In this paper, the mechanical behavior of a functionally graded nano-cylinder under a radial pressure is investigated. Strain gradient theory is used to include the small scale effects in this analysis. The variations in material properties along the thickness direction are included based on three different models. Due to slight variations in engineering materials, the Poisson’s ratio is assumed to be constant. The governing equation and its corresponding boundary conditions are obtained using Hamilton’s principle. Due to the complexity of the governed system of differential equations, numerical methods are employed to achieve a solution. The analysis is general and can be reduced to classical elasticity if the material length scale parameters are taken to be zero. The effect of material index n, variations in material properties and the applied internal and external pressures on the total and high-order stresses, are well examined. For the cases in which the applied external pressure at the inside (or outside) radius is zero, due to small effects in nano-cylinder, some components of the high-order radial stresses do not vanish at the boundaries. Based on the results, the material inhomogeneity index n, as well as the selected model through which the mechanical properties may vary along the thickness, have significant effects on the radial and circumferential stresses.

In this study, continuous contact problem in the functionally graded (FG) layer loaded with two rigid flat blocks resting on the elastic semi-infinite plane was analyzed by the finite element method. The two-dimensional numerical model of the FG layer was made with the software added to the ANSYS program. This software can be adapted to all contact problem types by making minor changes. The accuracy check of the program was performed by comparing with the analytical solution of the problem by homogeneous layer and its solution by the finite element method. So, fast and practical solutions can be obtained by the developed finite element method on many applications such as; automotive, aviation and space industry applications. The comparisons made showed that the proposed solution gave good results at acceptable levels. In the problem, it was thought that all surfaces were frictionless. The external loads P and Q were transmitted to the FG layer via two flat rigid blocks. Normal stresses between the FG layer and the elastic plane, initial separation loads, initial separation distances and contact stresses under the blocks were investigated for various dimensionless quantities.

In this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.

Microspeakers are key components of mobile devices in current consumer products; moreover, the user experience of multimedia products plays an essential role. The objective of this study was to investigate the acoustic performance of microspeakers in different enclosure parameters for mobile devices. Two methodologies are performed. The first model is an electro-mechano-acoustical model (EMA) of microspeaker along with distribution model of enclosure effect; the 2nd model, the details of diaphragms are taken into account in calculating the distribution models of microspeaker with enclosure parameters. They were combined and applied to determine microspeaker performance levels for mobile devices. Two methodologies show acceptable agreement with experimental results. The distribution model can well simulate the high frequency response than lumped model of microspeaker. The results can predict microspeaker system performance before industrial design and mechanism placement processes are executed.

Most vibration-based energy harvesters, including piezoelectric harvester system, perform efficiently at only its resonant frequency as linear resonators, usually at very high frequency which are out of the range of frequency of interest. In real life applications, these linear resonators are impractical since real ambient vibrations are simply having varying lower frequencies. Hence, design a tuneable vibration energy harvester at a lower and useful frequency range of interest are essential in allowing promising energy output to meet intended power input at a more practical approach. In this paper, the piezoelectric voltage energy harvester (PVEH) was designed with a flexible fixture with the aim to reduce its first fundamental natural frequency. Two thickness of elastic fixtures were applied to generate power on PVEH. Three experimental techniques were used to measure the vibration characteristics of PVEH. First, the full-field optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) measured simultaneously the resonant frequencies and mode shapes. This is followed by the pointwise measurement system, laser Doppler vibrometer (LDV) in which the resonant frequencies were measured by dynamic signal swept-sine analysis. The resonant frequencies and anti-resonant frequencies were also obtained by impedance analysis. The results obtained from experimental measurements were compared with finite element numerical calculation. It is found that the boundary conditions under the elastic fixtures can effectively reduce the resonant frequency of the PVEH with a reasonable voltage output. The fundamental natural frequency of PVEH with the thickness of 0.58-mm elastic fixture is reduced to 37 Hz maintaining at 7.1 volts (1.2 mW), in comparison with the natural frequency on cantilevered PVEH at 78 Hz that produces 7.7 volts (6.5 mW).

The study of the mechanical properties of polycrystalline alloy materials under dynamic impact, namely, the prediction of mechanical behavior after yield stress and the establishment of a constitutive model, has attracted much attention in the field of engineering. The stress-strain curves of 5083 aluminum alloy were obtained under strain rates varying from 0.0002 s-1 to 7130 s-1 through uniaxial compression experiments. The equipment used included a CRIMS RPL100 tester, Instron tester, and split Hopkinson test system. In addition, based on dislocation dynamics and the strengthening mechanism of metals, the plastic flow of the 5083 aluminum alloy was systematically analyzed under a wide range of strain rates. It was found that the abnormal yield behavior of the 5083 aluminum alloy under a wide range of strain rates increased, and the experimental phenomenon of hardening rate decreased with an increase in strain rate. This study also revealed that the abnormal yield behavior is caused by the different dislocation mechanisms of two-phase alloy elements under different strain rates. Based on the thermal activation theory and the experimental data, a constitutive model was developed. A comparison showed good agreement between the experimental and model curves. This indicates that this model has good plastic flow stress prediction ability for such types of materials.

This paper presents a numerical model for accurately representing the behaviors of lead-rubber bearings during earthquakes. This model, which is implemented in OpenSees as a user-defined element, accounts for the mechanical characteristics of bearings as follows: firstly, the bi-lateral interaction effect of hysteretic behaviors, as well as the variation in horizontal stiffness due to vertical load, is considered; secondly, the reduced vertical stiffness under large lateral displacement is incorporated by the piecewise linear formulation, and the linear reduction method is employed to determine the stability limit of bearings in the deformed configuration; furthermore, the cavitation and permanent damage effects in bearings are mathematically included. To validate the numerical model, simulation analyses are performed for a series of static and dynamic loading tests, and the numerical results show reasonable agreement with experimental ones, which indicates that the proposed model provides an effective tool for the failure mode analyses of bearings and the dynamic analyses of seismic isolated structures.

Most of previous work for modeling and analyzing various traditional linear elastic materials concentrated on numerical simulations based on lower-order absolute nodal coordinate formulation (ANCF) plate element, in which linear interpolation in transverse direction is utilized and stiffening effect caused by volumetric locking occurs. Relatively little attention is paid to modeling hyperelastic incompressible materials with nonlinear effect and large deformation. In view of this, a higher-order plate element formulation with quadratic interpolation in transverse direction for static and dynamic analysis of incompressible hyperelastic silicone material plate is developed in this investigation. The use of higher-order plate element can not only alleviate volumetric locking, but also improve accuracy in simulating large bending deformation as compared to improved lower-order plate element with selective reduced integration method and originally proposed lower-order plate element. Subsequently, experimental investigation that captures free-falling motion of silicone cantilever plate and corresponding simulations are implemented, the results obtained using higher-order plate element are in excellent accordance with experimental data, whereas the results gained applying other two types of plate elements are distinguished from experimental data. Finally, it is concluded that the developed higher-order plate element formulation achieves approving precision and has superiority in simulating large deformation motion of hyperelastic silicone plate.

It is of practical significance to develop a constitutive model which is able to predict the thermomechanical behaviors of the shape memory effect occurring in a shape memory polymer (SMP) accurately. The mechanism of shape memory effect of SMP is explained based on the assumption that SMP is composed by two phases, reversible phase and stationary phase. Especially the different flow elements are respectively added to the reversible phase and stationary phase in order to express the plastic behavior of SMP. There are two springs in series, one dashpot and one flow element in the reversible phase. There are two springs in parallel, one dashpot and one flow element in the stationary phase. A constitutive equation is developed to express the thermo-mechanical behaviors of shape memory effect in the SMP based on viscous-elastic mechanics and plastic theory. An internal variable, frozen ratio, is defined to follow the shape memory process in SMP, and the material properties are described as the functions of frozen ratio based on phase transition theorem. The developed constitutive model, which includes above constitutive equation and material parameter functions, is used to numerically simulate the thermo-mechanical behaviors of SMP under various load cycles. Results show that the developed constitutive model can not only predict the shape memory process of SMP accurately, but also express the rate-dependent behaviors of SMP effectively.

In rock engineering, evaluating the post-peak strength and deformation of rock is necessary. To explore the elasto-plastic behavior of sandstone in the post-peak stage, a series of strain-controlled triaxial tests were conducted under different confining pressures. According to the post-peak characteristics, a constitutive model based on nonlinear elasticity and generalized plasticity is proposed. This proposed model is characterized by the following features: (1) Nonlinear elasticity is observed under hydrostatic and shear loading; (2) the associated flow rule is followed; (3) substantial plastic deformation occurs during shear loading; and (4) post-peak softening behavior is accurately predicted. This model requires twelve material parameters, three for elasticity and nine for plasticity. The proposed model was validated by comparing the triaxial test results of Mushan sandstone at different hydrostatic pressures under dry and saturated conditions. In addition, the model is versatile; it can simulate the deformational behavior of two other sandstones. In summary, the proposed model can reasonably predict the complete stress–strain curve of sandstone.

In this paper, progressive crushing of prismatic multi-corner thin walled metal tubes under quasi-static axial load is investigated in detail. The novelty of the paper is mainly in considering strain hardening effect during plastic deformation instead of rigid plastic model and also the effect of curvature in forming the folds instead of plastic hinges. For this purpose, a new geometric model based on FEM and experimental observations is used which is capable of being adapted with new crushing configurations during crushing. Based on this model, the instantaneous energy associated with plastic deformation of different regions are calculated and finally by summing all energies and using minimum absorbed energy, mean crushing force and collapse parameters are determined. To evaluate the results, a detailed finite element study using ABAQUS and LS-Dyna solver is conducted on some regular polygonal mild steel tubes under axial crushing. Comparing the results of the new theoretical approach with FEM results show very good capability of that in predicting collapse behavior of these structures.

Vessel flexure can be triggered naturally by surgical operation, heart pulsation and body movement. It may affect the mechanical behavior of the stent and the existence of a stent may in turn cause vessel injury. In the present study, the finite element method is employed to study the interaction between stent and vessel during vessel flexure. Two- and four-link stents made of stainless steel 316L and magnesium alloy WE43 are considered. Results indicate that longitudinal deformation of the stent can be caused by vessel flexure, and the higher levels of stress exist in the link struts. The existence of the stent could induce significant stress concentration and straightened deformation on vessel wall in the course of vessel flexure. Stents with more links or made of harder materials show greater anti-deformation capability, thus inducing a more severe stress concentration and straightened deformation on the vessel wall. The bending direction also affects the mechanical performance of the vessel-stent system. The results obtained could provide useful information for better stent designs and clinical decisions.

Inhomogeneous materials (the ones exhibiting spatial variations in their, all or specific, material properties) present a great deal of interest for scientists and engineers in both academia and industry. For over a hundred years, the mechanical behavior of inhomogeneous materials excites numerous attempts in mathematical modeling and development of methods for proper analysis and verification. With this concern, the reach experience was gained by scientists of different scientific schools in many countries. Despite numerous significant achievements, some results, unfortunately, remain unnoticed by the wide scientific community. On the other hand, one can observe a growing number of publications which repeatedly publish the solutions reported years ago or deal with the similar problems with slight modifications. The main objective of this paper is to: i) present a brief survey of the development history of the elastic analysis of inhomogeneous solids and ii) characterize some dominant analytical and semi-analytical methods. It was not our intent here to provide a comprehensive list of references on the topic, which is nearly impossible to make in view of rapidly growing number of publications and other restrictions, but to emphasize some important, in our opinion, stages of the development, methods and results.

Flexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

This article deals with the analysis of free-free beams by an analytical method. The well-known Green's function method is employed, and exact solution for the problem is obtained. As a second problem, the simply supported-free beam with rotational rigid body motion is analyzed. It is initially shown that ordinary Green's functions cannot be constructed due to a mathematical contradiction. To remedy this limitation, the Fredholm Alternative Theorem is utilized. This theorem eliminates the contradiction and enables analysts to obtain modified Green's functions. The fundamental existence conditions are derived and thoroughly investigated from the structural point of view. Finally, the deflection functions of these beams are found using modified Green's functions.

The crystal plastic theory was used to examine the effect of film-cooling hole arrangements on mechanical properties of cooled turbine blade. The finite element method was used to analyze the maximum von Mises stress and resolved shear stress of an octahedral slip system considering the number of rows, diameter, spacing, and tangential-to-longitudinal hole spacing (h/l) ratio. The different arrangements were found to have a significant influence on the maximum von Mises stress and resolved shear stress. For the triangular arrangement, the von Mises stress and resolved shear stress were highest with double rows, followed by a single row and then triple rows. For the quadrilateral arrangement, the stresses were highest with double rows, followed by triple rows and then a single row. Increasing the spacing or decreasing the diameter reduced the maximum von Mises stress and weakened the multi-hole interference effect. Both the maximum von Mises stress and resolved shear stress decreased with the h/l ratio.

In the dynamic analysis of discretized elastic bodies with contacts/impacts, the common formulations to model contact force include the penalty method and the Lagrangian method, which are different in the constraint imposition strategies. Traditionally, the Lagrangian method is thought to be less efficient due to additional multipliers and numerical complexity, however, the viewpoint is challenged in this paper. The goal of this paper is to investigate how numerical efficiency and accuracy using the two different methods are influenced by some non-physical chosen parameters such as stiffness coefficient, time step size and spatial discretization. An experimental sphere-rod impact problem and a multi-point impact problem are solved to evaluate certain numerical intricacies of the two implementations. The results show that in dealing with normal impact problems, the choice of penalty factor and time step size using the penalty method is not an omissible act to obtain accuracy and stability, while there are no such manually-defined parameters using the Lagrangian method. Moreover, there seems to be a clear advantage of the Lagrangian method in which much less mesh elements are needed to achieve the same accuracy compared to those of the penalty method.

The exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

The concepts of nodal value and grid average in cell centered finite volume method (FVM) are clarified in this work, strict distinction between the two concepts in constructing numerical schemes is made, and common fault in misidentifying the two concepts is pointed out. The expansion based on grid average, similar to Taylor’s expansion, is deduced to construct correct scheme in terms of grid average and to obtain modified partial differential equation (MPDE) which determines the order of accuracy of numerical scheme theoretically. Correct high order scheme, taking QUICK (Quadratic Upstream Interpolation for Convective Kinematics) scheme as an example, is constructed in different approaches. Furthermore, the property of interpolation coefficients is analyzed. We also pointed out that for high order schemes, round-off error dominates the absolute error in fine grid and truncation error dominates the absolute error in coarse grid.

A multi-scale strategy is employed in the paper to investigate the thermo-mechanical properties of 2.5D angle-interlock woven shape memory polymer composites (SMPCs). In the study, the mesoscopic model of 2.5D woven SMPCs and microscopic model of yarns are firstly developed. After that, the themo-viscoelastic constitutive relationship of the yarn is described in the form of hereditary integral and the parameters of relaxation moduli are obtained from nonlinear fitting of Prony series based on the results of finite element method (FEM). Based on the multi-scale models and the constitutive relationship, the effects of warp and weft arranged densities on viscoelastic properties of 2.5D woven SMPCs are studied in detail. Finally, the shape memory behavior along the warp direction in small strain region is also analyzed. The research in the paper lays a foundation for design and application of woven SMPCs in engineering.