Scielo RSS <![CDATA[Latin American Journal of Solids and Structures]]> vol. 13 num. 3 lang. en <![CDATA[SciELO Logo]]> <![CDATA[Pulse Shaper and Dynamic Compressive Property Investigation on Ice Using a Large-Sized Modified Split Hopkinson Pressure Bar]]> Abstract The dynamic compressive behavior of ice is investigated using a large-sized (37 mm in diameter) modified aluminum split Hopkinson pressure bar (SHPB) with pulse shaper at the strain rate from 500 s-1 to 1200 s-1. A series of relatively stable experimental results of dynamic compressive strength versus strain rate and a linear fitting curve have been obtained by controlling data scatter within 25%. The composition of incident wave has been discussed. The effects of pulse shaper diameter and velocity of striker bar have been tested. The properties and principles of incident wave in different stage has been elaborated when using pulse shaper. A theoretical analysis of pulse shaper and bar size effects on the rising time of incident wave has been conducted. Results show the thickness of pulse shaper is proportional to the rising time. Enlarging the diameter and reducing the velocity of the striker bar could increase the rising time and suppress the dispersion. The diameter and wave impedance of bars also contribute to the rising time. <![CDATA[Stress Analysis of Thick Spherical Pressure Vessel Composed of Transversely Isotropic Functionally Graded Incompressible Hyperelastic Materials]]> Abstract In this paper closed form analytical solution for stress components of thick spherical shell made of transversely isotropic functionally graded hyperelastic material subjected to internal and external pressure is presented. Reinforced neo-Hookean strain energy function with variable material parameters is used to model pressure vessel material. The material constants of strain energy function are graded along the radial direction based on a power law function and have been calculated from experimental data by using Levenberg-Marquardt nonlinear regression method. Stress components and stretches of pressure vessel have been obtained for centrally symmetric condition. Following this, profiles of extension ratio, deformed radius of sphere, normalized radial stress and normalized circumferential stress are plotted as a function of radius of sphere in the undeformed configuration for different material inhomogeneity parameter (m). The obtained results show that the inhomogeneity properties of FGMs structure parameter have a significant influence on the displacement, stretch and stresses distribution along the radial direction. <![CDATA[Effect of Thermal Residual Stresses on Buckling and Post-Buckling Properties of Laminated Composites Perimetrally Reinforced]]> Abstract Several mechanical properties can be affected by the occurrence of residual stresses due to curing, and their effects are more pronounced in laminated composites. The effect of the thermal residual stresses on the buckling and post-buckling properties of perimetrally reinforced laminated composites is experimentally characterized. Carbon/epoxy laminates were prepared using two different techniques. One group of laminates was prepared by co-curing the reinforcement at 177 °C. The second group of laminates was prepared by secondary bonding of the reinforcement to the laminate at room temperature (22°C). Topogrammetry equipment was utilized in order to determine the buckling and post-buckling properties of these two groups of laminates. A numerical model was achieved using commercial software for comparison with the experimental results. Suitable accuracy was observed when comparing experimental and numerical results. The co-cured laminates developed considerably higher critical load for buckling values than those obtained for laminates produced with secondary bonding at room temperature. The experimental and numerical results of this study demonstrate the importance of curing-induced thermal residual stresses on the mechanical behavior of laminate composites. <![CDATA[Vibration and Buckling Analysis of Functionally Graded Plates Using New Eight-Unknown Higher Order Shear Deformation Theory]]> Abstract In this paper a new eight-unknown higher order shear deformation theory is proposed to study the buckling and free vibration of functionally graded (FG) material plates. The theory bases on full twelve-unknown higher order shear deformation theory, simultaneously satisfies zero transverse shear stress at the top and bottom surfaces of FG plates. Equations of motion are derived from Hamilton's principle. The critical buckling load and the vibration natural frequency are analyzed. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. The effect of power law index of functionally graded material, side-to-thickness ratio on buckling and free vibration responses of FG plates is investigated. <![CDATA[Application of Higher Order Hamiltonian Approach to the Nonlinear Vibration of Micro Electro Mechanical Systems]]> Abstract This paper implements the higher order Hamiltonian method to analyze an electrostatically actuated nonlinear micro beam-based micro electro mechanical oscillator. First, second and third approximate solutions are obtained, and the frequency responses of the system are compared with energy balance method solution and previously solved Variational Approach (VA) and exact solution. After driving the equation of motion based on the Euler-Bernoulli beam theory, Galerkin method has been used to simplify the nonlinear equation of motion. Higher order Hamiltonian approach has been used to solve the problem and introduce a design strategy. Phase plane diagram of electrostatically actuated micro beam has plotted to show the stability of presented nonlinear system and natural frequencies are calculated to use for resonator design. According to the numerical results, the second approximate is more acceptable and results show that one could obtain a predesign strategy by prediction of effects of mechanical properties and electrical coefficients on the stability and free vibration of common electrostatically actuated micro beam. <![CDATA[Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory]]> Abstract This paper investigates the vibration behavior of micro-resonators based on the strain gradient theory, a non-classical continuum theory capable of capturing the size effect appearing in micro-scale structures. The micro-resonator is modeled as a clamped-clamped micro-beam with an attached mass subjected to an axial force. The governing equations of motion and both classical and non-classical sets of boundary conditions are developed based on the strain gradient theory. The normalized natural frequency of the micro-resonator is evaluated and the influences of various parameters are assessed. In addition, the current results are compared to those of the classical and modified couple stress continuum theories. <![CDATA[Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory]]> Abstract In the present study, a simple trigonometric shear deformation theory is applied for the bending, buckling and free vibration of cross-ply laminated composite plates. The theory involves four unknown variables which are five in first order shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The transverse displacement includes bending and shear components. The present theory satisfies the zero shear stress conditions at top and bottom surfaces of plates without using shear correction factor. Equations of motion associated with the present theory are obtained using the dynamic version of virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The displacements, stresses, critical buckling loads and natural frequencies obtained using present theory are compared with previously published results and found to agree well with those. <![CDATA[Stiffening Effect of Bolt-On Transducers on Strain Measurements]]> Abstract The strain of a structural element is often measured indirectly by determining the strain of a transducer that is supposed to follow the deformation of the element perfectly, and with negligible interaction, around the mounting point. However, this assumption is not always true, and depends on the stiffness of the transducer relative to the local stiffness of the piece to which it is attached. This paper deals with the problem of evaluating the influence that a relatively rigid transducer (the HBM SLB-700A was chosen as an example) has on the strain field, studied from both the theoretical and the experimental points of view. The findings of the research have shown that, in order to interpret the measurements obtained from this kind of instruments correctly, the perturbation induced on the strain field cannot be disregarded. A corrective factor, obtained numerically by means of the FEM and discussed in the paper, can be used as a first approximation to evaluate the true strain, stress and forces in common structural steel elements. <![CDATA[Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory]]> Abstract Free vibration of a magnetoelectroelastic rectangular plate is investigated based on the Reddy's third-order shear deformation theory. The plate rests on an elastic foundation and it is considered to have different boundary conditions. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single partial differential equation and then by using the Galerkin method, the ordinary differential equation of motion as well as an analytical relation for the natural frequency of the plate is obtained. Some numerical examples are presented to validate the proposed model and to investigate the effects of several parameters on the vibration frequency of the considered smart plate. <![CDATA[Hygrothermoelastic Analysis of Orthotropic Cylindrical Shells]]> Abstract In this work, the combined effect of moisture and temperature on the bending behavior of simply supported orthotropic cylindrical shells has been investigated. Initially three dimensional equilibrium equations of thermoelasticity, simplified to the case of generalized plane strain deformations in the axial direction are solved analytically for an orthotropic cylindrical shell strip under thermal loading. Based on the realistic variation of displacements from the elasticity approach, a new higher order shear deformation theory was proposed for the analysis of an orthotropic cylindrical shell strip under hygrothermal and mechanical loading. The zigzag form of the displacement is incorporated via the Murakami zigzag function. Results are presented for mechanical and thermal loading for various layups and they are validated against the derived elasticity solution. The significance of retaining various higher-order terms in the present model, in evaluating the stresses and deflection for composite laminates is brought out clearly through parametric study. Useful results for combined hygrothermal loading are presented in tabular and graphical form. It is expected that the numerical results presented herein will serve as bench mark in future.