Nanoindentation technique has been used to measure the elastic modulus of virus capsids, capsules, vesicles, and tubules. The principle of the nanoindentation technique is based on the elastic solution of an isotropic, homogeneous, semi-infinite material, which limits the use of nanoindentation in measuring the mechanical properties of materials of small scales. To address this limitation, Reissner's thin shell model, which is based on the point indentation on a thin shell, has been used in analyzing the indentation of thin shells. In this work, the indentation of elastic hemispherical shells of various thicknesses by a rigid, spherical indenter is analyzed, using the finite element method. The simulation results reveal the limitation of the Reissner's thin shell model. A semi-analytical relationship between the indentation depth and the indentation load is proposed, which consists of the contributions of the Hertz's local deformation, the Reissner's local flattening, and the Pogorelov's deflection of the shell. This relationship provides an analytical basis of using nanoindentation to determine the nominal contact modulus of spherical shells. The comparison between the numerical results and the experimental results in literature supports the proposed semi-analytical relationship and reveals the effect of viscoelastic characteristic of shell structures on the indentation deformation.

In this study, a damped centrifugally driven order-tuned vibration absorber designed for vibration reduction in rotating flexible structures, bladed disk assemblies and blisk such as turbine blades, compressor and fan blades, pump and helicopter rotor blades etc. during steady operation with constant speed and under engine order excitation (e.o excitation). Effect of mistuning is disregarded. System is assumed with fully cyclic symmetry. The disk is imposed as being rigid. Elastic behavior for blades is supposed. A model with two degree of freedom is extracted for the blades. Each blade is fitted with nominally identical damped order-tuned vibration absorber that is moved in a circular path. Aerodynamic damping and coupling effects between the blades are considered. Optimal values of parameters of the absorber, to suppress blade vibration especially in resonance condition, are derived by Genetic Algorithm (GA) and MATLAB software. H2 optimization criterion is used. It is observed that with the deviation of each parameter from the optimal condition, the system response is moved away from the ideal design situation and all of the absorbers’ design parameters have definite effects on the system frequency response and on the dissipated energy during vibration. Therefore, ignorance of the effect of one of those parameters (which was happened in literature) affected the system response completely. Literature is reviewed and validity of the results is confirmed.

The conformational (structural) change of proteins plays an essential role in their functions. Experiments have been conducted to try to understand the conformational change of proteins, but they have not been successful in providing information on the atomic scale. Simulation methods have been developed to understand the conformational change at an atomic scale in detail. Coarse-grained methods have been developed to calculate protein dynamics with computational efficiency when compared with than all-atom models. A structure-based mass-spring model called the elastic network model (ENM) showed excellent performance in various protein studies. Coarse-grained ENM was modified in various ways to improve the computational efficiency, and consequently to reduce required computational cost for studying the large-scale protein structures. Our previous studies report a modified mass-spring model, which was developed based on condensation method applicable to ENM, and show that the model is able to accurately predict the fluctuation behavior of proteins. We applied this modified mass-spring model to analyze the conformational changes in proteins. We consider two model proteins as an example, where these two proteins exhibit different functions and molecular sizes. It is shown that the modified mass-spring model allows for accurately predicting the pathways of conformation changes for proteins. Our model provides structural insights into the conformation change of proteins related to the biological functions of large protein complexes.

Analytical closed-form solution to the stress distribution associated with a hole in finite plates subjected to tension has not been obtained yet. Wherefore, a method developed in this paper is based on a Beltrami-Michell methodology analyzing the Kirsch's problem under finite dimensions conditions of both plane stress and plane strain. This aimed ability is achieved by combining the Beltrami-Michell plane equations, isochromatic information on the boundaries only; and the finite difference method into an effectual hybrid method for analyzing rectangular plates of finite width with circular holes. Furthermore, the Beltrami-Michell methodology suggested may be applied on other plate and cut-out forms.

The main objective of the present paper is to analyze the effects of phase-lag on thick circular plate with heat sources in modified couple stress thermoelastic medium. The mathematical formulation is prepared for three-phase-lag heat conduction model subjected to prescribed normal heat flux along with stress free boundary. Laplace and Hankel transforms are used to deal the problem. The displacements, stresses and temperature change are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. The results obtained numerically for these quantities are presented graphically. Some particular cases are also discussed in the present problem.

Abstract-The dynamic stresses around three collinear cracks in an infinite orthotropic plate are solved. In this configuration, two equal cracks are situated symmetrically on either side of a central crack, and time-harmonic elastic waves impinge perpendicularly to the cracks. The problem is solved by superimposing two types of solutions. One solution is that for a crack in an infinite orthotropic plate, and the other is for two collinear cracks. The unknown coefficients in the superimposed solution are determined by applying the boundary conditions at the surfaces of the three cracks using the Schmidt method. The dynamic stress intensity factors are calculated numerically for an orthotropic plate that corresponds to the elastic properties of a boron-epoxy composite.

2-D graphene nanosheets (GNS) not only have superior mechanical properties, but stacking of GNS in composites is expected to inhibit moisture absorption. In this paper, moisture effect on tensile strength of graphene/epoxy nanocomposites is investigated. Two kinds of graphene reinforcements are used including graphene oxide (GO) and reduced graphene oxide (RGO) with reinforcement weight fraction WGO or WRGO in the range of 0.5 to 3.0wt%. A dispersion agent acetone is added in nanocomposites to enhance graphene dispersion. To evaluate moisture influence, those nanocomposites are soaked in two kinds of liquid including deionized water (DIW) and salt water (saline solution) for seven kinds of soaking periods of time including 24, 48, 72, 100, 400 hours, 30 days, and 60 days. After soaking test, diffusion coefficients of various composites are evaluated; besides tensile strengths of composites are measured by microforce testing machine. In order to correlate the strength with microstructure evolution, several techniques are adopted to analyze morphologies and functionalities of reinforcements and fracture surface of composites. They include Raman spectroscope, X-ray photoelectron spectroscope, and SEM. 2-D GNS are found to effectively enhance nanocomposites by moisture attack, and their corresponding reinforcing mechanisms are proposed.

The high speed milling represents the most important process to produce parts in different fields such as aeronautics, automotive and mould. It allows obtaining parts with complex form and with the best surface quality. So, it remains essential to understand the impact of both the cutting force model and its parameters on the tool tip response. Consequently, the mastering of chatter vibration in milling and surface properties of the work piece is essential. In this paper, the simulation of machining is applied to determine the cutting forces distribution. A spindle system modeling is presented using a new approach: Both rigid and flexible modes of the spindle's shaft are taken into account. The shaft is discretized with the Timoshenko beam finite elements with different circular sections. Nonlinear electromagnetic loads exerted by AMBs are computed in terms of the nominal air gap between bearings and spindle, the control current and the displacement of each node. A parametric study is performed to determine the influence of some parameters, such as the feed rate, the tangential cutting coefficient, the spindle speed and the axial depth of the cut on the cutting forces and the chatter vibrations in milling.

In linear system, in-plane motions are decoupled from out-of-plane motions for planar frame structures. A theoretical method is proposed that permits the efficient calculations of modal characteristics of planar multi-story frame structures. There are 3 × m beam components for a planar m-story frame structure. By analyzing the transverse and longitudinal motions of each component simultaneously and considering the compatibility requirements across each frame joint, the undetermined variables of the entire m-story frame structure system can be reduced to six, regardless of the number of stories, and that can be determined by the application of the boundary conditions. The main feature of this method is to decrease the dimensions of the matrix involved in the finite element methods and certain other analytical methods.

A fractional model generalized from the Zener model is proposed for the prediction of temperature-dependent free recovery behaviors of amorphous shape memory polymers (SMPs). This model differs from the Zener model in that it involves nonlinear differential equations of fractional, not integer, order. The theoretical solution based on this fractional model is utilized to simulate the isothermal and nonisothermal free recovery of an amorphous SMP compared with the one based on the Zener model. The results show a reasonable improvement in the prediction of the strain recovery response of SMP by the fractional calculus method.

Magnesium (Mg) alloy sheet has received increasing attention in automotive, transportation, and aerospace industries. It is widely recognized that magnesium sheet has a poor formability at room temperature. While at elevated temperature, its formability can be dramatically improved. To better understand the warm forming properties of magnesium alloy sheet, an accurate description of the mechanical behavior at elevated temperature is required.

In this paper, both uniaxial tensile tests and uniaxial compression tests were carried out at warm temperature for Mg AZ31B alloy sheets. The tensile tests were conducted under various strain rates and material orientations, while the compression tests only considered different material orientations. Based on the orthotropic yield criterion for hexagonal close packed (HCP) metals proposed by Cazacu et al., 2006, a viscoplasticity model has been developed to describe the initial yield anisotropy and asymmetry hardening behavior in tensile and compression of Mg sheet. This model was incorporated into ABAQUS through a user-defined material subroutine. The numerical results show a good agreement with experimental data in a large range of deformation.

An innovative optimization technique is presented for the design of composite laminated plates subjected to in-plane loads. A list of quasi-homogeneous laminates that can be used as angle-ply materials is proposed as a comprehensive solution for optimum lay-up. Two optimization procedures are performed: Dimensioning of the flexural stiffness and the elastic modulus, which provides the optimal orientations for the layers and offer highest in-plane resistance to composite laminated structures. The polar formalism for plane anisotropy is used to represent the flexural stiffness and elastic modulus tensors. Numerical examples are resolved for two materials with different elastic moduli.

The present paper is aimed at studying the effects of viscosity and time on the propagation of thermoelastic waves in a homogeneous and isotropic three-dimensional medium whose surface is acted upon by a thermal load under the purview of temperature-rate-dependent thermoelasticity. The normal mode analysis technique has been employed to solve the resulting non-dimensional coupled field equations and hence the exact expressions for displacement component, stress, temperature field and strain are obtained. The problem is further illustrated by computing the numerical values of the field variables for a copper- like material and depicting them graphically. Numerical results predict finite speed of propagation for thermoelastic waves.

A new approach in meshless methods has been introduced for stress assessment around a crack in two-dimensional elastic solids. This method with the name VDLSM (Voronoi Based Discrete Least Squares Meshless) is a pure meshless method which does not implement nodal mesh for trial and test functions. Rather, it uses a collection of the scattered nodal points and implements the discrete least squares approach to discretize the strong form of the governing differential equations on the domain of interest. This can reduce considerably the pre-processing cost of the analysis. Meshless methods generally are faced with some difficulty to accommodate the stress analysis in the vicinity of sharply concave surfaces such as cracks. Some techniques have been used to fix that problem such as visibility, transparency and diffraction, but these methods require some additional back corrective analyses for those parts of the domain located near the crack, which lengthen the time consumed for the solution and, moreover, do not provide the desired accuracy for the unknowns in these regions. VDLSM as a new, straightforward and easy applicable method has been suggested here for overcoming such deficiency using the algorithm of the Voronoi tessellation for constructing the Moving Least Squares (MLS) shape functions.

In this paper, the effect of delamination on free vibration and primary resonance behaviors of composite circular plate with circular delamination is investigated. Through Reissner Variational Principle, the nonlinear dynamic equilibrium equations, the generalized displacements continuity conditions and the generalized forces equilibrium conditions across delamination front and consistent boundary conditions of delaminated circular plate are obtained. In the work, by introducing Bessel Function and Modified Bessel Function and using Galerkin discretization method, the nonlinear dynamic partial differential equations of delaminated circular plate are transferred into a set of nonlinear ordinary differential equations. Then by using semi-analytic method and multiple scales method, the effects of delamination radius and delamination depth in the thickness-wise on the natural frequency and primary resonance behaviors of delaminated circular plate are presented. The Results show that delamination has considerable effects on the natural frequency and its primary resonance behaviors of delaminated plate.

We obtain values for the shear coefficient both below and above the critical frequency by comparing the results of the Timoshenko beam theory with experimental data published recently. The best results are obtained, by a least-square fitting, when different values of the shear coefficient are used below and above the critical frequency.

In the present study, an exact solution for free vibration analysis of piezoelectric nanobeams based on the nonlocal theory is obtained. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The model has been verified with the previously published works and found a good agreement with them. A detailed parametric study is conducted to discuss the influences of the nonlocal parameter, on the vibration characteristics of piezoelectric nanobeams. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

This note presents an elasto-capillary model of a cantilever subject to capillary stiction during drying process of removing sacrificial layers in MEMS. Similar to the dynamic analysis of the electrostatic pull-in of electrostatic micro actuators, the cantilever beam tends to be pulled down to the substrate due to the nonlinear capillary force with respect to the gap. The critical one-half gap deformation and the corresponding critical wetting area for pulling down a micro cantilever by surface tension are analytically found herein. The instability situation of a generalized critical deformation for power-law surface force with respect to gap is also predicted accordingly. Some prior MEMS works are exemplified to justify this critical one-half gap deformation for capillary stiction.

Analyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Based on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.