Scielo RSS <![CDATA[Latin American Journal of Solids and Structures]]> vol. 13 num. 7 lang. en <![CDATA[SciELO Logo]]> <![CDATA[Study of Vibrations in a Short-Span Bridge Under Resonance Conditions Considering Train-Track Interaction]]> Abstract Resonance is a phenomenon of utmost importance in railways engineering, leading to vast damages both in track and vehicles. A short-span bridge has been modeled by means of a finite elements method model, calibrated and validated with real data, to study resonance vibrations induced by the passage of trains. Furthermore, the influence of vehicle speed and track damping on the vibrations registered on the rail, the sleeper and the bridge has been assessed. Different track and vehicle pathologies have been proposed and their effect on the resonance of the bridge has been evaluated. <![CDATA[Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams]]> Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load. <![CDATA[Free Vibration Analysis of a Liquid in a Circular Cylindrical Rigid Tank Using the Hierarchical Finite Element Method]]> Abstract A hierarchical finite element is developed for the free vibration analysis of a liquid in a rigid cylindrical tank with or without a free surface. It is a hierarchical quadrilateral element and has the advantage that the hierarchical mode number is allowed to vary independently of direction. Liquid behavior in tanks with large aspect ratios can therefore be solved very accurately by using a higher hierarchical mode number in the longer direction than in the shorter one. Furthermore, it is possible to idealize the liquid by using only one element. The solution can therefore be obtained to any desired degree of accuracy simply by increasing the hierarchical mode number. In this method, the liquid behavior is described by the displacements alone. The pressure and velocity potential are not considered as unknowns. The results are compared with other methods and show good agreement. <![CDATA[Simplified Analytical Approach to Evaluate the Nonlinear Dynamics of Elastic Cylindrical Shells Under Lateral Blast Loads]]> Abstract This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic thin-walled cylindrical shells under suddenly applied loads. Interest in this problem is motivated by effects due to explosions on fluid-storage metal tanks. The model is based on the energy criterion due to Lagrange, in which the kinematic nonlinear relations are assumed using Donnell's simplified shell theory. Solution is achieved as a series summation in terms of trigonometric functions in the axial and circumferential directions, whereas the degrees of freedom depend on time. A blast load is assumed to represent effects due to explosions on the shell as time-dependent pressures with a given circumferential distribution (a cosine square distribution in terms of the central angle). The procedure is validated by comparison with a nonlinear finite element model under the same load conditions. The influence of load level and shell geometry on the transient response is investigated by mean of parametric studies. Good accuracy is found in the results for the range of shells which are representative of horizontal, fuel storage tanks in the oil industry. <![CDATA[Reflection and Refraction of Waves at the Boundary of a Non-Viscous Porous Solid Saturated with Single Fluid and a Porous Solid Saturated with Two Immiscible Fluids]]> Abstract The phenomenon of reflection and refraction is studied at the welded interface between two different porous solids. One is saturated with single non-viscous fluid and other is saturated with two immiscible viscous fluids. The incidence of Pf, Ps or SV wave through porous solid saturated with non-viscous fluid results in the three reflected waves and the four waves refracted to porous medium saturated with two immiscible viscous fluids. For the presence of viscosity in pore-fluids, the waves refracted to corresponding medium attenuate in the direction normal to the interface. It is also revealed that for the post-critical incidence of Ps wave, the reflected Pf and SV waves becomes evanescent and for the post-critical incidence of SV wave, the reflected Pf wave becomes evanescent. While, the occurrence of critical incidence is not observed for the incidence of Pf wave. The ratios of amplitudes of reflected and refracted waves to that of incident wave are expressed through a non-singular system of linear algebraic equations. These amplitude ratios are used further to calculate the shares of different scattered waves in the energy of incident wave. For a particular numerical model, the energy shares are computed for incident direction varying from normal incidence to grazing incidence. The conservation of energy across the interface is verified. Effects of non-wet saturation of pores, frequency of wave and porosity on the energy partitions are depicted graphically and discussed. <![CDATA[A Doubly Curved Axisymmetric Finite Element for Subsea Sandwich Domes]]> Abstract The paper focuses on the analysis of sandwich domes using a newly developed doubly curved axisymmetric sandwich finite element. The simple equivalent single layer finite element employs a cubic polynomial approximation for transverse displacement and meridional displacement. The present element accounts for the transverse shear strains of the facing and core using quadratic polynomial. The relation between inplane stresses and strains for axisymmetric deformation has been represented by a state of generalized plane stress. The stiffness matrix has been derived using the variational principle. The numerical examples have been presented to illustrate the element capabilities and accuracy of the results achieved using the newly developed sandwich shell element. <![CDATA[Time-Domain Three Dimensional BE-FE Method for Transient Response of Floating Structures Under Unsteady Loads]]> Abstract This paper presents a direct time-domain three dimensional (3D) numerical procedure to simulate the transient response of very large floating structures (VLFS) subjected to unsteady external loads as well as moving mass. The proposed procedure employs the Boundary Element and Finite Element methods (FEM-BEM). The floating structure and the surrounding fluid are discretized by 4-node isoparametric finite elements (FE) and by 4-node constant boundary elements (BE), respectively. Structural analysis is based on Mindlin's plate theory. The equation of motion is constructed taking into account the effect of inertia loading due to the moving mass. In order to obtain the hydrodynamic forces (added mass and radiation damping), the coupled natural frequencies are first obtained by an iterative method, since hydrodynamic forces become frequency-dependent. Then the Newark integration method is employed to solve the equation of motion for structural system. In order to prove the validity of the present method, a FORTRAN program is developed and numerical examples are carried out to compare its results with those of published experimental results of a scale model of VLFS under a weight drop and airplane landing and takeoff in still water condition. The comparisons show very good agreement. <![CDATA[Numerical Study on the Structural Performance of Steel Beams with Slant End-plate Connections]]> Abstract Thermal effects can be one of the most harmful conditions that any steel structure should expect throughout its service life. To counteract this effect, a new beam, with a capability to dissipate thermally induced axial force by slanting of end-plate connection at both ends, is proposed. The beam was examined in terms of its elastic mechanical behavior under symmetric transverse load in presence of an elevated temperature by means of direct stiffness finite element model. The performance of such connection is defined under two resisting mechanisms; by friction force dissipation between faces of slant connection and by small upward crawling on slant plane. The presented numerical method is relatively easy and useful to evaluate the behavior of the proposed beam of various dimensions at different temperatures. Its applicability is evident through satisfactory results verification with those from experimental, analytical and commercially available finite element software. Based on the good agreement between theoretical and experimental methods, a series of design curves were developed as a safe-practical range for the slant end-plate connections which are depend on the conditions of the connection. <![CDATA[Topological and Topographical Optimization of Automotive Spring Lower Seat]]> Abstract The design of a suspension system emphasizes weight reduction in this high-computation technology era. Understanding that the reduction of suspension mass can lead to cost and material reduction is important; moreover, the riding performance of the vehicle should be improved. Topology and topography structure optimization for the spring lower seat is performed to reduce the weight of a passenger car spring lower seat design under stress and structure compliance constraints. Topology optimization is performed to identify the density of the required elements, whereas topography optimization is utilized to strengthen the structure of the lower seat by applying bead parameters in the model. Based on topology optimization, the mass of the model is improved by a reduction of 36.5%. Topography optimization is subsequently performed to fine-tune the topology-optimized model. Beads are added to the model to strengthen the stiffness of the structure. The topography-optimized model has successfully increased compliance by 27% compared with the sole topological optimized design. With the combination of topology and topography optimization techniques, the weight of coil spring lower seat has been successfully reduced while preserving the strength. Suitable sheet materials are proposed to match the optimized coil spring lower seat design. <![CDATA[Enhanced Biogeography-based Optimization: A New Method for Size and Shape Optimization of Truss Structures with Natural Frequency Constraints]]> Abstract The current study presents an enhanced biogeography-based optimization (EBBO) algorithm for size and shape optimization of truss structures with natural frequency constraints. The BBO algorithm is one of the recently developed meta-heuristic algorithms inspired by the mathematical models in biogeography science and is based on the migration behavior of species among the habitats in the nature. In this study, the overall performance of the standard BBO algorithm is enhanced by new migration and mutation operators. The efficiency of the proposed algorithm is demonstrated by utilizing four benchmark truss design examples with frequency constraints. Numerical results show that the proposed EBBO algorithm not only significantly improves the performance of the standard BBO algorithm, but also finds competitive results compared with recently developed optimization methods.