Showing papers in "Latin American Journal of Solids and Structures in 2013"

Thermomechanial buckling of temperature-dependent fgm beams.

Abstract: BUCKLING OF BEAMS MADE OF FUNCTIONALLY GRADED MATERIALS (FGM) UNDER THERMOMECHANICAL LOADING IS ANALYSED HEREIN PROPERTIES OF THE CONSTITUENTS ARE CONSIDERED TO BE FUNCTIONS OF TEMPERATURE AND THICKNESS COORDINATE THE DERIVATION OF THE EQUATIONS IS BASED ON THE TIMOSHENKO BEAM THEORY, WHERE THE EFFECT OF SHEAR IS INCLUDED IT IS ASSUMED THAT THE MECHANICAL AND THERMAL NONHOMOGENEOUS PROPERTIES OF BEAM VARY SMOOTHLY BY DISTRIBUTION OF THE POWER LAW INDEX ACROSS THE THICKNESS OF THE BEAM THE EQUILIBRIUM AND STABILITY EQUATIONS FOR AN FGM BEAM ARE DERIVED AND THE EXISTENCE OF BIFURCATION BUCKLING IS EXAMINED THE BEAM IS ASSUMED UNDER THREE NTYPES OF THERMAL LOADINGS; NAMELY, THE UNIFORM TEMPERATURE RISE, HEAT CONDUCTION ACROSS THE THICKNESS, AND LINEAR DISTRIBTION ACROSS THE THICKNESS VARIOUS TYPES OF BOUNDARY CONDITIONS ARE ASSUMED FOR THE BEAM WITH COMBINATION OF ROLLER, CLAMPED, AND SIMPLY-SUPPORTED EDGES IN EACH CASE OF BOUNDARY CONDITIONS AND LOADING, CLOSED FORM SOLUTIONS FOR THE CRITICAL BUCKLING TEMPERATURE OF THE BEAM IS PRESENTED THE RESULTS ARE COMPARED WITH THE ISOTROPIC HOMOGENEOUS BEAMS, THAT ARE REPORTED IN THE LITERATURE, BY REDUCING THE RESULTS OF THE FUNCTIONALLY GRADED BEAM TO THE ISOTROPIC HOMOGENEOUS BEAMN

Acoustical performance of porous absorber made from recycled rubber and polyurethane resin

Abstract: This paper reports an investigation of a new kind of material and its acoustical performance. The main component of this porous absorber is the ground tyre rubber (GTR) with different particle sizes, from the shredding of tyres of heavy vehicles, mixed with different proportion of polyurethane resin. Acoustical properties were assessed according to ISO 10534 - 2: 1998. The data obtained show porous absorbers having a high sound absorption performance with low thicknesses and compared to some of the current models for the prediction of their absorptive properties. The use of this model constitutes a good tool in order to design a new sound absorber to solve two environmental problems, noise and environmental pollution.

The strainârate effect of engineering materials and its unified

Abstract: The test data of metals, brittle materials and polymers in high, medium and low strain-rate range were summarized. It was found that the dynamic strength or yield stress of these materials was not sensitive to strain-rate in the low and high strain-rate range (corresponding to weak sensitivity area and saturated zone). But in the medium strain-rate range (strong sensitivity area), the dynamic strength or yield stress of these materials was extremely sensitive to strain-rate. The strain-rate effect function in classic Johnson-Cook constitutive model could not describe these phenomena in the range of low to high strain-rate. Therefore, the strain-rate effect function in classic Johnson-Cook constitutive model has been modified to a strain-rate effect expression which is suitable for different materials. This new model can better describe the phenomena of the weak sensitivity area, strong sensitivity area and saturated zone. With this model, the fitted curves are in good agreement with the test data, and the parameters are different for different materials. Finally, the fitting parameters are given.

An ant colony algorithm applied to lay-up optimization of laminated composite plates

Abstract: ANT COLONY OPTIMIZATION (ACO) IS A CLASS OF HEURISTIC ALGORITHMS PROPOSED TO SOLVE OPTIMIZATION PROBLEMS. THE IDEA WAS INSPIRED BY THE BEHAVIOR OF REAL ANTS, RELATED TO THEIR ABILITY TO FIND THE SHORTEST PATH BETWEEN THE NEST AND THE FOOD SOURCE. ACO HAS BEEN APPLIED SUCCESSFULLY TO DIFFERENT KINDS OF PROBLEMS. SO, THIS MANUSCRIPT DESCRIBES THE DEVELOPMENT AND APPLICATION OF AN ACO ALGORITHM TO FIND THE OPTIMAL STACKING SEQUENCE OF LAMINATED COMPOSITE PLATES. THE DEVELOPED ACO ALGORITHM IS EVALUATED ON FOUR EXAMPLES FOR SYMMETRIC AND BALANCED LAY-UP. THE RESULTS OF THE FIRST THREE CASES, IN WHICH THE CLASSICAL LAMINATION THEORY IS USED TO OBTAIN THE STRUCTURAL RESPONSE OF RECTANGULAR PLATES, ARE COMPARED TO THOSE OBTAINED FROM THE LITERATURE USING GENETIC ALGORITHMS (GA) AND OTHER ACO ALGORITHM. THE FOURTH EXAMPLE INVESTIGATES THE MAXIMIZATION OF FUNDAMENTAL FREQUENCIES OF RECTANGULAR PLATES WITH CENTRAL HOLES, WHERE THE STRUCTURAL RESPONSE IS OBTAINED BY FINITE ELEMENT ANALYSIS, SHOWING THAT THIS OPTIMIZATION TECHNIQUE MAY BE SUCCESSFULLY APPLIED TO A BROAD CLASS OF STACKING SEQUENCE PROBLEMS FOR LAMINATED COMPOSITES.

Non-linear FEM analysis of seismic induced pounding between neighbouring multi-storey structures

Abstract: Pounding of neighbouring construction of structures due to seismic excitation increases the damage of structural components or even causes collapse of structures Among the possible building damages, earthquake induced pounding has been commonly observed in several earthquakes Therefore it is imperative to consider pounding effect for structures This study aims to understand the response behaviour of adjacent buildings with dissimilar heights under earthquake induced pounding Effects of different separation distances between structures are also investigated Nonlinear finite element analysis in time domain has been carried out for pounding of neighbouring structures having varying heights To show the importance of avoiding pounding in structures the results obtained were compared with model having no pounding phenomena The results were obtained in the form of storey shear, pounding force, storey drift, point displacement and acceleration The acceleration at pounding level significantly increases during collision of building The generated extra pounding force may cause severe damage to structural members of structures Pounding produces shear at various story levels, which are greater than those obtained from no pounding case Building with more height suffers greater damage than shorter building when pounding occurs Increasing gap distance tends to reduce story shear in consistent manner The results also show that the conventional modelling of building considering only beams and columns underestimates pounding effects More realistic modelling such as beams, columns and slabs shall be adopted to accurately understand the pounding phenomenon

Vibrations of beams with a variable cross-section fixed on rotational rigid disks

Abstract: The work is focused on the problem of vibrating beams with a variable cross-section fixed on a rotational rigid disk. The beam is loaded by a transversal time varying force orthogonal to an axis of the beam and simultaneously parallel to the disk's plane. There are many ways of usage of the technical moveable systems composed of elements with the variable cross-sections. The main applications are used in numerous types of turbines and pumps. The paper is a kind of introduction to the dynamic analysis of above mentioned beam systems. The equations of motion of rotational beams fixed on the rigid disks were derived. After introducing the Coriolis forces and the centrifugal forces, the transportation effect in the mathematical model was considered. This particular project is the first stage research, where there were proposed certain solutions of problems connected with the linear variable cross-sections systems. The further investigation considering the nonlinear systems has been proceeding. The results, analysis and comparison will be presented in the future works.

Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms

Abstract: We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.

Prototypes and modulation functions of classical and novel configurations of optical chopper wheels

Abstract: Optical choppers with rotating wheels are some of the most used macroscopic optomechatronic devices for the controlled modulation, attenuation or obscuration of light in a wide area of applications. We discuss and compare the modulation functions produced by two types of chopper wheels: the classical device, with windows with linear edges, and the eclipse chopper (with windows with circular edges) that, to the best of our knowledge, we have introduced. This discussion is based on the analysis and the design we have previously developed for these various devices, for top-hat (constant over the entire section) light beam distributions. While the comparison of the different shapes of transmitted signals allows for the proper choice of the most appropriate device and parameters to obtain the modulation function that is fit for a certain application, the present work also presents the mechanical setup we have designed and manufactured for testing choppers with rotating wheels. A series of prototype wheels with different, optimized profiles were obtained for the purpose. The simulation and the electro-erosion programs for the wire electro-erosion of aluminum plates to manufacture the wheels are presented. An advantageous double wheel solution has been developed to obtain wheels with windows of different shapes and sizes, and the testing of this final assembly concludes the study.

Damage of plates due to impact, dynamic pressure and explosive loads

Abstract: It is the purpose of this article to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects. The damage is characterised as the final or permanent transverse displacement of a plate. The theoretical method predicts values for the maximum permanent transverse displacements which agree reasonably well with the corresponding experimental results generated on aluminium alloy circular, square and rectangular plates. Thus, the equations presented in this article are valuable for preliminary design purposes and for forensic studies, while the experimental data can be used for validating numerical schemes.

Flexure of thick orthotropic plates by exponential shear deformation theory

Abstract: In the present paper, a variationally consistent exponential shear deformation theory taking into account transverse shear deformation effect is presented for the flexural analysis of thick orthotropic plates. The inplane displacement field uses exponential function in terms of thickness coordinate to include the shear deformation effect. The transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate, hence the theory does not require shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexure of simply supported orthotropic plates are compared with those of other refined theories and elasticity solution wherever applicable. The results obtained by present theory are in excellent agreement with those of exact results and other higher order theories. Thus the efficacy of the present refined theory is established.

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

Abstract: This paper presents effects of boundary conditions and axial loading on frequency characteristics of rotating laminated conical shells with meridional and circumferential stiffeners, i.e., stringers and rings, using Generalized Differential Quadrature Method (GDQM). Hamilton's principle is applied when the stiffeners are treated as discrete elements. The conical shells are stiffened at uniform intervals and it is assumed that the stiffeners have similar material and geometric properties. Equations of motion as well as equations of the boundary condition are transformed into a set of algebraic equations by applying the GDQM. Obtained results discuss the effects of parameters such as rotating velocities, depth to width ratios of the stiffeners, number of stiffeners, cone angles, and boundary conditions on natural frequency of the shell. The results will then be compared with those of other published works particularly with a non-stiffened conical shell and a special case where angle of the stiffened conical shell approaches zero, i.e. a stiffened cylindrical shell. In addition, another comparison is made with present FE method for a non-rotating stiffened conical shell. These comparisons confirm reliability of the present work as a measure to approximate solutions to the problem of rotating stiffened conical shells.

Boundary element method applied to the bending analysis of thin functionally graded plates

Abstract: The present work introduces the boundary element method applied to the bending analysis of functionally graded plates. It is assumed that material properties are graded through the thickness direction of the plate according to a power law distribution. The neutral surface position for such plate is determined and the classical plate theory based on the exact neutral surface position is employed to extract the equilibrium equations. A direct approach based on the Green's identity is used to formulate boundary element method. By introducing a novel approach, domain integrals which arise from distributed transverse loads are transformed into boundary integrals. In case studies, three geometrical shapes including, rectangular, circular and elliptic for functionally graded plates with/without hole are considered. Comparative studies are first carried out to evaluate the sufficiency of the proposed method for bending analysis of isotropic and functionally graded plates subjected to the transverse loads. Then, a series parametric study is performed to examine the influences of the power of functionally graded material, boundary conditions and geometrical parameters on the deformation and stress of functionally graded plates.

Material and geometric nonlinear analysis of reinforced concrete frame structures considering the influence of shear strength complementary mechanisms

Abstract: A mechanical model for the analysis of reinforced concrete frame structures based on the Finite Element Method (FEM) is proposed in this paper. The nonlinear behavior of the steel and concrete is modeled by plasticity and damage models, respectively. In addition, geometric nonlinearity is considered by an updated lagrangian description, which allows writing the structure equilibrium in the last balanced configuration. To improve the modeling of the shear influence, concrete strength complementary mechanisms, such as aggregate interlock and dowel action are taken into account. A simplified model to compute the shear reinforcement contribution is also proposed. The main advantage of such a model is that it incorporates all these effects in a one-dimensional finite element formulation. Two tests were performed to compare the provided numerical solutions with experimental results and other one- and bi-dimensional numerical approaches. The tests have shown a good agreement between the proposed model and experimental results, especially when the shear complementary mechanisms are considered. All the numerical applications were performed considering monotonic loading.

Analysis of laminated composite skew shells using higher order shear deformation theory

Abstract: Static analysis of skew composite shells is presented by developing a C0 finite element (FE) model based on higher order shear deformation theory (HSDT). In this theory the transverse shear stresses are taken as zero at the shell top and bottom. A realistic parabolic variation of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Sander's approximations are considered to include the effect of three curvature terms in the strain components of composite shells. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature on the problem of skew composite shell based on HSDT, present results are validated with few results available on composite plates/shells. Many new results are presented on the static response of laminated composite skew shells considering different geometry, boundary conditions, ply orientation, loadings and skew angles. Shell forms considered in this study include spherical, conical, cylindrical and hypar shells.

Dynamic response of functionally graded skew shell panel

Abstract: The dynamic response of functionally graded skew shell is investigated using a C0 finite element formulation. Reddy's higher order theory has been employed to perform the analysis and the volume fractions of the ceramic and metallic components are assumed to follow simple linear distribution law. The present study attempts to focus mainly on the influence of skew angle on frequency parameter and displacement of shell panel with various geometries. Comprehensive numerical results are demonstrated for cylindrical, spherical and hypar shells for different boundary conditions and skew angles.The findings obtained for functionally graded skew shell panels are new and can be used as bench mark for researchers in this field.

Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

Abstract: In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He’s Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

Three-dimensional compatible finite element stress analysis of spinning two-directional FGM annular plates and disks with load and elastic foundation non-uniformities

Abstract: Three-dimensional bending and stress analyses of the rotating two-directional functionally graded annular/circular plates or disks have not been accomplished so far. This task is performed in the present paper, employing a finite element formulation with a C1-continuity. Therefore, both transversely graded and radiallygraded plates may be analyzed as special cases of the present research. Distribution of the transverse loads as well as coefficients of the elastic foundation may be non-uniform. Mixed stress-based and displacement-based edge conditions are considered to cover many practical applications. Compatible Hermitian elements are employed to develop a consistent formulation and avoid jumps in the stress components at the elements interfaces. In contrast to the very limited works presented for the rotating functionally graded circular plates so far, the transverse flexibility and the transverse stress components are also considered in the present research. Finally, influences of the material properties distribution, angular speed, geometric parameters, and the elastic foundation on distributions of the stress and displacement components are investigated for a variety of edge and boundary conditions and some design criteria are extracted.

Fe analysis of laminated composite plates using a higher order shear defor-mation theory with assumed strains

Abstract: A STUDY ON THE FINITE ELEMENT (FE) ANALYSIS OF LAMINATED COMPOSITE PLATES IS DESCRIBED IN THIS PAPER. IN ORDER TO INVESTIGATE STRUCTURAL BEHAVIOR OF LAMINATED COMPOSITE PLATES, A FOUR-NODE LAMINATED PLATE ELEMENT IS NEWLY DEVELOPED BY USING A HIGHER ORDER SHEAR DEFORMATION THEORY (HSDT). IN PARTICULAR, ASSUMED NATURAL STRAINS ARE INTRODUCED IN THE PRESENT FE FORMULATION TO ALLEVIATE THE LOCKING PHENOMENON. SEVERAL NUMERICAL EXAMPLES ARE CARRIED OUT AND ITS RESULTS ARE THEN COMPARED WITH THE EXISTING REFERENCE SOLUTIONS. IT IS FOUND TO BE THAT THE PROPOSED FE IS VERY EFFECTIVE TO REMOVE THE LOCKING PHENOMENON AND PRODUCES RELIABLE NUMERICAL SOLUTIONS FOR MOST LAMINATED COMPOSITE PLATE STRUCTURES.

Transverse load distribution of skew cast-in-place concrete multicell box- girder bridges subjected to traffic condition

Abstract: Concrete multicell box-girder bridges are a common choice among the designers for various ranges of bridges. In order to provide safer and greater speed of traffic, the roadway is built as straight as possible. The use of skewed bridges has increased considerably in the recent years for roadway. The skewed bridges have quite different mechanical behavior from the straight bridges, although for skew angles less than 20 degrees, it is reasonably safe to ignore the effect of skew angles and analyze that at the straight bridge. In this study, in developing an analytical solution, an extensive parametric study was carried out to determine the maximum positive and negative stress distribution factors and to calculate the maximum distribution factor of deflection along the mid-span of skewed multicell box-girder bridges. A total of 240 representative bridges numerical models were selected and analyzed using SAP2000 finite element software. It was found that the span length, number of boxes, number of lanes and skew angles significantly affected the distribution factors of stress and deflection. Finally, several equations were proposed for stress and deflection distribution factors of multicell box-girder bridges for the application of American Association of State Highway and Transportation officials load and resistance factor design live loads.

Large amplitude free vibration of orthotropic shallow shells of complex shapes with variable thickness

Abstract: The present formulation of the analysed problem is based on Donell’s nonlinear shallow shell theory, which adopts Kirchhoff’s hypothesis. Transverse shear deformations and rotary inertia of a shell are neglected. According to this theory, the non-linear strain-displacement relations at the shell midsurface has been proposed. The validity and reliability of the proposed approach has been illustrated and discussed, and then a few examples of either linear or non-linear dynamics of shells with variable thickness and complex shapes have been presented and

Propagation of plane waves at the interface of an elastic solid half-space and a microstretch thermoelastic diffusion solid half-space

Abstract: The problem of reflection and refraction phenomenon due to plane waves incident obliquely at a plane interface between uniform elastic solid half-space and microstretch thermoelastic diffusion solid half-space has been studied. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the microstretch thermoelastic diffusion properties of the media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios have been computed numerically for a particular model. The variations of energy ratios with angle of incidence are shown for thermoelastic diffusion media in the context of Lord-Shulman (L-S) (1967) and Green-Lindsay (G-L) (1972) theories. The conservation of energy at the interface is verified. Some particular cases are also deduced from the present investigation.

New design chart for basic wind speeds in Brazil

Abstract: The design charts for basic wind speeds currently in use in Brazil [1] were created in 1977, based on wind speed records from 1950 to 1974. The database covered up to 25 years of wind records obtained in 49 weather stations, totaling 919 station×years of data. Since 1974, additional 37 years of wind records became available, but have not been incorporated in the design code. Hence, the updated wind charts proposed in this paper are long overdue. In this paper, 62 years of wind records in Brazil are gathered in order to construct updated and more reliable wind charts. The original data by Padaratz [2] are complemented by data from 104 airport weather stations, made available through the Wolfram Research Database [3]. In total, 4142 station×years of data are used in the present study, hence providing much better cover in terms of space and time span. Maximum annual wind speeds for the individual stations are fitted to Gumbel distributions, from which basic wind speeds are evaluated (mean return period of 50 years). Basic wind speeds are used to build a non-linear regression model, using the p-value of the Anderson-Darling goodness-of-fit test as regression weight. This ensures that extreme value wind distributions for which a good fit is obtained are given more importance in the regression model, reducing the influence of spurious data. The regression model developed herein is used to plot a new design chart for basic wind speeds in Brazil. It is proposed that this new wind chart be incorporated in the Brazilian code for design of structures subject to wind [1]. In this regard, it is observed that basic wind speeds obtained herein are higher than the wind speeds of the current chart for significant parts of Brazil (notably the center, northeast and north), and are the same or smaller in some parts of the south and southeast. It is shown herein that the main differences between the current and the proposed charts are not due to different modeling assumptions, but are mainly due to the new data. The proposed chart is updated, and is more reliable than the chart currently in use, as it reflects 4142 station×years of data, and covers up to 62 years of wind records.

Determination of the rheological properties of thin plate under transient vibration

Abstract: The article deals with systematic analysis of the transient vibration of rectangular viscoelastic orthotropic thin 2D plate. The analysis is focused on specific deformation models of plate and for specific linear models of rheological properties. The viscoelastic isotropic and anisotropic (orthotropic) materials were investigated. The plate is loaded by general transient impulse. The time and coordinate dependencies of the fundamental quantities - displacements, rotations, stress and deformations in arbitrary points of plate under transient vibration, e. g. the analysis of stress and deformation waves in plates were investigated. The selected models are defined by constitutive equations for stress and deformation dependence. The isotropic and orthotropic model is considered. The analysis results depend on quality of the determined mechanical properties of the materials. The standard methods commonly used are time-consuming and not accurate enough. The new methodology of determining the material parameters directly from investigated plate is proposed and proven.

Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

Abstract: Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

On dynamic self-organization: examples from magmatic and other geochemical systems

Abstract: Standard Liesegang banding is the display of parallel bands of precipitate formed periodically when co-precipitate ions interdiffuse in a gel medium. The most striking resemblance with Liesegang patterns in Nature lies in the diverse scenery of banded textural features commonly observed in some geological materials, such as geodes, agates, malachites, as well as stratigraphic units of certain rock formations. Here, we explore the possible relationship between the Liesegang banding scenario and magmatic-type pattern formation, such as zonations in km-scale circular zoned plutons and anorogenic ring complexes, cyclic layering in large mafic - ultramafic layered intrusions and orbicular granites, as well as in mm-scale crystal zonations. We also investigate magmatic processes such as fractional crystallization, and the ranges of T and p that are compatible with operating conditions for Liesegang banding. For geochemical self-organization to operate via a Liesegang-type mechanism, a necessary condition is that the system be transiently out of equilibrium, and be described by complex nonlinear kinetic laws. We examine the viability of the development of geochemical patterns, in relation with the various requirements for the growth of Liesegang structures.

An object-oriented class design for the generalized finite element method programming

Abstract: The Generalized Finite Element Method (GFEM) is a numerical method based on the Finite Element Method (FEM), presenting as its main feature the possibility of improving the solution by means of local enrichment functions. In spite of its advantages, the method demands a complex data structure, which can be especially benefited by the Object-Oriented Programming (OOP). Even though the OOP for the traditional FEM has been extensively described in the technical literature, specific design issues related to the GFEM are yet little discussed and not clearly defined. In the present article it is described an Object-Oriented (OO) class design for the GFEM, aiming to achieve a computational code that presents a flexible class structure, circumventing the difficulties associated to the method characteristics. The proposed design is evaluated by means of some numerical examples, computed using a code implemented in Python programming language.

A numerical simulation of metallic cylindrical sandwich shell subjected to air blast loading

Abstract: The dynamic response of cylindrical sandwich shells with aluminum foam cores subjected to air blast loading was investigated numerically in this paper. According to KNR theory, the nonlinear compressibility of the air and finite shock conditions were taken into account in the finite element model. Numerical simulation results show that the compression strain, which plays a key role on energy absorption, increases approximately linearly with normalized impulse, and reduces with increasing relative density or the ratio of face-sheet thickness and core thickness. An increase of the impulse will delay the equalization of top and bottom face-sheet velocities of sandwich shell, but there is a maximum value in the studied bound. A limited study of weight optimization was carried out for sandwich shells with respect to the respective geometric parameters, including face-sheet thickness, core thickness and core relative density. These numerical results are of worth to theoretical prediction and engineering application of cellular metal sandwich structures.

High precise analysis of lateral vibration of quintic nonlinear beam

Abstract: This article intends to achieve a new formulation of beam vibration with quintic nonlinearity, including exact expressions for the beam curvature To attain a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system In this direction, new powerful analytical method called Parameter Expansion Method (PEM) is employed to obtain the exact solution of frequency-amplitude relationship Afterwards, it is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of mentioned system Finally, preciseness of the present analytic procedures is evaluated in contrast with numerical calculations methods, giving excellent results

Large deformation analysis of homogeneous rubber-like materials via shell finite elements

Abstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubber-like materials is presented. The element is a triangular shell of any-order with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the Reissner-Mindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cook's membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking.

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

Abstract: In the present work, a layerwise trigonometric shear deformation theory is used for the analysis of two layered (90/0) cross ply laminated simply supported and fixed beams subjected to sinusoidal load. The displacement field of the present theory consists of trigonometric sine function in terms of thickness coordinate to take into account the effect of transverse shear deformation. Theory satisfies the trans-verse shear stress free boundary conditions at top and bottom surfaces of the beam. This model satisfies the constitutive relationship between shear stress and shear strain in both the layers and the axial displacement compatibility at the interface. Virtual work principle is employed to obtain governing equations and boundary conditions. Closed form solution technique has the limitation of simply supported boundary condition. In the present work general solution technique is developed, which can be used for any type of boundary and loading conditions. The transverse shear stresses are obtained using constitu-tive relation as well from the use of equilibrium equations. The results of displacements and stresses obtained by present theory are compared with the available results in the literature.