International Journal of Applied Mechanics

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

This study concerns dynamic behavior of a partially connected double-beam system. This beam system is composed of two single beams and these beams are connected to each other by the distributed stiffness of which are located at certain regions. The governing equation of this double-beam system is composed of two fourth-order differential equations for each single beam. These two governing equations are coupled to each other by the partially distributed stiffness. And the coupling in the governing equations makes it difficult to analyze the dynamic behavior of this system. In this study, therefore, the difficulty has been overcome by using one assumption and one concept. The assumption is that the double beam is composed of two equivalent single beams. And the concept is concerned with the relative displacement between the two layers. In addition, the transfer matrix method is used to take problems concerned with discontinuity into account, which are generated by the distributed stiffness. And it is predicted that there will be the slap phenomenon in the double-beam system when the amplitude of the relative displacement is larger than the natural gap distance between the two layers. This phenomenon has been identified in experimental measurements.

The motivation of this paper is to highlight and discuss critically the details of two main aspects related to Eringen’s nonlocal constitutive model. The first aspect is to point out the inconsistency of the integral and differential forms of Eringen’s nonlocal constitutive model. In addition, to point out the ill-posed form and physical infeasibility of the results which may be obtained by using the differential form of the model. The critical analysis focuses on the lack of consistency between the set of the boundary constraints required by the differential form of Eringen’s model and the set of the prescribed boundary conditions of the nonlocal static equilibrium problem. Because of this lack of consistency between the two constitutive forms, it can be concluded that the formulation in context of the differential form is ill-posed and the existence of a feasible solution is questionable and might not be admitted. The second aspect deals with the intractability of the analytical solution of the nonlocal continuum problems based on the integral form of Eringen’s nonlocal constitutive model (IENCM). In the meantime, it mentions the cumbersome of numerical work required by the direct computational methods such as the nonlocal finite element method. The complexity of using the integral form of Eringen’s constitutive model and the lack of existence of a feasible solution by using the differential form of Eringen’s constitutive model lead to the mandatory need for developing an efficient iterative computational approach based on the integral form of Eringen’s constitutive model. In this paper, an iterative computational method, based on the nonlocality residual formulation for nonlocal continuums, capable to investigate different elasticity problems, is proposed. The traditional local continuum solution is taken as an initial solution. To point out the inconsistences between the integral and differential forms of Eringen’s nonlocal constitutive model, and to illustrate the efficiency and capability of the proposed iterative model, four static bending of beam problems with different nature are solved.

Both functionally graded materials (FGMs) and fluid-conveying pipes have wide applications in engineering communities. In this paper, the transverse vibration and stability of multi-span viscoelastic FGM pipes conveying fluid are investigated. Volume fraction laws including power law, sigmoid law and exponential law are introduced to describe the variations of material properties in FGM pipes. A hybrid method which combines reverberation-ray matrix method and wave propagation method is developed to calculate the natural frequencies, and the results determined by present method are compared with the existing results in literature. Then, a comparative study is performed to investigate the effects of fluid velocity, volume fraction laws and internal damping on transverse vibration and stability of the FGM pipes conveying fluid. The results demonstrate that the present method has high precision in dynamic analysis of multi-span pipes conveying fluid. It is also found that natural frequencies of FGM pipes can be adjusted by devising the volume fractions laws. This particular feature can be tailored to fulfill the special applications in engineering.

This paper presents an innovative methodology for the measurement of the mechanical properties of thin films. The purpose is to identify the elastic properties of thin film materials considering the effects of thickness and substrate simultaneously. The new approach is based on the Dimensional Analysis Method (DAM) and the Finite Element Method (FEM) to develop the model’s explicit form. Using the reverse analysis method, numerical indentation tests were carried out to obtain the Young’s modulus of the film. Therefore, the identified film modulus was completely consistent with the input modulus, which ensures the reliability and the effectiveness of the proposed method. Moreover, a case study of TiN nanocoating deposited on Zr-Based Metallic Glasses was considered to validate the proposed model. This model is useful for thin film materials and can be used in different technological applications.

In the present study, we consider the theory of thermoelastodynamics with double porosity structure. Two situations are studied: for bounded domains, the impossibility of time localization of solutions is obtained, which is equivalent to the uniqueness of solutions for the backward in time problem. For the second study, in the case of semi-infinite cylinders, a Phragmen–Lindelof alternative, as well as an upper bound for the amplitude term when solutions decay, are obtained.

In clinical practice, bone healing is monitored with X-rays and manipulation. Its assessment is thus subjective, depending on the skills of the operator. Alternative and quantitative approaches have been proposed, generally based on the estimation of bone stiffness, which is known to increase with the healing process.

The present study investigates the application of experimental modal analysis to fracture healing assessment focusing on fractures treated with an external fixator. The aim is to ascertain the capability of this approach to detect changes in the bone-callus stiffness as variations in the resonant frequencies despite the presence of the fixator, which might hide the bone response. In vitro tests were performed on a tibia phantom where the healing process was simulated creating three different types of callus surrogates, using glue and resin. The resonant frequencies of the phantom with screwed pins and of the phantom with the complete fixator were estimated. Results confirm an increase in the frequencies as the simulated bone-callus stiffness increases, encouraging the application of experimental modal analysis to fracture healing monitoring. This approach can offer remarkable advantages with respect to the actual standards: being non-invasive and quantitative, it would allow a more frequent healing monitoring.

The polymer yield behavior is affected by temperature, strain rate and pressure. In this work, tensile yield stress of polyetheretherketone (PEEK) is characterized for temperature ranging between $223^{\circ }\mathrm{\text{K}}$ and $433^{\circ }\mathrm{\text{K}}$ ($-50^{\circ }$C and $160^{\circ }$C). The tensile yield stress is decreasing in terms of temperature. Two temperature transitions are observed: $320^{\circ }\mathrm{\text{K}}$ ($\sim 37^{\circ }$C) and the glass transition temperature. The temperature sensitivity is well captured by the modified-Eyring equation proposed by the authors. This paper completes three previous works where the PEEK’s yield behavior was described under compression on wide ranges of strain rate and temperature and under tension on a wide range of strain rates. Thus, the pressure effect is analyzed in terms of temperature and strain rate. Using either the experimental data or the modified-Eyring equation, the effect of the hydrostatic pressure is increasing with temperature and decreasing with strain rate.

In this paper, forced vibration responses of functionally graded (FG) nanobeams are presented for modified couple stress theory (MCST) with damping effect. The FG nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. Mechanical properties of FG beam depends on the position. The Kelvin–Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Influences of the geometry and material parameters on forced vibration responses of FG nanobeams are examined and discussed.

The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocation methods computationally efficient. In the incremental–iterative process, how to accurately reflect the change in the slope of the load–deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.

Phononic crystal is an artificial periodic structure with the ability to regulate and control the wave propagation of particular frequencies and has been widely used in many applications. The adhesive layer bonding different constituents in the periodic structure of phononic crystals is usually a viscoelastic material, which has frequency-dependent material properties. In this paper, an analytical model based on the transfer matrix method is developed to study the bandgap structures of SH-wave (a shear wave with the propagation direction normal to the motion plane) in a one-dimensional phononic crystal consisting of two different elastic constituents bonded by the viscoelastic adhesive layer. The results show that the viscosity of the adhesive layer has a significant influence on the bandgap structure at the region of high frequency. The effects of various material parameters of the viscoelastic adhesive layer such as the relaxation time, the final-state modulus and the initial-state modulus are systematically studied. These results are very helpful in the practical design of phononic crystals involving the viscoelastic adhesive layers.

In this paper, employing photo-thermal sensitive (PTS) hydrogels, a photosensitive bio-compatible micro-valve is investigated. In this regard, the energy representation and governing equations of PTS hydrogels are described. Two benchmark problems common in micro-fluidic designs are solved using the presented theory, and the deformation and stress distributions are calculated. The theory is implemented into a finite element (FE) framework by developing a user-defined subroutine. To properly validate the FE model, the FE results are compared with the proposed analytical results. The confirmed numerical method is then employed to investigate two different realistic micro-valve structures. The constructions are composed of three jacket-pillar structures arranged in two different patterns. In this step, the nonlinear contact between the components of structures and presumptive rigid walls are added to the thermo-mechanical deformation of the photosensitive micro-jackets. The contact length and contact pressure are investigated. By calculating all necessary mechanical parameters, the analysis results can be utilized in the design procedure of a photosensitive micro-valve and pave the way for the industrial production of the next generation micro-fluidic devices.

The transverse vibration of axially travelling web may lead to poor quality of product in roll-to-roll manufacture, especially for the web with long span, which is usually installed with some elastic supports intermediately. This paper presents a mechanical model for predicting the dynamic behaviors of axially travelling web with intermediate elastic supports. Both of the axial movement and intermediate support are considered in this proposed model. The web is modeled as a thin plate and the elastic supports are modeled as monaxial springs. The derived equations of in-plane motion are linear and uncoupled with the transverse motion, whereas the equation of transverse motion is nonlinear and coupled with the in-plane motions. The Galerkin method is used to discretize the governing equations and compute natural frequencies. The numerical results agree well with the finite element results for the natural frequencies. The dynamic responses of the web are computed by employing the generalized-$\alpha$ time integration method. A single intermediate elastic support case as well as multiple supports case are considered in this paper. The effects of the support position and stiffness on the natural frequency, stability and dynamic response of the travelling web are discussed.

Nonlinear dynamic characteristics of functionally graded material (FGM) cylindrical shells surrounded by nonlinear elastic foundation under axial static and lateral dynamic loads in thermal environment are investigated in the current paper. The main emphasis is on the simulation of the elastic foundation model and thermal loads. Nonlinear tri-parametric elastic foundation including linear and nonlinear parameters is used to model the reaction of the elastic foundation on the cylindrical shell. Different thermal loading scenarios are applied to the system to study the effects of thermal environment, including uniform, linear and nonlinear temperature distribution across the shell thickness. Governing equations are derived based on the Donnell’s thin shell theory. Material properties of the FGM are assumed to be variable through the shell thickness according to a power law function. Discretization of the obtained governing equations is performed using the Galerkin’s method. An averaging method and the Runge–Kutta method are applied to obtain the frequency–amplitude relation and time–deflection relation, respectively. Comprehensive numerical results are given for investigating the effects of thermo-mechanical loads, material and geometrical properties and nonlinear elastic foundation parameters on nonlinear dynamic characteristics of the functionally graded cylindrical shells (FGCSs). Present formulations are validated by comparing the results with the published data for some specific cases.

Piezoelectric materials possess special characteristics of electromechanical coupling behavior and thus have found numerous applications such as transducers, sensors, actuators. Fracture of piezoelectric materials has drawn substantial attention of the research community and is being widely investigated for predicting their failure. Most of the research on piezoelectric materials is based on impermeable crack conditions. In the present study semi-permeable crack boundary conditions has been analyzed using the extended finite element method (XFEM). Combined Mechanical and Electrical loading with quasi-static crack growth has been considered on a pre-cracked rectangular plate with crack at its edge and center. Stress intensity factors have been evaluated by interaction integral approach using the asymptotic crack tip fields. Effect of presence of minor cracks and holes have been analyzed on the intensity factors of semi-permeable major crack.