# Top PDF Strain resolving method of composite plane plates

### Strain resolving method of composite plane plates

Abstract: The paper deals with the extension of isotropic plates problem to the case of composite plates. In order to perform it, the Kirchhoff-Love hypotheses were “softened” by some additional ones. Considering the constitutive laws for composite materials the stress functions were eliminated by using Cauchy equations. As a result a partial derivative equation in displacements was obtained. Finally the boundary condition formulation was extended for the case of complex composite plates.

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### Energy based collocation method to predict progressive damage behavior of imperfect composite plates under compression

Finite Strip Method (FSM) is another universally applicable method for buckling and post-buckling analyses of plates and plate structures. It can be considered as a particular kind of simplified finite element method in which a special element called strip is used. Finite strip method is based on discretization of the domain into lon- gitudinal strips and interpolates the behavior in the longitudinal direction by different functions and in the trans- verse direction by polynomial functions. Cheung (1976) may be considered as the pioneer who ﬁrst proposed the concept of FSM. Cheung established FSM for the analysis of simply supported plates. The studies presented by Smith and Sridharan (1978) proposed FSM for buckling of isotropic plate under edge loading. Recently, Ovesy, Ghannadpour and their co-workers (Ovesy et al. 2005) have made a contribution by introducing two different versions of finite strip methods, namely the full-energy and semi-energy finite strip approaches. Two other differ- ent versions of finite strip method, namely spline and semi-analytical methods are also developed by them for predicting the response of rectangular laminates with non-symmetric and symmetric forms of initial imperfec- tion. They used both formulations to predict the non-linear response of channel sections when subjected to uni- form end-shortening in their plane (Ovesy et al. 2006). An exact finite strip is introduced by Ghannadpour and Ovesy (2008) to investigate the exact relative post-buckling stiffness of I-section struts. To extend their works, they developed a high accuracy finite strip for the buckling and post-buckling analyses of moderately thick sym- metric cross-ply composite plates based on FSDT (Ovesy et al. 2016).
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### Buckling Analysis of Laminated Anisotropic Kirchhoff’s Plates via The Boundary Element Method

The bending problem of thin plates can be modelled by the Classical Plate Theory (CPT) (or Kirchhoff-Love theory) when the out-of-plane displacement is small and shear deformations are negligible. The first works using BEM to analyze the bending of thin plates with Kirchhoff-love's theory were presented in the 1970s. Some of those works can be found in Bézine (1978), Altiero and Sikarskie (1978), and Stern (1979). More recently, Dirgantara and Aliabadi (1999, 2006) investigated the bending and the large deflection of shells. Albuquerque et al. (2006) studied the bending of laminated composite Kirchhoff plates. Katsikadelis and Babouskos (2009) used BEM with the analog equation method to study bending and vibration of thick plates.
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### Optimal dynamic control of laminated adaptive structures using a higher order model and a genetic algorithm

Batra and Liang 11 used a three-dimensional linear theory of elasticity to find the optimal location of an actuator on a simple-supported rectangular laminated plate with embedded PZT layers. The optimal design is obtained by fixing the applied voltage and the size of the actuator and moving it around in order to find the maximum out-of-plane displacement. Liang et al. 12 proposed a model for the optimization of the induced-strain actuator location and configuration for active vibration control. Correia et al. 13 presented refined finite element models based on higher order displacement fields applied to the optimal design of laminated composite plates with embedded or surface bonded piezoelectric actuators and sensors.
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### Lat. Am. j. solids struct. vol.10 número3

shear deformation through the thickness direction of the plates. In particular, The HSDTs do not required shear correction factor and it can generally guarantee zero transverse shear stress values on the top and bottom surfaces of the plate. Some important and early works on HSDT can be found in the open literatures [1-5] where more realistic representation of transverse shear deformation were generally tried to be provided. Later, Zhang and Yang [6] described some recent developments of the FEs based on various laminated composite plate theories. Reddy [1] suggested a simple but very useful HSDT for laminated composite plates. His version of HSDT is based on equivalent single layer plate theory and it allows parabolic variation of transverse shear stress and also satisfies zero shear stress boundary conditions at the top and bottom surfaces of the plate. Moreover, it does not involve any unknown fields which do not have any physical meaning. Bose and Reddy [7, 8] ana- lyzed laminated plates by using a unified third-order laminate plate theory that contains classical, first-order and third-order theories and they presented analytical method using the Navier and Levy equations and the FE method using the unified third order laminate plate theory. A review on the various methods used in the estimation of transverse and inter-laminar stresses for laminated com- posite plates and shell including both analytical and numerical methods was provided by Kant and Swaminathan [9]. Kant and Manjunatha [10] provided the FE based on HSDT having twelve de- grees of freedom per node. They presented three-dimensional stress and strain states to investigate the flexure-membrane coupling behavior of unsymmetrical laminated plate. Akhars and Li [11] de- veloped a spline finite strip method for static and free vibration analysis of composite plates using Reddy’s HSDT. Pervez et al [12] developed a two dimensional serendipity FE based on a refined HSDT having seven degrees of freedom per node to perform the linear static analysis of laminated orthotropic composite plates. Latheswary et al [13] studied the behavior of laminated composite plates under static loading by using a four-node nonconforming element based on HSDT. Goswami [14] presented a simple C^0 FE formulation for nine-node FE with six degrees of freedom based on HSDT.
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### Lat. Am. j. solids struct. vol.11 número12

Owing to the fact that the stiffened plate elements of ships are thin-walled, their out-of-plane stress is negligible but their in-plane stress is determinant. Hence, the modeling of these components is precise enough with shell elements. Therefore, the element Shell 181, that is appropriate for mod- eling the thin and relatively thick plates and is constructed based on Classic Plate Strain and Mindlin theories, was used in the analyses. These elements are composed of 4 nodes and each node has 6 degrees of freedom. This element is appropriate for linear and nonlinear solutions with large deformations and great angle variations. Also, this element can be used for modeling the composite and laminated materials.
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### Finite Element Simulation of Interlaminar and Intralaminar Damage in Laminated Composite Plates Subjected to Impact

Here In this study, the composite laminates subjected to transverse impact with consideration interlaminar and intralaminar damage based on Cohesive Zone Model (CZM) and Progressive Damage Model (PDM) are investigated by numerical analysis using ABAQUS commercial finite element code. The delamination in stacking ply with the same fiber orientation is considered as interlaminar damage and the delamination in an inner layer of any cluster is ignored. Hashin criterion is used for intralaminar damage initiation and evolution without using any subroutine. First, the appropriate procedure for delamination on composite specimen was suggested based on CZM approach in double cantilever beam to verify the intralaminar damage simulation. Then by considering several case studies with different impact energies, the results of present simulation is verified with the relevant and available experimental results and numerical references in the existing literature. According to the available experimental results the present simulation results are more acceptable and accurate than the results of similar numerical works, especially in higher impactor velocity.
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### Method of Obtaining a Composite Material Based on Small-Dispersed Particles

In this work a method of obtaining a composite material based on small-dispersed particles is consid- ered. Proposed method consists of two steps of separation, mechanical – rough separation and plasma – soft separation, and also of step of deposition a catalytic nanolayer by wet impregnation of separated parti- cles in an aqueous solution of nickel nitrate. During such procedure a composite powder of small-dispersed zeolite particles with average diameter of 5 m and catalytic nickel layer was obtained. All obtained sam- ples were studied on a Quanta 3D 200i scanning electron microscope. Microscopic analysis and obtained experimental results show, that increasing of dispersion of separated powder allows for increasing a mass of catalyst in the composite, and the used separation method in plasma for obtaining of particles with high dispersion do not erode a catalytic layer.
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### Microstructure and Mechanical Properties of AA6061AZ31BAA6061 Composite Plates Fabricated by Vertical Explosive Welding and Subsequent Hot Rolling

Figure 7 exhibits the interface microstructure of magnesium alloys in the rolled sample under various annealing conditions. Figure 7a is the microstructure of magnesium alloys in the rolled sample without annealing. It shows the typical nonuniform bimodal microstructure, fine grain sharing the submicrometer dimensions in comparison with the largest elongated grain with the size of 29.2 µm, indicating nonuniform deformation during hot rolling process. Figure 7b is the OM images of the middle zone of Mg alloys obtained from rolled sample without annealing. Due to incomplete dynamic recrystallization in the process of hot rolling, a certain amount of fine recrystallization structure appeared. Figure 7c-e exhibits the optical micrographs of Mg alloys near the interface in the rolled samples annealed at different temperatures for 1 h. Figure 7c and d shows small Figure 4. SEM images of the composite interfaces after explosive welding (a) big waveform (c) mini waveform.
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### Mat. Res. vol.17 número5

Figure 8 presents the variation of the maximal thermal stresses in the plate and the composite patches as a function of the ratio c/R deined previously for comparison between circular and elliptical patches. The stresses are calculated in the ibre direction (parallel to the direction of the applied load). We can see the process of adhesive curing involves relatively high level of thermal stresses along the ibre axis in the plate and the sign of this stresses is positive. It means that, according to the ibre direction, the aluminum plate is under tensile stresses. This is due to the fact that during the cooling the composite patch prevents the return of the aluminum plate to its initial position after dilatation. This behavior leaves the plate in tension.
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### Finit element model for active control of adaptive laminated structures

Abstract. A finite element formulation for active vibration control of thin plate laminated structures with integrated piezoelectric layers, acting as sensors and actuators is presented. The finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric element layer, and is based on the Kirchhoff classical laminated theory. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers, and Newmark method is used to calculate the dynamic response of the laminated structures. The model is applied in the solution of several illustrative cases, and the results are presented and discussed.
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### Lat. Am. j. solids struct. vol.14 número3

The dynamic behavior of variable stiffness composite laminated (VSCL) plate with curvilinear fiber orientation subjected to in- plane end-loads is investigated. A variable stiffness design can increase the laminated composite structural performance and also provides flexibility for trading-offs between various structural prop- erties. In each ply of the VSCL plate, the fiber-orientation angle assumed to be changed linearly with respect to horizontal geometry coordinate. The spline finite strip method based on both classical as well as higher order shear deformation plate theories is formulated to explain the structural behavior. The panel is assumed containing internal square delamination regions with friction and contact conditions at delaminated interfaces are not considered. In order to demonstrate the capabilities of the developed method in predicting the structural dynamic behavior, some representing results are obtained and compared with those available in the literature. The effects of change in curvilinear fiber orientation angles on the struc- tural stability is studied. The obtained results show very good conformity in comparison with those exists in the available litera- ture .
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### Lat. Am. j. solids struct. vol.14 número12

In order to evaluate the performance of the developed element for the study of free vibration response of irregular plates, a five layer symmetric cross-ply skew laminated plates (90/0/90/0/90) with simply supported edges is considered. The geometry of the skew plates is shown in Figure 7. The material properties MM5 of Table 2 is used for this analysis. The skew angle α is varied from 0°, 15°, 30°, 45° and 60°. The non-dimensional natural frequencies for the first four modes are reported in Table 6, considering the thickness ratios (a/h) as 10. A mesh size of 12×12 is considered for the analysis. The first six flexural mode shapes obtained for α = 45° are shown in Figure. 8. The comparison was made with the analytical solutions of Wang (1997) using B-spline Rayleigh-Ritz method, the solution of Ferreira et al. (2005) based on Radial Basic Function (RBF), as well as with the finite element models of Nguyen-Van (2009) and Garg et al. (2006). The results of the comparison show the effectiveness of the present element in the analysis of this type of structures.
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### Core and patch position optimizations for vibration control of piezolaminated structures

For discrete variable structural problems, a variety of methods including simulated annealing can be used [14,23,24]. As pointed out by Correia et al [24,25], among others, the main advantage of this method, in comparison with gradient-based methods, is the ability to overcome the premature convergence towards a local optimum. By other hand, the main disadvantage is related with the computational lost, because of the high number of objective function evaluations usually required to reach the optimal solution, which is especially relevant when the objective function evaluation is computationally expensive. The implemented simulated annealing procedure employs a random search that generates feasible sets of design variables, accepting not only changes in the design variables that decrease the objective function but also changes that increase it. The latter changes are accepted with a certain probability. The basic functioning of the simulated annealing algorithm can de easily described as follows [16,23]:
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### Lat. Am. j. solids struct. vol.10 número1

The problem of nonlinear vibrations and stability analysis for the symmetric laminated plates with complex shape, loaded by static or periodic load in-plane is considered. In general case research of stability and parametric vibrations is connected with many mathematical difficulties. For this reason we propose approach based on application of R-functions theory and varia- tional methods (RFM).The developed method takes into ac- count pre-buckle stress state of the plate. The proposed ap- proach is demonstrated on testing problems and applied to laminated plates with cutouts. The effects of geometrical pa- rameters, load, boundary conditions on stability regions and nonlinear vibrations are investigated.
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### Adhesive joints for vegetal natural fibres reinforced composites

Today the search for new, recyclable and renewable materials is leading the researchers in new ways. Natural products applications are emerging and some research is starting in this matter. The work presented here analyse the utilization of adhesives single lap joints at joining processes to assemble of different parts made with natural vegetal sisal fibres reinforced composite materials. Some different sisal/epoxy composite plates are made utilising sisal fibres with different surface treatments, with the purpose of increasing the adhesion between the fibres and the matrix, and consequently to improve mechanical behaviour of the composite material [1,2 and 3] and the adhesives joints. The treatment used is called mercerization, and is described below. Before the treatment application the natural fibres were cleaned in order to remove contaminating agents.
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### Optimal design of beam-column connections of plane steel frames using the component method

In recent years, there has been a great growth of industrial buildings and residences structured in steel. The steel structures are formed by the connection of several structural elements aiming the efficient conduction of the external forces acting on the structures for the foundations. The steel has advantageous physical and mechanical characteristics for use in the construction of plane frames, such as: good relationship between strength and structural weight, adaptability to various architectural forms, wide variety of profiles available in the market, great control in the manufacturing process in the mills which results in greater reliability in the use of these buildings.
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### Mat. Res. vol.6 número1

The optical bandgap energies (OBGE) of 3C, 15R, 6H and 4H-SiC have been investigate experimentally by transmission and photoacoustic spectroscopies. The measurements were per- formed on 470 µm thick wafers. The OBGE obtained from both spectroscopies for different polytypes show very good agreement. In order to have a better understanding of these materials calculations of eletronic band structure were performed by the full-potential linearized augmented plane wave (FPLAPW) method. For the OBGE the results are compared to the measurements agreeing closely over the energies of those polytypes.
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