Latin American Journal of Solids and Structures, Volume: 15, Issue: 10, Published: 2018
• ## Optimization of reinforced concrete polygonal sections under biaxial bending with axial force Original Article

Silva, Amilton R.; Faria, Flávia C.

Abstract in English:

Abstract Concrete is the world’s most utilized material for production of the structural elements employed in civil construction. Due to its low tensile strength and brittle nature it is reinforced with steel bars forming the reinforced concrete (RC structure). Linear elements of reinforced concrete are commonly employed in multi-story buildings, bridges, industrial sheds, among others. In this study an optimization algorithm is presented to define the amount of steel and its location within a concrete polygonal section subjected to biaxial bending with axial force, so that the amount of steel would be the minimum needed to resist the soliciting forces. Therefore, the project variables are: location, diameter and number of steel bars to be distributed within the concrete polygonal section. The sequential linear programming method is used to determine the optimized section. In this method, the non-linear problem of determining the resistance forces of the section in relation to the project variables is approximated by a sequence of linear problems, which would have its optimal point defined for each step using the Simplex method. Formulation validation is done through results of examples found in literature, and also by means of analytical solutions of simple problems, such as rectangular sections under axial force and moment in only one axis of symmetry. The results show the efficiency of the algorithm implemented in the optimized determination of the quantity and position of the bars of a given diameter in the polygonal section of reinforced concrete under biaxial bending with axial force.
• ## Mechanism of hermetic single-cell structure interfering with shaped charge jet Original Article

Min, Guo; Xu-dong, Zu; Zheng-xiang, Huang; Xiao-jun, Shen

Abstract in English:

Abstract On the basis of visual origin, shock wave reflection, and jet interference theories, this study aims to (1) divide the process of jet penetration into a hermetic single-cell structure into six parts, (2) establish a theoretical model of a single-cell structure interacting with a jet during its penetration into a structure, and (3) obtain the time expressions of a hermetic single-cell structure interfering with a jet. A residual penetration experiment is conducted to verify the accuracy of the model.
• ## Reinforced Concrete Beam-Column Inverted Knee Joint Behaviour after Ground Corner Column Loss-Numerical Analysis Original Article

Abdelwahed, B.; Belkassem, B.; Vantomme, J.

Abstract in English:

Abstract Beam-column joints are critical component in the load path of reinforced concrete (RC) frames, due to their role in transferring loads among different RC frame components. The loss of a ground corner column in a RC frame turns an exterior joint into an inverted knee joint and recent code provisions for exterior joints are not sufficient to knee joints because of reinforcement defects in terms of joint vertical stirrups and improper column bar anchorage. This paper investigates numerically the behaviour of these joints under a closing moment using nonlinear finite element (FE) analysis with LS-DYNA. Beam’s bar anchorage type and joint vertical stirrups are the main parameters considered next to concrete compressive strength, longitudinal reinforcement ratio and lateral beam effect. This study indicates that, anchorage beam’s bar with U shaped produces better behaviour than 90° standard hooks or headed ends. Contribution of joint vertical stirrups is more influential with headed bars anchorage. Increasing concrete compressive strength and beam reinforcement ratio improve joint ultimate capacity. The presence of lateral beams reduces the rate of concrete degradation in the joint after reaching ultimate capacity and increases joint carrying capacity.
• ## Aspects of Finite Element Modeling of Punching Shear Behavior of Reinforced Concrete Flat Slabs Original Article

D., Rafael A. Sanabria; Oliveira, Leonardo H. B. de; Trautwein, Leandro Mouta; Almeida, Luiz Carlos de; Santos, Antônio Carlos dos

Abstract in English:

Abstract A series of nonlinear FE analyses was conducted in this paper to model the punching shear failure of RC flat slabs. The analyses were carried out in the software DIANA using three-dimensional continuum elements. These analyses involve the test of different modeling choices in order to evaluate their influences on punching shear failure modeling. The parameters examined are the size of the FE mesh, the convergence methods and the concrete material input parameters. These parameters were investigated by comparing the results of load carrying capacity, load-deflection response and crack patterns from the FE analyses with a reliable experimental test. From the results obtained, it could be concluded that the numerical model was able to reproduce accurately the behavior of the tested slab and capture the punching shear failure.
• ## Finite element formulation and analysis of a functionally graded Timoshenko beam subjected to an accelerating mass including inertial effects of the mass Original Articles

ESEN, İsmail; KOÇ, Mehmet Akif; ÇAY, Yusuf

Abstract in English:

Abstract This study describes a new finite element method that can be used to analyse transverse and axial vibrations of a Functionally Graded Material (FGM) beam under an accelerating / decelerating mass. The differential equations of the FGM beam are obtained using First-order Shear Deformation Theory (FSDT). In these equations, the interaction terms of mass inertia are derived from the second-order exact differentiation of displacement functions with respect to mass contact point. The FGM beam is made of two different materials (Steel and Alumina Al2O3), which vary in thickness with a power law. Including the effects of neutral axis shift and mass inertia, the proposed method can be used when the dynamic behaviour of the FGM Timoshenko beams is to be analysed in transverse and axial directions, depending on the interaction with the acceleration of the moving loads. After validating this work with literature studies, new investigations and findings are presented for both moving load and mass assumptions. In addition, the obtained results of Timoshenko Beam (TBT) and Euler Bernoulli beam theory (EBT) are compared for FGM beams with various speeds and accelerations of moving mass.
• ## Recommended Finite Element Formulations for the Analysis of Offshore Blast Walls in an Explosion Original Articles

Kim, D.K.; Ng, W.C.K.; Hwang, O.J.; Sohn, J.M.; Lee, E.B.

Abstract in English:

Abstract This study suggests relevant finite element (FE) formulations for the structural analysis of offshore blast walls subjected to blast loadings due to hydrocarbon explosions. The present blast wall model adopted from HSE (2003) consists of a corrugated panel and supporting members, and was modelled with shell, thick-shell, and solid element combinations in LS-DYNA, an explicit finite element analysis (FEA) solver. Stainless and mild steels were employed as materials for the blast wall model, with consideration of strain rate effect throughout ten (10) pulse pressure load regimes. The obtained FEA results were validated by experimental data from HSE (2003) with decent agreement. In the present study, recommended FE formulations with additional hourglass control functions were widely discussed from the perspectives of solution accuracy and computational cost based on a statistical approach. The obtained outcomes could be used for the structural analysis and design of offshore blast walls in the estimations of maximum and permanent deformations under blast loadings.
• ## Single variable new first-order shear deformation theory for isotropic plates Original article

Shimpi, Rameshchandra P.; Guruprasad, P. J.; Pakhare, Kedar S.

Abstract in English:

Abstract This paper presents a single variable new first-order shear deformation plate theory with only one fourth-order partial governing differential equation. It may be noted that, first-order shear deformation plate theory of Mindlin has three coupled partial governing differential equations involving three unknown functions. Even a recently developed new first-order shear deformation plate theory has two uncoupled partial governing differential equations involving two unknown functions for static problems. The displacement functions of the proposed theory give rise to constant transverse shear strains through thickness of the plate and, as is the case of Mindlin plate theory, the proposed theory also requires a shear correction factor. The governing differential equation, expressions for moments and shear forces of the proposed theory have a striking resemblance to the corresponding expressions of classical plate theory. The proposed theory is the only first-order shear deformation plate theory with two different types of physically meaningful clamped boundary conditions. To obtain solutions for the flexure of the plate, efforts required using the proposed theory are comparable to those involved in the case of classical plate theory. The effectiveness of the proposed theory is demonstrated through illustrative examples and by comparing results obtained with other plate theories.
• ## Finite element evaluation of the effects of curvature in Lamb waves for composites structural health monitoring Original Article

Santana, Guilherme André; Malekan, Mohammad; Araújo, Alexandre Martins; Donadon, Lázaro Valentim; Cimini, Carlos Alberto

Abstract in English:

Abstract This work presents the effect of the high curvature to thickness ratio on the characteristics of Lamb Waves propagating over the skins of composite structures. It is accessed how the curvature on composite skins affects the group velocity of the symmetrical (S0) and asymmetrical (A0) wave modes. It is also accessed the gradient of curvature effect, when the wave propagates from a flat to a curved part on the skin. The results are intended to be used for the improvement of structural health monitoring of wings and wind turbine blades. This is accomplished through dynamic explicit linear finite element method simulations of plates with flat and curved parts made of Eglass-epoxy bidirectional laminate. As the skin structures are often designed to withstand torsional loads, the fibers are aligned with 45 degrees from the leading edge (curved region) throughout the analysis. Several skins with different curvature to thickness ratios are generated and simulated. Results and trends are presented and can be used to improve the algorithms for damage detection on those structures. It is shown that the group velocity of the incoming waves change considerably with the presence of curvature, for both main modes of vibration.
• ## Experimental Study of Fatigue Crack Behavior of Rib-To-Rib Butt Welded Connections in Orthotropic Steel Decks Original Article

Saifaldien-Shakir,; Alemdar, Fatih

Abstract in English:

Abstract Rib-to-rib (RR) butt welded connections are one of the most sensitive locations for encountering fatigue failure in orthotropic steel decks (OSDs), and numerous fatigue cracks arising from these areas have been identified in existing OSD bridges. Due to dynamic factors in their service life bridges with an orthotropic steel deck (OSD) are prone to fatigue cracking and failure. Studies concerning the cases which use (RR) butt-welded connections are limited in the literature. In this study a cyclic loading experiment is carried out for the investigation of the fatigue life and crack propagation characteristics of butt-welded connections. A static numerical simulation was performed, and the experimental setup was verified with strain gage measurements at the beginning of the tests. Failure modes and stiffness curves were obtained. Crack growth characteristics are observed as provided by dye-penetrant and dynamic stiffness crack detection methods. Crack lengths against the number of cycles were obtained and failure cycles were recorded for construction of the fatigue strength (S-N) Curves as given in AASHTO (2007). Cracked specimens performed in E’ category while the control specimen showed infinite fatigue life. Also it is seen that dye-penetrant method is more efficient than the dynamic stiffness detection method.
• ## Fatigue lifespan of a fillet welded joint - Hybrid approach to obtain the S-N curve with a reduced number of tests Original Article

Goedel, Fábio; Mezzomo, Gustavo P.; Pravia, Zacarias M. Chamberlain

Abstract in English:

Abstract This paper introduces a hybrid approach for obtaining S-N curves with reduced number of tests associated to statistically simulated data. In order to validate the proposal, two validation process were developed. One using a methodology to generate S-N curves based on Monte Carlo simulations and other using actual data according Zhao et al. (1998), allowing to compare the hybrid approach with the experimental curve S-N obtained with high replication. In both validation process, a good accuracy was verified. Subsequently, the fatigue analysis of a fillet welded joint was carried out using finite element analysis to evaluate the cumulative damage and fatigue life, enabling comparison between the proposed method and standard NBR 8800 (2008). The results obtained with the proposed methodology allowed more accuracy results and less conservative than standard for the same weld detail class, both for fatigue life and for cumulative fatigue damage evaluations.
• ## Preface to the special issue of the International Symposium on Solid Mechanics (MecSol 2017) Thematic Section: Solid Mechanics in Brazil 2017

Vaz, Miguel; Medeiros, Ricardo de; Cardoso, Eduardo Lenz; Rojas, Pablo Andrés Muñoz

Abstract in English:

Abstract The International Symposium on Solid Mechanics (MecSol) is a biennial conference which aims to provide a forum to discuss relevant issues associated with solid mechanics. The MecSol 2017 edition was held in the city of Joinville, Brazil, on 26-28 April 2017. Plenary lectures were delivered by researchers from five different countries. The main topics discussed in the conference are as follows: composite materials, optimization, constitutive modelling, fatigue, impact, nonlinear analyses, structural reliability, X-FEM, G-FEM, and BEM numerical methods. The participants were invited to submit full papers, which, after peer review, compound this special issue of the Latin American Journal of Solids and Structures. This article highlights the main topics addressed in the conference.
• ## Multi-objective optimization with Kriging surrogates using “moko”, an open source package Thematic Section: Solid Mechanics in Brazil 2017

Passos, Adriano Gonçalves dos; Luersen, Marco Antônio

Abstract in English:

Abstract Many modern real-world designs rely on the optimization of multiple competing goals. For example, most components designed for the aerospace industry must meet some conflicting expectations. In such applications, low weight, low cost, high reliability, and easy manufacturability are desirable. In some cases, bounds for these requirements are not clear, and performing mono-objective optimizations might not provide a good landscape of the required optimal design choices. For these cases, finding a set of Pareto optimal designs might give the designer a comprehensive set of options from which to choose the best design. This article shows the main features and functionalities of an open source package, developed by the present authors, to solve constrained multi-objective problems. The package, named moko (acronym for Multi-Objective Kriging Optimization), was built under the open source programming language R. Popular Kriging based multi-objective optimization strategies, as the expected volume improvement and the weighted expected improvement, are available in the package. In addition, an approach proposed by the authors, based on the exploration using a predicted Pareto front is implemented. The latter approach showed to be more efficient than the two other techniques in some case studies performed by the authors with moko.
• ## On the use of thermographic method to measure fatigue limits Thematic Section: Solid Mechanics in Brazil 2017

Bandeira, Carlos Filipe Cardoso; Kenedi, Paulo Pedro; Castro, Jaime Tupiassú Pinho de

Abstract in English:

Abstract Traditional fatigue limit measurements are expensive and time consuming, requiring a large number of specimens and a long time to be completed. An alternative approach is used in this work to obtain the fatigue limit of a cold drawn steel, in a rotating bending machine, by monitoring temperature variations induced by different load range levels in just a few specimens. Comparisons with Dixon’s traditional up-and-down method confirm that this thermographic approach is indeed a much more efficient, faster, and cheaper method to obtain fatigue limits.
• ## Sensitivity analysis of 3D frictional contact with BEM using complex-step differentiation Thematic Section: Solid Mechanics in Brazil 2017

Ubessi, C.J.B.; Marczak, R. J.

Abstract in English:

Abstract This paper presents a study of the complex step differentiation method applied to a parameter sensitivity analysis for 3D elastic contact problem. The analysis is performed with the Boundary Element Method (BEM) using discontinuous elements and the Generalized Newton Method with line search (GNMls). A standard BEM implementation is used and the contact restrictions are fulfilled through the augmented Lagrangian method. This methodology in conjunction with the BEM avoids the calculation of the nonlinear derivatives during the solution process, allowing a fast and reliable solution procedure. The parameter sensitivity is evaluated using complex-step differentiation. This well-known method approximates the derivative of a function analogously to the standard finite differences method, with the advantages of being numerically exact and nearly insensitive to the step-size. As an example, a Hertz-type problem is solved and the sensitivity of the contact pressures with respect to the Young Modulus variation is evaluated. The obtained results are compared with analytical and numerical solutions found in the literature.
• ## Stress effects on the kinetics of hydride formation and growth in metals Thematic Section: Solid Mechanics in Brazil 2017

Souza, Angela C.; Cruz, Antônio G.B. da; Duda, Fernando P.

Abstract in English:

Abstract Although metal hydrides are considered promising candidates for solid-state hydrogen storage, their use for practical applications remains a challenge due to the limitation imposed by the slow kinetics of hydrogen uptake and release, which has driven the interest in using metal nanoparticles as advanced materials of new hydrogen-storage systems since they display fast hydrogenation and dehydrogenation kinetics. Nevertheless, the understanding of the adsorption/release kinetics requires the investigation of the role played by the stress which appears to accommodate the misfit between the metal and hydride phases. In this paper, we present a continuum theory capable of assessing how the misfit stress affects the kinetics of hydride formation and growth in metallic nanoparticles. The theory is then applied to study the kinetics of adsorption/release in spherical particles. This work extends Duda and Tomassetti (2015, 2016) by considering stress-dependent hydrogen mobility.
• ## Boundary Layer Effects in a Finite Linearly Elastic Peridynamic Bar Thematic Section: Solid Mechanics in Brazil 2017

Aguiar, Adair R.; Patriota, Túlio V. Berbert; Royer-Carfagni, Gianni; Seitenfuss, Alan B.

Abstract in English:

Abstract The peridynamic theory is an extension of the classical continuum mechanics theory. The peridynamic governing equations involve integrals of interaction forces between near particles separated by finite distances. These forces depend upon the relative displacements between material points within a body. On the other hand, the classical governing equations involve the divergence of a tensor field, which depends upon the spatial derivatives of displacements. Thus, the peridynamic governing equations are valid not only in the interior of a body, but also on its boundary, which may include a Griffith crack, and on interfaces between two bodies with different mechanical properties. Near the boundary, the solution of a peridynamic problem may be very different from the classical solution. In this work, we investigate the behavior of the displacement field of a unidimensional linearly elastic bar of length L near its ends in the context of the peridynamic theory. The bar is in equilibrium without body force, is fixed at one end, and is subjected to an imposed displacement at the other end. The bar has micromodulus C, which is related to the Young's modulus E in the classical theory and is given by different expressions found in the literature. We find that, depending on the expression of C, the displacement field may be singular near the ends, which is in contrast to the linear behavior of the displacement field observed in the classical linear elasticity. In spite of the above, we show that the peridynamic displacement field converges to its classical counterpart as a length scale, called peridynamic horizon, tends to zero.
• ## Numerical simulation of bolted connections Thematic Section: Solid Mechanics in Brazil 2017

Vilela, Paula Moura Leite; Carvalho, Hermes; Baião, Oswaldo Teixeira

Abstract in English:

Abstract This article presents the modeling of a complete bolted connection based on a model with one bolt connecting two or three plates. Initially, the behavior of this model with one bolt is analyzed by comparing it with existing bibliography for 3 different types of applied load: tension, shear and a combination of these two. This model includes all necessary considerations: contacts between the plates and the nut, head and shank of the bolt; contact between the plates, as well as friction between them; and pre-load on the bolt. The model also responds properly to loads parallel and perpendicular to the contact surface between the plates, including prying action effects. These calibrated models are then introduced as super-elements in empty spaces left on the full connection, through a relatively simple process using the finite element software ANSYS®. Upon filling these spaces, two complete connection models are evaluated: one with a single plate and one between two T-stubs. The results obtained with these models are compared with standard forecasts. These two connection types have a practical application in the way they will be analyzed, and also as part of more complex connections: bolted girder splices (in the region of web beam), beam-to-column connections with splice plates or end plate connections, beam splices with end-plates, etc.
• ## Calibration and evaluation of the Lemaitre damage model using axial- torsion fatigue tests on five engineering alloys Thematic Section: Solid Mechanics in Brazil 2017

Castro, Fábio; Bemfica, Cainã

Abstract in English:

Abstract The Lemaitre damage model is evaluated using fatigue test data from five engineering alloys: 1045 steel, 16MnR steel, 7075-T651 Al alloy, extruded AZ61A Mg alloy, and extruded AZ31B Mg alloy. Tension-compression, torsion, proportional axial-torsion, and 90° out-of-phase axial-torsion loadings were investigated. The results show that the overall accuracy of the fatigue life estimates made by using the Lemaitre model is comparable to those obtained by fatigue models that require the definition of a loading cycle. A simple and effective method is described for determining the material constants of the Lemaitre model.
• ## Buckling Analysis of Laminated Anisotropic Kirchhoff’s Plates via The Boundary Element Method Thematic Section: Solid Mechanics in Brazil 2017

Monteiro, José I. L.; Daros, C. H.

Abstract in English:

Abstract A new fundamental solution for laminated anisotropic Kirchhoff’s plates with out-of-plane and in-plane compressive loads is derived here. The multicompressed solution for both isotropic and anisotropic cases is obtained via the Radon Transform. Some fundamental kernels of the integral equations are described in detail. BEM results of displacements and critical buckling loads of several plates with different boundary conditions and geometries are presented. Comparisons with available analytical solutions and some published numerical results confirm the reliability and accuracy of the proposed formulation.
• ## A Model Updating Method for Plate Elements Using Particle Swarm Optimization (PSO), Modeling the Boundary Flexibility, Including Uncertainties on Material and Dimensional Properties Thematic Section: Solid Mechanics in Brazil 2017

Negri, Doglas; Fiorentin, Felipe Klein; Crichigno, Joel Martins

Abstract in English:

Abstract It is a well-known fact that, in a real engineering situation, fixtures are not ideally stiff, so numerical simulations using them are unlikely to present results that are consistent with the experimental ones. The present paper intends to describe a model updating methodology inserting translational and rotational springs in order to better represent the real clamping. For that purpose, the PSO stochastic optimization method will be used to determine the spring stiffness in an iterative way. In addition, uncertainties regarding the material properties, such as density and Young’s Modulus, as well as workpiece dimensions, will also be taken into account in the optimization algorithm. Once the experimental natural frequencies and the geometry of the studied parts are known, the algorithm automatically updates the model, approximating the natural frequencies obtained from the numerical model to the experimentally obtained ones as closely as possible. In addition, the modal shapes of the updated simulation will be compared to the experimental data and to a rigid boundary simulation. Results will demonstrate that the proposed methodology efficiently represents the fixturing flexibility: both natural frequencies and mode shapes found were close to the real dynamic system.
• ## Experimental study of brass properties through perforation tests using a thermal chamber for elevated temperatures Thematic Section: Solid Mechanics in Brazil 2017

Klosak, Maciej; Rusinek, Alexis; Bendarma, Amine; Jankowiak, Tomasz; Lodygowski, Tomasz

Abstract in English:

Abstract Experimental analysis on standard brass alloy has been carried out using a high pressure gas gun. Perforation tests have been performed for a variety of impact velocities from 40 to 120 m/s in order to study the material behaviour and to define failure modes. The main aim of the study has been to provide results using an innovative thermal chamber that allows to heat specimens before impact. The range of available temperatures is from the room temperature up to 260 ˚C. The experimental study has allowed to discuss the ballistic properties of the structure. The ballistic resistance of sheet plates is strongly dependent on the material behaviour under dynamic loading and changes with temperature. The ballistic properties are also intensely related to interaction between the projectile and thin brass target. The results in terms of the ballistic curve VR (residual velocity) versus V0 (initial velocity) have shown the temperature effect on the residual kinetic energy and thus on the energy absorbed by the plate, revealing a thermal softening of the brass. The ballistic limit corresponding to the maximum impact velocity without complete perforation has decreased by 5-7% for the highest temperature considered. A changing failure pattern is observed. The number of petals varies as a function of impact velocity and temperature. It can be concluded based on experimental observations that thermal softening is a key point on the process of perforation. Preliminary temperature records have been provided using a thermal imaging camera.
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