Scielo RSS <![CDATA[Latin American Journal of Solids and Structures]]> vol. 14 num. 9 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[High-velocity Penetration of Concrete Targets with Three Types of Projectiles: Experiments and Analysis]]> Abstract This study conducted high-velocity penetration experiments using conventional ogive-nose, double-ogive-nose, and grooved-tapered projectiles of approximately 2.5 kg and initial velocities between 1000 and 1360 m/s to penetrate or perforate concrete targets with unconfined compressive strengths of nominally 40MPa. The penetration performance data of these three types of projectiles with two different types of materials (i.e., AerMet100 and DT300) were obtained. The crater depth model considering both the projectile mass and the initial velocity was proposed based on the test results and a theoretical analysis. The penetration ability and the trajectory stability of these three projectile types were compared and analyzed accordingly. The results showed that, under these experimental conditions, the effects of these two different kinds of projectile materials on the penetration depth and mass erosion rate of projectile were not obvious. The existing models could not reflect the crater depths for projectiles of greater weights or higher velocities, whereas the new model established in this study was reliable. The double-ogive-nose has a certain effect of drag reduction. Thus, the double-ogive-nose projectile has a higher penetration ability than the conventional ogive-nose projectile. Meanwhile, the grooved-tapered projectile has a better trajectory stability, because the convex parts of tapered shank generated the restoring moment to stabilize the trajectory. <![CDATA[Stress-Based Finite Element Methods for Dynamics Analysis of Euler-Bernoulli Beams with Various Boundary Conditions]]> Abstract In this research, two stress-based finite element methods including the curvature-based finite element method (CFE) and the curvature-derivative-based finite element method (CDFE) are developed for dynamics analysis of Euler-Bernoulli beams with different boundary conditions. In CFE, the curvature distribution of the Euler-Bernoulli beams is approximated by its nodal curvatures then the displacement distribution is obtained by its integration. In CDFE, the displacement distribution is approximated in terms of nodal curvature derivatives by integration of the curvature derivative distribution. In the introduced methods, compared with displacement-based finite element method (DFE), not only the required number of degrees of freedom is reduced, but also the continuity of stress at nodal points is satisfied. In this paper, the natural frequencies of beams with different type of boundary conditions are obtained using both CFE and CDFE methods. Furthermore, some numerical examples for the static and dynamic response of some beams are solved and compared with those obtained by DFE method. <![CDATA[Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape]]> Abstract Geometrically nonlinear vibrations of functionally graded shallow shells of complex planform are studied. The paper deals with a power-law distribution of the volume fraction of ceramics and metal through the thickness. The analysis is performed with the use of the R-functions theory and variational Ritz method. Moreover, the Bubnov-Galerkin and the Runge-Kutta methods are employed. A novel approach of discretization of the equation of motion with respect to time is proposed. According to the developed approach, the eigenfunctions of the linear vibration problem and some auxiliary functions are appropriately matched to fit unknown functions of the input nonlinear problem. Application of the R-functions theory on every step has allowed the extension of the proposed approach to study shallow shells with an arbitrary shape and different kinds of boundary conditions. Numerical realization of the proposed method is performed only for one-mode approximation with respect to time. Simultaneously, the developed method is validated by investigating test problems for shallow shells with rectangular and elliptical planforms, and then applied to new kinds of dynamic problems for shallow shells having complex planforms. <![CDATA[Dynamic Compressive Strength and Failure of Natural Lake Ice Under Moderate Strain Rates at Near Melting Point Temperature]]> Abstract This paper presents a series of uniaxial compressive experiments on natural lake ice under moderate strain-rate in the range of 10−1 to 102 s−1 at −0.1 °C. Natural lake ice samples of 8 cm by 8 cm in cross section and 20 cm high were used to investigate strain-rate dependence of uniaxial compressive strength and flaw effects on ice strength under moderate strain rates. The fracture modes of ice at moderate strain rates were also systematically investigated by using high-speed camera. It is found uniaxial compressive strength of natural lake ice increases with increasing strain-rate in the employed moderate strain-rate range. And natural flaws such as air bubble have a significant effect on uniaxial compressive strength of ice under moderate strain-rate, higher air content ice possesses lower compressive strength. Ice fracture mode depends on strain-rate (or compressive velocity) of ice specimen, varying from splitting at strain rates lower than 10 s−1 to crushing at strain rates higher than 10 s−1. Ice specimen crushes into fine fragments may due to insufficient time for micro cracks to propagate, thus results in higher strength. In addition, dependence of compressive strength on strain-rate in a wide strain-rate range is also discussed. <![CDATA[Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method]]> Abstract In this paper, we present a new numerical method for nonlinear vibrational analysis of Euler-Bernoulli beams. Our approach is based on the continuous Galerkin-Petrov time discretization method. The Euler-Bernoulli beam equation which governs its vibrations is transformed into set of ordinary differential equations and the presented method is employed in order to investigate the vibrational response. A comparison is made between present method and different other methods available in literature. It is observed that the obtained results are in strong agreement with other results in literature. We conclude that the present method has a great potential to deal with nonlinear vibration analysis problems of beams and related structures like rods and shafts. <![CDATA[Numerical Investigation of Structural Response of Corrugated Blast Wall Depending on Blast Load Pulse Shapes]]> Abstract Hydrocarbon explosions are one of most hazardous events for workers on offshore platforms. To protect structures against explosion loads, corrugated blast walls are typically installed. However, the profiles of real explosion loads are quite different depending on the congestion and confinement of Topside structures. As the level of congestion and confinement increases, the explosion load increases by up to 8 bar, and the rising time of the load decreases. This study primarily aims to investigate the structural behavior characteristics of corrugated blast walls under different types of explosion loadings. Four loading shapes were applied in the structural response analysis, which utilized a dynamic nonlinear finite element method. <![CDATA[The Equivalent Linearization Method with a Weighted Averaging for Analyzing of Nonlinear Vibrating Systems]]> Abstract In this paper, the Equivalent Linearization Method (ELM) with a weighted averaging, which is proposed by Anh (Anh, 2015), is applied to analyze some vibrating systems with nonlinearities. The strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the other strongly nonlinear oscillators and the cubic Duffing with discontinuity are considered. The results obtained via this method are compared with the ones achieved by the Min-Max Approach (MMA), the Modified Lindstedt - Poincare Method (MLPM), the Parameter - Expansion Method (PEM), the Homotopy Perturbation Method (HPM) and 4th order Runge-Kutta method. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully exerted to a lot of practical engineering and physical problems. <![CDATA[An Analytical Time Domain Solution for the Forced Vibration Analysis of Thick-Walled Cylinders]]> Abstract In this paper, we propose a time domain analytical solution for the forced vibration analysis of thick-walled hollow cylinders in presence of polar orthotropy. In this regard, solution of the governing equation is decomposed into two parts. The role of the first one is to satisfy boundary conditions utilizing the method of separation of variables besides of Fourier series expansion of the non-homogenous boundary conditions. The second part has been also expressed as the series of orthogonal characteristic functions with the aim of satisfaction of initial conditions. The proposed analytical solution has been implemented to evaluate the dynamic response of the cylinder in solution of some sample problems which are chosen from previous studies. <![CDATA[Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams]]> Abstract In this paper, authors present the study of free vibration of bending multiple cracked functionally graded material (FGM) beam. Vibration equations of multiple cracked FGM beam were established by using the rotational spring model of cracks, dynamic stiffness method (DSM) and actual position of neutral plane. The frequency equation obtained was in a simple form, that provides an effective approach to study not only free vibration of the beams but also inverse problems like identification of material and crack parameters in structure. The obtained numerical results show good agreement with other previous published results. Thence, numerical computation has been carried out to investigate the effect of each crack, the number of cracks, material and geometric parameters on the natural frequencies of multiple cracked Timoshenko FGM beams. <![CDATA[Quasi-Static Crushing and Energy Absorption Characteristics of Thin-Walled Cylinders with Geometric Discontinuities of Various Aspect Ratios]]> Abstract In this paper, energy absorption and deformation capacity of circular thin-walled members with elliptical cut-outs are investigated both numerically and experimentally. Thin-walled members possess the uniform height, thickness, average cross sectional area, material and volume are subjected to axial quasi-static loading. To conduct such tests, special fixture arrangement is designed for placing the specimen in the compression loading machine. The deformation mechanisms and the corresponding collapse mode along with its energy absorption of the thin-walled tubes were investigated in detail for various aspect ratios (0.315, 0.523, 0.854, 1, 3.375 and 4.08). The explicit finite element code ABAQUS was then employed to perform the numerical studies inview of mitigating the influence of cutout shape, location and symmetry on energy absorption and crush characteristics. In aspect ratio of 4.08, whose major axis length of 24.5 mm observed maximum crash force efficiency (CFE) of 14% possessing symmetric discontinuity. The results of experimental and simulations are in good agreement and shows that the location and symmetry of cutouts had considerable effect on collapse crushing behaviour.