Acta Mechanica最新文献

Full stress/displacement compatibility conditions at interfaces by considering the bilinear elasto-plastic core are investigated for the first time. The paper uses the concepts of the improved high-order sandwich panel theory (IHSAPT) and generalizes the approach to account for the bending response based on the unique mechanism of geometrical and material nonlinearity. The analytical results of the model are presented and compared with the experimental results. Emphasis is placed on satisfying shear stress compatibility conditions at the interface along with the effects of the plastic modulus of the core to provide a unique perspective on the bending response of sandwich panels. The results of the present approach are in good agreement with experimental results in terms of load–displacement, including the localized effects attributed to the flexible core. It is also shown that the present model can identify and quantify the localized effects of shear stress continuity at interfaces while conventional high-order sandwich panel models available in the literature fail to do so. The results of the study contribute to the effects of shear and normal plastic modules of the core on transverse normal and shear stress distributions at top and bottom interfaces, stress and displacement components through the thickness of the core as well as the force and moment resultants, and transverse displacements in the face sheets, which may be used as benchmark results for future studies.

This work analyzes the dynamic responses of plates with an elastic foundation under a concentrated moving mass. The plate is made of fluid-saturated functionally graded porous material (FFGPM). The material properties of the FFGPM plate are assumed to vary smoothly across the thickness, with symmetric, asymmetric, and uniform patterns for porosity distribution. The governing equations of the FFGPM plate are developed using Reddy’s third-order shear deformation plate theory (Reddy’s TSDT), Biot’s poroelasticity theory, pb2-Ritz formulation, and the Lagrange equation. In the numerical results, the Newmark scheme is used to obtain the deflection response of the FFGPM plate with the traveling mass. Two approaches are considered and discussed, including moving load and moving mass. Moreover, the influences of the porosity coefficient, distribution patterns, different boundary conditions, elastic foundations, geometry parameters, Skempton coefficient, moving mass velocity, and the mass of moving mass on the dynamic characteristics of the FFGPM plate are studied.

An analytical method to investigate the nonlinear forced vibration of the sandwich plate resting on Pasternak-type foundations subjected to the combination of the mechanical, thermal, electric and magnetic loadings is presented in this paper. The sandwich plate is composed of penta-graphene core with negative Poisson’s ratio and two magneto-electro-elastic face sheets. The temperature-dependent elastic characteristics of penta-graphene core are determined by density functional theory. For magneto-electro-elastic material, the material properties depend on the volume fraction of piezoelectric and piezomagnetic phases which are assumed to be equal. The Hamilton’s principle and Reddy’s higher order shear deformation plate theory are used to derive basic equations of motion. The effects of different parameters such as magnetic and electric potentials, elastic foundations coefficients, temperature increment, initial imperfection, viscous damping and geometrical parameters on the natural frequency, nonlinear to linear frequency ratio and dynamic response of the sandwich plate are discussed in details. The numerical results of this work are also compared with the results available in the literature in order to ensure the reliability and accuracy of the proposed model.

A phase field modeling framework for fatigue fracture was proposed in functionally graded materials (FGMs). This framework is constructed based on homogenization theory and takes into consideration the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Several exemplary cases are shown according to the model to prove the capabilities of the presented framework. These cases present fatigue crack propagation and crack length variation, and the influences of cyclic load, the nonhomogeneous and geometric parameters on crack propagation and crack length. The framework enables capture fatigue crack propagation in FGMs under cyclic loading and considering the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Furthermore, a monolithic scheme applying the quasi-Newton method to address the issue of fatigue fracture in FGMs is proposes.

The deep operator network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an (R^2) value of above 0.99 and a relative (L_2) error of less than 10% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model are highly efficient and accurate.

Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin–Voigt, Maxwell’s, and Jeffreys’ types are analysed in linear one-dimensional situations as far as the propagation of waves and their dispersion and attenuation. These gradient extensions are then presented in the large-strain nonlinear variants where they are sometimes used rather for purely analytical reasons either in the Lagrangian or the Eulerian formulations without realizing this wave propagation context. The interconnection between these two modelling aspects is thus revealed in particular selected cases.

The paper discusses systems with viscoelastic elements that exhibit repeated eigenvalues in the eigenvalue problem. The mechanical behavior of viscoelastic elements can be described using classical rheological models as well as models that involve fractional derivatives. Formulas have been derived to calculate first- and second-order sensitivities of repeated eigenvalues and their corresponding eigenvectors. A specific case was also examined, where the first derivatives of eigenvalues are repeated. Calculating derivatives of eigenvectors associated with repeated eigenvalues is complex because they are not unique. To compute their derivatives, it is necessary to identify appropriate adjacent eigenvectors to ensure stable control of eigenvector changes. The derivatives of eigenvectors are obtained by dividing them into particular and homogeneous solutions. Additionally, in the paper, a special factor in the coefficient matrix has been introduced to reduce its condition number. The provided examples validate the correctness of the derived formulas and offer a more detailed analysis of structural behavior for structures with viscoelastic elements when altering a single design parameter or simultaneously changing multiple parameters.

This study delves into the vibrational behavior of a variable thickness sandwich beam which rests on a three-parameter elastic foundation. The beam’s thickness gradually decreases along its length. The core of the sandwich beam is made from functionally graded porous materials, and the facesheets are reinforced by graphene nanoplatelets. As the distribution pattern of these reinforcements varies with the beam's height, stress transformations at specific angles are necessary to compute the equivalent properties of the materials. Through the utilization of Hamilton's principle and a variational approach, the governing motion equations and the corresponding boundary conditions are deduced. Generalized differential quadrature method as a powerful numerical scheme is employed solve the derived equations under various combinations of boundary conditions to analyze the effects of parameters such as geometry, porosity coefficient, various distribution porosity and graphene dispersion patterns, and the angle of transformation on the natural frequencies.

Deployable thin-film structure is an ideal requirement for space structures used for deep space exploration. One of the obstacles encountered by this structure is the problem of film surface accuracy caused by in-orbit temperature changes and plastic creases created by folding storage. This paper investigates how temperature and crease affect the wrinkling behaviors of thin films. A constitutive model accounting for temperature and crease effects is first derived, and by combining the maximum strain energy principle of tension field theory with the provided model, a numerical analysis method is established to analyze wrinkling films. The stress distribution and wrinkling direction of a rectangular film with or without crease under different temperatures are calculated using this method. Some important and interesting features are observed from the analysis results. The crease and temperature can affect the stress distribution and wrinkling angle of the wrinkling film. Furthermore, the wrinkling angle is more heavily affected by the crease, and the temperature’s impact on the wrinkling angle of the creased film is magnified. This work explains the physical mechanism of the effects of both crease and temperature on wrinkles in deployable film structures and provides a simulation method for studying the wrinkling characteristics of thin films, considering the effects of both the temperature and the crease.

Torsional vibration response of a circular nanoshaft, which is restrained by the means of elastic springs at both ends, is a matter of great concern in the field of nano-/micromechanics. Hence, the complexities arising from the deformable boundary conditions present a formidable obstacle to the attainment of closed-form solutions. In this study, a general method is presented to calculate the torsional vibration frequencies of functionally graded porous tube nanoshafts under both deformable and rigid boundary conditions. Classical continuum theory, upgraded with nonlocal strain gradient elasticity theory, is employed to reformulate the partial differential equation of the nanoshaft. First, torsional vibration equation based on the nonlocal strain gradient theory is derived for functionally graded porous nanoshaft embedded in an elastic media via Hamilton’s principle. The ordinary differential equation is found by discretizing the partial differential equation with the separation of variables method. Then, Fourier sine series is used as the rotation function. The necessary Stokes' transformation is applied to establish the general eigenvalue problem including the different parameters. For the first time in the literature, a solution that can analyze the torsional vibration frequencies of functionally graded porous tube shafts embedded in an elastic media under general (elastic and rigid) boundary conditions on the basis of nonlocal strain gradient theory is presented in this study. The results obtained show that while the increase in the material length scale parameter, elastic media and spring stiffnesses increase the frequencies of nanoshafts, the increase in the nonlocal parameter and functionally grading index values decreases the frequencies of nanoshafts. The detailed effects of these parameters are discussed in the article.