Purpose: The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye- care professional. We have developed a **finite** **element** **model** of the cornea, that tries to predicts keratoconus-like behavior and its evolution based on material properties of the corneal tissue. Methods: Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye **model**. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. Results: The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized pro- tuberance and increase in curvature when compared to the remaining portion of the cornea. Conclusions: This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented **model** has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

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In this work, a bone damage resorption **finite** **element** **model** based on the disruption of the inhibitory signal transmitted between osteocytes cells in bone due to damage accumulation is developed and discussed. A strain-based stimulus function coupled to a damage-dependent spatial function is proposed to represent the connection between two osteocytes embedded in the bone tissue. The signal is transmitted to the bone surface to activate bone resorption. The proposed **model** is based on the idea that the osteocyte signal reduction is not related to the reduction of the stimulus sensed locally by osteocytes due to damage, but to the difficulties for the signal in travelling along a disrupted area due to microcracks that can destroy connections of the intercellular network between osteocytes and bone-lining cells. To check the potential of the proposed **model** to predict the damage resorption process, two bone resorption mechano-regulation rules corresponding to two mechanotransduction approaches have been implemented and tested: 1) Bone resorption based on a coupled strain-damage stimulus function without ruptured osteocyte connections (NROC); and 2) Bone resorption based on a strain stimulus function with ruptured osteocyte connections (ROC). The comparison between the results obtained by both models, shows that the proposed **model** based on ruptured osteocytes connections predicts realistic results in conformity with previously published findings concerning the fatigue damage repair in bone.

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The table in Fig. 5 shows the tip vertical displacements obtained with a refined shell **finite** **element** **model** and GBT, the latter using 50 **finite** elements and different combinations of the following mode sets: (i) rigid-body (RB), (ii) Vlasov distortional (D) and (iii) local-plate modes (LP). The shear (S) and transverse extension (TE) modes have virtually null influence on the results and were left out. The GBT solution including only the RB modes leads to very inaccurate results due to the influence of the D (mostly) and the LP modes, whose inclusion in the analysis leads to displacements that virtually match those of the shell **model**. This is clearly displayed in the deformed configurations presented in Fig. 5. As in the case of prismatic open sections, this shows that including only the RB+D+LP modes in the analysis is generally sufficient to achieve very accurate results.

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In this article it was used the commercial software ANSYS WORKBENCH v14.0 to evaluate SCF produced by a shallow notch broached on HSS specimen. For numerical **model** purposes the speci- men material was considered isotropic and linear elastic. The mesh was generated with hexahedrons elements PLANE 186 with plane stress option, with one node at each vertex, as shown in Fig. 6.a. The **finite** **element** **model** was created in 2-D dimension (in the X-Y plane) to reduce the computa- tional effort, as shown in Fig. 6.b.

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Other engineering applications using **finite** **element** **model** of smart structures have been reported. Ledda et al. (1999) presented the development of a **finite** **element** method to determine theoretically the first resonance frequency of a PVDF-TrFE transducer and Lopes et al. (2000) used the **finite** **element** formulation in order to generate the training data for a neural network to correlate the frequency response function (FRF) and the electrical impedance of smart structures.

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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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With considering numerous failures which exist in flexible pavements, a huge amount of money is spending on treatment and reconstructing pavements. Many researches have been performed to with improving pavement quality, increased the performance and pavements life. One type of long lasting pavements is perpetual pavement. In this research ABAQUS software is used to simulate pavement. . Materials are modelled as visco-elastic type and loading wheel is assumed to be moving. After gaining results, the effects of different parameters on pavements function is assessed. Modelling movements of loading wheel is very effective in viscoelastic condition, increase more accuracy of the **finite**-**element** **model**.

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The focus of this article will be the use of FEA for mechanical analysis of the cornea. We will review how this method has been applied to examine the cornea under different loads such as intraocular pres- sure (IOP), impact from a foreign object, or incisions. The method can also be used to examine how the shape is affected by changes in material properties, such as those occurring during keratoconus. It is worth mentioning briefly, though, that the method can be applied to a wide variety of problems. It has been used to study thermal, electri- cal, and other physical responses as well as ionic transport. Shafahi and Vafai (17) used a thermal **finite** **element** **model** of the eye to study

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Results indicate that position of neutral surface is very important in functionally graded materials. Kadoli et al. (2008) implemented displacement field based on higher order shear deformation theory to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Najeeb and Alam (2012) presented a one dimensional **finite** **element** **model** using an efficient layerwise (zigzag) theory for the dynamic analysis of laminated beams integrated with piezoelectric sensors and actuators. Mohanty et al. (2012) presented the evaluation of static and dynamic behavior of functionally graded ordinary (FGO) beam and functionally graded sandwich (FGSW) beam for pined–pined end condition. The variation of material properties along the thickness is assumed to follow exponential and power law. A **finite** **element** method is used assuming first order shear deformation theory for the analysis. Furqan and Naushad (2013) assessed higher order theory of laminated beams under static mechanical loads. The Third order theory and First order shear deformation theory are assessed by comparison with the exact two-dimensional elasticity solution of the simply-supported beam. Mehta et al. (2013) used **finite** **element** method in modelling the dynamic behavior of FGM to determine its natural frequency. The properties in the functionally graded ma- terial are assumed to vary according to power law. The natural frequencies were obtained for FG beams under various boundary conditions including Clamped-Fixed, Simply supported-Fixed, Clamped-Clamped, Simply supported-Simply-supported, and Clamped-Simply supported. Shi-rong Li et al. (2014) studied the free vibration of functionally graded material (FGM) beams based on both the classical and the first-order shear deformation beam theories. Nguyen et al. (2014) presented the analytical solutions for the static analysis of the transversely or axially functionally graded beams with tapered cross-section. The elastic modulus of the beam varies according to the power form.

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f k = re + off × (9) In this research, the main aim is to maximise the power output, which is calculated by using Eq. (7). However, this equation must be verified before proceeding with the analysis. Therefore, a comparison is made between the existing technique (the Roundy method [3]), experimental results, and the proposed technique. Under the same setup in each case, but varying the resistance, Eq. (2) is calculated and plotted in Fig. 4 (“theory”). To calculate the power output using the proposed method, a **finite** **element** **model** of the rectangular piezoelectric cantilever beam was developed for use in predicting the behaviour of the beam under a concentrated load at the free end, as shown in Fig. 2. The average **element** stress and the vertical deflection are obtained in the analysis. The obtained values are substituted into Eq. (7) and the results are plotted in Fig. 4 as “ANSYS simulation”.

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The main tasks of the **Finite** **Element** **Model** class are to compute the nodal d.o.f., to assemble the global vectors and matrices used by the analysis algorithms, to update nodal displacements, and to print com- puted results after convergence. Moreover, during the result computation it also calls, if necessary, the methods of the post-processing classes: Smoothing, Error, and Design Sensitivity Analysis, which are used for stress smoothing, discretization error assessment, and sensitivity computation, respectively. Node class basically stores the nodal data read from the input file (coordinates, springs, support condi- tions, and concentrated loads), as well as some variables computed during the program execution, as the nodal d.o.f. and the current displacements. It also provides a number of methods to query and to update the stored data.

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plates has been used for active vibration control study of smart beams and plates by many researchers [10, 14, 19]. The classical theory used in these studies to **model** the structures is based on Kirchhoff-Love’s assumption and hence neglects the transverse shear deformation effects. First order shear deformation theory has been employed for active vibration control of smart beams and plates by [4, 11–13, 21]. This theory however include the effects of transverse shear deformation but require shear correction factors which is a difficult task for the study of smart composite structures with arbitrary lay-up. To overcome these drawbacks, Reddy [17] developed third order shear deformation theory for plates. Peng, et al [16] presented the **finite** **element** **model** for the active vibration control of laminated beams using consistent third order theory. Zhou et al. [24] presented coupled **finite** **element** **model** based on third order theory for dynamic response of smart composite plates. Few studies [7, 22] on active vibration control smart plates have been performed using 3D solid elements but the computation cost is high due to increased number of degrees of freedom.

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In this research, **finite** **element** and boundary **element** meth- ods are coupled together to **model** the interaction of a piezo- electric ceramic working as an actuator with an elastic ma- terial. Piezoelectric-elastic material’s interaction occurs in smart structures. This work is aimed at determining the ac- tuation effects being transferred from the actuators to the host and the resulting overall structural response. To ob- tain the amount of these actuations, the system of the host structure and an actuator has been modeled by using cou- pled **finite** **element** boundary **element** method in frequency domain. The host structure, which is assumed as an isotropic elastic solid region is modeled as a half space. The piezo- electric ceramic region is modeled by the 3-D **finite** **element** method, while the elastic half space with boundary **element** method. **Finite** **element** **model** of piezoelectric ceramic and boundary **element** **model** of the elastic half space are cou- pled together at their interface such that the vibrations of the piezo-actuator induce vibrations in the elastic half space. A couple of examples are given to show the induced dis- placement field around the piezo-actuator on the surface of the elastic medium. The results show that high jump in magnitude of horizontal displacements at the corners of the actuator attached to the structure occurs, which is an indi- cation of high stress concentration, of the shear stress type at the corners. This stress concentration sometimes causes complete debonding of the actuator from the base structure. By using the suggested BEM-FEM coupled **model** for actu- ators with different dimensions or material properties much useful information concerning the amount of actuation and load transfer can be obtained. The presented work is a step towards modeling of structural health monitoring systems. Keywords

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Reinforced concrete (RC) beam-column connections especially those without transverse reinforcement in joint region can exhibit brittle behavior when intensive damage is concentrated in the joint region during an earthquake event. Brittle behavior in the joint region can compromise the ductile design philosophy and the expected overall performance of structure when subjected to seismic loading. Con- sidering the importance of joint shear failure influences on strength, ductility and stability of RC moment resisting frames, a **finite** **element** modeling which focuses on joint shear behavior is present- ed in this article. Nonlinear **finite** **element** analysis (FEA) of RC beam-column connections is performed in order to investigate the joint shear failure mode in terms of joint shear capacity, defor- mations and cracking pattern. A 3D **finite** **element** **model** capable of appropriately modeling the concrete stress-strain behavior, tensile cracking and compressive damage of concrete and indirect modeling of steel-concrete bond is used. In order to define nonlinear behavior of concrete material, the concrete damage plasticity is applied to the numerical **model** as a distributed plasticity over the whole geometry. **Finite** **element** **model** is then verified against experi- mental results of two non-ductile beam-column connections (one exterior and one interior) which are vulnerable to joint shear fail- ure. The comparison between experimental and numerical results indicates that the FE **model** is able to simulate the performance of the beam-column connections and is able to capture the joint shear failure in RC beam-column connections.

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2013)). Also, a nonlinear **finite** **element** **model** is developed for the general third-order theory of beams. To date no such study is reported in the literature. Since most nanoscale devices involve beam-like elements that may be functionally graded and undergo moderately large rotations, the newly developed third-order beam theory can be used to capture the size effects in functionally graded microbeams. Moreover, the bending-extensional coupling is captured through the von Ká- rmán nonlinear strains.

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All mentioned investigators studied about curved beams with the constant radius of curvature. In addition, few papers have focused on the variable-curvature structures. Marquis and Wang (1989) used the energy principles to solve parabolic arches. It is worth emphasizing that most of the proposed schemes have not offered a general **finite** **element** **model**. In fact, these solution techniques have only considered a few particular cases that were more reachable. These investigators calculated the stiffness matrix by considering the effect of special boundary conditions Gutierrez et al. (1989) Lin and Huang (2007) Lin and Hsieh (2007) Lee and Wilson (1989) Lee et al. (2008) Tarnopolskaya et al. (1996). Haung et al. (1998) utilized polynomial functions and power series to **model** the be- havior of beams with variable curvatures and cross sections. In 1999, Oh et al. (1999) solved equi- librium equations numerically, and found the first four natural frequencies of sinusoidal, elliptical and parabolic beams for the special cases. This procedure was used by many researchers Huang et al. (1998) Oh et al. (2000) Gimena et al. (2010). Another way of finding the structural stiffness matrix is the flexibility-based method. Litewka and Rakowski (1998), Molari and Ubertini (2006), and Attarnejad et al. (2013) utilized this approach in their study. Attarnejad and his coworkers (2013) defined Basic Displacement Function (BDF) as the nodal displacement by applying unit load technique. On the other hand, Molar & Ubertini (2006) employed a parametric cubic interpolation to **model** geometry of the structure. These investigators considered two parameters for the versatili- ty of interpolation function.

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Hierarchical multi-scale modeling: PFM into FEM The PFM and **finite** **element** **model** (FEM) were established within a two-dimensional square shape domain, which has 256 m m on one side, as shown in Fig. 1. The domain is divided into 5116511 elements (or grids) in both calculations. This fine mesh system is needed because localized micro-stress field, which is caused by the volume change due to nucleation and growth of a newly formed phase, should be evaluated precisely to analyze the transformation plasticity. According to Greenwood and Johnson’s **model** [1] and other previous studies [2–5], the localized micro- stress field can generate transformation plasticity, which originates from the micro-plasticity of the weaker phase. Fig. 2 shows the flow of a hierarchical multi-scale simulation that makes a connection between the PFM and FEM. Phase information for each **element** and each time step obtained from the PFM calculation is transferred into the FEM. However, for the temperature information, the temperature history in both cases Table 2. Densities of austenite and ferrite phase as a function

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The purpose of this paper is to present a finite element model for optimal design of composite laminated thin-walled beam structures, with geometrically nonlinear behaviour, inc[r]

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A secant function based shear deformable **finite** **element** **model** is developed for the flexural behavior of laminated composite and sandwich plates with various conditions. The structural kinematics of the plate is expressed by means of secant function based shear deformation theory newly developed by the authors. The theory possesses non-linear shear deformation and also satisfies the zero transverse shear conditions on top and bottom surfaces of the plate. The field variables are elegantly utilized in order to ensure C 0 continuity requirement. Penalty parameter is implemented to secure the constraints arising due to independent field variables. A biquadratic quadrilateral **element** with eight nodes and 56 degrees of freedom is employed to discretize the domain. Extensive nume- rical tests for the flexural behavior of laminated composite and sandwich plates are conducted to affirm the validity of the present **finite** **element** **model** in conjunction with the improved structural kinematics. Influences of boundary conditions, loading conditions, lamination sequences, aspect ratio, span-thickness ratio, etc on the flexural behavior are investigated specifically and compared with the existing results in order to indicate the performance of the present mathematical treatment.

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The following data was supplied to the network: a set of patterns which represent the **finite** elements in compliance with the codification given in Section 5.2; the initial values for the weights were obtained randomly; and the neighbouring shape was rectangular, in compliance with the description in Section 4.2. For the training of the SOM networks, an initially high training rate, close to one (1), was used, that should be gradually decreased until a certain acceptable or previously informed value. Up to five hundred (500) iteration cycles were necessary, so that this network could achieve the expected learning rate of the order of 0.01 and equivalent to the one percent (1%) error rate in the results during its execution. This network topology needed a total of fifty thousand (50,000) iteration cycles to reach the proper performance. For this training stage, a sample of fifty percent (50%) of the total elements was used as the set of the network supplied input patterns, to represent the **finite** elements of the continuous bi-dimensional and tri-dimensional space families shown in Table 7.

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