudinal splice (SLS) joints. To predict assembly damage in the design process, it is usually necessary to combine uncertainty analysis with finite element analysis (FEA) methods. However, this field has limited progress due to the large size of the analyzed objects relative to their span and the large number of constraints that increase computational costs and complexity. In this study, we employed a linear elastic method to analyze the assembly process of thin-walled components. We achieved the uncertainty propagation (UP) and uncertainty quantification (UQ) of profile deviation random fields by using sub-modeling techniques, and obtained the stress distribution around the connection holes. The validity of the method was confirmed through a comparison with a full-process FEA of a three-hole SLS model. By integrating our method with the Hashin damage criterion, we proposed a statistical analysis approach for predicting assembly failure in SLS joints. The results demonstrated that considering only the profile deviation of the composite panel wall had a significant impact on material damage.

This study presents a fifth-order shear deformation theory for analyzing the displacement and stress of laminated and sandwich beams subjected to sinusoidal, uniformly distributed, and linearly varying loads. The theory's displacement field takes normal deformations and transverse shear effects into account. On both the upper and lower surfaces of the beams, the requirement of zero transverse shear stresses is fulfilled. Hence present theory does not require a shear correction factor. Governing equations and boundary conditions of laminated and sandwich beams are derived using the principle of virtual work. From the stress-equilibrium equations of the theory of elasticity, transverse shear stresses are recovered. Both the stress-free boundary conditions at the external surfaces and the continuity condition at the layer interface are satisfied by the transverse stresses that arise from this approach. Closed-form solutions for simply supported beams are obtained using Navier’s solution method. A MATLAB program is developed based on the present formulation to generate numerical results. A comparison result of present 5th OSDTs and those of the 3rd OSDTs, FSDT, and CBT are presented. The inclusion of transverse normal strain into the theory resulted in significant variation in the displacements and stresses of laminated and sandwich beams when compared to the results predicted from the lower-order theories discarding transverse normal strain.

Determination of the elastic field developed in a heterogeneous material provides useful information for calculating its overall elastic properties. When dimensions of inhomogeneities in such a material are comparable to the intrinsic length scale of its constituents, classical elasticity ceases to produce reliable solutions. Mindlin’s first strain-gradient elasticity, as an enhanced continuum mechanics theory, has proved its success in dealing with such a problem. Hence, this theory is utilized in the present paper to obtain an exact solution of the elastic displacement field induced in an infinite isotropic medium that contains a circular cylindrical inhomogeneity and is subjected to an anti-plane loading. The obtained solution demonstrates the size effect on the elastic field of the medium. On the other hand, an extended version of the equivalent inclusion method which is adapted to Mindlin’s first strain-gradient theory is developed to attack the same problem, leading to an approximate solution. Subsequently, by solving some numerical examples, a comparison between these exact and approximate solutions is provided in this paper.