Journal of Solid Mechanics
Volume:4 Issue: 2, Spring 2012

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data. The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function. This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon. The analytical solution is demonstrated by developing a reference solution from which selected “measurement” points are used. An artificial error is then randomly added to “measurement” points for studying the stability of the reconstruction method utilizing Tikhonov-Morozov regularization technique. It is found that there is an excellent agreement between the model prediction and limited set of residual stress data in the sense of least-square approximation.

In this study, the free vibration behavior of orthotropic rectangular graphene sheet embedded in an elastic medium under biaxial pre-load is studied. Using the nonlocal elasticity theory, the governing equation is derived for single-layered graphene sheets (SLGS). Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a Navier’s approach is also developed. DQM results are successfully verified with those of the Navier’s approach. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, Winkler and Pasternak foundations and material properties on natural frequencies are investigated. The results are shown that with the decrease of in-plane pre-loads the curves isotropic and orthotropic non-dimensional frequency in approaches close to each other.

In this study, free vibration of a foam-core orthotropic smart composite cylindrical shell (SCCS) filled with a non-viscous compressible fluid, subjected to combined electro-thermo-mechanical loads is investigated. Piezoelectric polymeric cylindrical shell, is made from polyvinylidene fluoride (PVDF) and reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). Characteristics of the equivalent composite are determined using micro-electro-mechanical models. The poly ethylene (PE) foam-core is modeled based on Winkler and Pasternak foundations. Employing the charge equation for coupling electrical and mechanical fields, the problem is turned into an eigenvalue one, for which analytical frequency equations are derived considering free electrical and simply supported mechanical boundary conditions at circular surfaces at either ends of the cylindrical shell. The influence of electric potential generated, filled-fluid, orientation angle of DWBNNTs, foam-core and a few other parameters on the resonance frequency of SCCS are investigated. Results show that SCCS and consequently the generated Φ improve sensor and actuator applications in several process industries, because it not only increases the vibration frequency, but also extends economic viability of the smart structure.

This paper reports an analytical method to show the effect of electrostatic and Casimir forces on the pull-in instability and vibration of single nano-plate (SNP) carrying a moving nanoparticle. Governing equations for nonlocal forced vibration of the SNP under a moving nanoparticle considering electrostatic and Casimir forces are derived by using Hamilton’s principle for the case when two ends are simply supported. The problem is solved by using the analytically and the time integration methods. The detailed parametric study is considered, focusing on the remarkable effects of the nanoparticle position, nonlocal parameters, nano-plate length, mode number, electric voltage of the Casimir parameter, and dielectric spacer with an initial gap on vibration of SNP.

The goal of this study is investigating reduction of residual stresses from welding carbon steel plates through vibration stress relief method vs. thermal method. In order to carry out the required experimental tests, carbon steel plates were welded together under specific conditions as samples. Some of the samples were vibration stress relieved, some were thermal stress relieved while the rest remained without any stress relief operation. Several destructive and non-destructive tests were performed on all the stress relieved and non-relieved specimens and the data obtained from these tests were compared in order to reach the optimum vibration effect on stress relieved welded joints. The results attained for vibration method indicated an acceptable amount of reduction of residual stresses in the joints. In addition, some improvements in mechanical properties achieved vibration stress relief method were used.

All impact analyses performed so far for the composite plates, have treated central impacts. Furthermore, investigations on influences of the in-plane biaxial compression, tension, or tension-compression preloads on various responses of the low-velocity impact, especially the indentation, have not been performed so far. In the present research, a finite element formulation is presented for response prediction of a low-velocity eccentric impact between a rigid spherical indenter and a laminated composite rectangular plate with asymmetric lamination scheme. Different contact laws are considered for the loading and unloading phases. A parametric study is performed to investigate influence of the specifications of the plates and the indenter, the eccentric value, and the in-plane preloads on the indentation and force time histories. Results show that the compressive and tensile in-plane preloads reduce and increase the contact force (and consequently, the indentation values), respectively. Therefore, the extensive tensile preloads may lead to higher damages.

The present investigation is concerned with the reflection of plane waves from a free surface of a micropolar thermoelastic diffusion half space in the context of coupled theory of thermoelastic diffusion. The amplitude ratios of various reflected waves are obtained in a closed form. The dependence of these amplitude ratios with an angle of propagation as well as other material parameter are shown graphically. Effects of micropolarity and diffusion are observed on these amplitude ratios. Some special cases of interest are also deduced from the present investigation.

The present investigation is concerned with the reflection and transmission coefficients of plane waves at the interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half- space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for specific model. Some special and particular cases are also deduced from the present investigation.