Finite Element Model

Detection of crack in a beam is performed in two steps. First, the finite element model of the cracked cantilever beam is established. The beam is discretized into a number of elements, and the crack position is assumed to be in each of the elements. Next, for each position of the crack in each element, depth of the crack is varied. Modal analysis for each position and depth is then performed to find the natural frequencies of the beam. Using these results, a class of three dimensional surfaces is constructed for the first three modes of vibration, which indicate natural frequencies in terms of the dimensionless crack depth and crack position.

Heat conduction in combustion chamber wall was modeled in [10] to simulate multidimensional combustion in SI engine. However, comprehensive study of combustion chamber wall was found in [11-13]. The study highlights the model validation, the grid optimization, and the effect of geometry and material on the wall temperature. The heat conduction between the engine body and other components were also extensively investigated using FEM. Finite element model of a cylinder structure with a twin-cam 16- valve was presented in [14]. They used the commercial FE code to predict thermal and stress/strain results at various loading conditions and operating environments. The structural analyses of a cylinder head under engine operating conditions were performed in [15, 16] using finite element simulation. It was reported that the capacity of gasket sealing was principally dependent on the pre-stressing of the bolts, which was the source of the maximum external loading on the inner structure of the cylinder head. In

Abstract - Arch dams are designed for the same loads as other dams with the exception of the temperature load, which has a significant influence in arch dam design as compared to gravity dam design. In concrete arch dams, because of the particular geometry, solar radiation shares of exposed surfaces vary spatially through downstream face. In this case, three- dimensional temperature distribution analysis is unavoidable. When a transient heat transfer analysis is performed in a dam safety evaluation, it would be convenient to identify the most critical time to carry out a complete stress analysis. To investigate the seismic safety of concrete dams, it is essential to quantify the static state of stress and strain that exist at the time the earthquake occurs, which may vary significantly from winter to summer conditions. In this paper, a three dimensional finite element model implemented in ABAQUS is used for simulating the temperature behavior in operational phase of typical arch dam. Then an elastic analysis is carried out and the associated thermal stresses are calculated and combined with other static loadings (self-weight and hydrostatic) and dynamic one. For dynamic analysis, a coupled system of dam and reservoir is considered. The static loads are compared and combined with earthquake load. Results show significant thermally induced tensile stresses in the crest region and at the downstream face of the dam, which is the most vulnerable zone for seismic induced damage. At the upstream face, due to the effect of reservoir water, the thermal tensile stresses have small magnitude while dynamic stresses are excessively increased.

This paper presents a finite element model for different breast tissues including soft, benign, and malignant tis- sues. This model can be considered as a software phantom that can be used to study breast cancer effects. Re- sults from the model were compared with real data taken at National Cancer Institute in Cairo, Egypt by HITASHI sonograph. Results from the model and real data agreed to very good extent. As a metric for this agreement we calculated the coefficient of variation factor which was about 5% that indicates a good agreement.

The goal of this study is to investigate the biomechanical properties of locked plates as a function of screw configuration, fracture gap, and interface gap using a finite element model (FEM). The literature on the subject has differed recommendations on optimal screw number and configuration, which is mostly based on empiric evidence. There are a few biomechanical studies on the subject [11] [13]; however, there is much to be learned regarding the biomechanics of locked plating. This current investigation seeks to build upon this knowledge by attempting to more closely simulate the in vivo biomechanics of fracture fixation in a transverse diaphyseal fe- mur fracture. While this study developed a model on the LCP (DePuy-Synthes Warsaw, IN, USA) which offers screw holes for both locking and conventional screws, only the locking screw configuration was investigated.

A finite element model is composed of three aspects: the geometric representation, the material representation (constitutive laws) and the boundary conditions (loading and restraints). First, it is advisable to define the actual geometry of the cervical spine as closely as possible. One of technique, known as computed tomography (CT), is commonly used to provide the appropriate 3D bone details of the spine. Using CT data enables viewing a subject based upon the specific requirements of the problem (7, 13, 19, 21, 22, 48). As an alternative to the CT technique, direct digitization of dried or embalmed cadaveric bones may provide excellent geometric fidelity at the expense of an extensive period of time (15, 26, 27, 28, 40, 41, 50). Another major concern in FE modeling of the spine involves the material properties of the spinal components, which vary broadly, even within a specific structure. These properties have predominantly been identified via in vitro studies (13, 45). Finally, applying boundary conditions similar to those of in vitro studies prepare the model for simulation.

The special advantage in finite element approach is it enables stand alone part by part simulation of human body other than full body simulation. Present studies conducted by Fressmann et al. (2007) on the development of human mod- eling in this approach shows that in the future finite element model will come with the creation of skeleton and will be able to define the right material prop- erties to be used in dummy models. Furthermore, it provides more detailed and accurate deformation of the human body in terms of injuries during crash.

Methods: A Galerkin-based finite element model was developed and implemented to solve a system of two coupled partial differential equations governing biomolecule transport and reaction in live cells. The simulator was coupled, in the framework of an inverse modeling strategy, with an optimization algorithm and an experimental time series, obtained by the Fluorescence Recovery after Photobleaching (FRAP) technique, to estimate biomolecule mass transport and reaction rate parameters. In the inverse algorithm, an adaptive method was implemented to calculate sensitivity matrix. A multi-criteria termination rule was developed to stop the inverse code at the solution. The applicability of the model was illustrated by simulating the mobility and binding of GFP-tagged glucocorticoid receptor in the nucleoplasm of mouse adenocarcinoma.

There are several simplifying assumptions in the finite element model of the face in this study. The nature of the connection between the skin and hypodermis needs to be established, as well as the connection between the hypodermis and bony structures. The material parameters for the facial muscles also need to be determined from experimental measurements. The current passive muscle parameters are based on properties of the biceps brachii (Blemker et al. 2005). More accurate facial muscle properties would likely result in changes to the muscle activations needed to generate each facial expression. Human skin exhibits viscoelastic behaviour (Flynn et al. 2011), which has been ignored in the proposed model. Indeed, the material parameters of the skin layer and the applied in vivo tensions are based on forearm skin experimental data (Evans and Holt 2009, Flynn et al. 2011). The model would be improved if material parameters specific to facial skin were used in the constitutive equation. There is a relative dearth of experimental data in the literature that characterises the anisotropic behaviour of facial skin. Most

Finite element analysis is a method of computer simu- lation in which the reference data is usually obtained from traditional experiments. The accuracy of material properties assigned to tissues, the partitioning of meshes, the type of elements used, and the load and boundary conditions directly affect the accuracy of a finite element model. The validation of a finite element model may con- sist of two stages. The first is the comparison of the ap- pearance and structure of the model with the simulated object. The model presented in this study demonstrated excellent agreement with the structure and appearance of the simulated object. The second stage of validation con- sists of the comparison of the results obtained from the model with that of a similar experiment or from results obtained from published literature. Because of the diffi- culty of obtaining cadaveric specimens with DS, in vitro biomechanical experiments of DS cannot be found in the literature, so the second stage of validation was completed with reference to an in vitro biomechanical experiment of lumbar segments. When comparing the results obtained from the normal model and the DS model to the data pre- sented by Chen et al., it is clear that the normal model ex- hibits behavior similar to that of the young population even though the geometry matches that of a patient with DS. It is also clear from the data presented that the range of motion of the DS model, with material properties defined specifically to mimic the characteristics of DS, is similar to that of the elderly population. This finding un- derscores the importance of assigning disease-appropriate material properties in the construction of a finite element model of DS.

Grillage method is a fast and simpler approach compared to the finite element method, and has been used by engineers to analyses bride deck over a long time on the other hand the finite element method is thought to be better model for the slab analysis because of its capability to represent the structure more realistically.

Ve 2D případech je pro výstavbu konečně-prvko- vého modelu použito skořepinových prvků (např. SHELL99). Tyto, na strojový čas méně náročné modely, jsou vhodné především pro popis chování desek s jednotnou tloušťkou, vícevrstvé desky (např. překližované kompozity) s libovolnými vlastnostmi (tloušťka, orientace, materiál) vrstev. Fyzikální model předpokládá teorii pro chování skořepin (Kohnke, 1998; Kolář, 1997). Pro popis desek s nejednotnou tloušťkou jsou vhodné 3D modely. Konečně-prvkové modely jsou v tomto případě přednostně založeny na hexahedrálních (šestistěnných) lineárních elementech (osmiuzlový SOLID45) a kvadratických elementech (dvacetiuzlový SOLID95). Vzhledem k poměrně jed- noduché geometrii „holé“ desky nebylo nutné použít tetrahedrálních (čtyřstěnných) prvků, jejichž síť navy- šuje celkový počet stupňů volnosti úloh (tedy i tech- nické nároky výpočtů).

Pro výpočet bylo použito výpočetního konečně- prvkového systému ANSyS 7.1. Výpočet byl reali- zován v OS Linux na zařízení HP Proliant DL380 na Ústavu nauky o dřevě Lesnické a dřevařské fakulty MZLU v Brně. Model předpokládá lineární elastic- kou odezvu systému všech použitých materiálů. S ohledem na možný vývoj rozsáhlých deformací pro materiál dřeva v oblasti elastické odezvy byla použita modifikace vznikajících deformací ve smyslu Henc- kyho deformací (Hughes, 1984). Model při hrubé síti konečných prvků zahrnuje cca 4,8 mil. stupňů volnos- ti. jelikož se jedná o rozsáhlý model, byl použit řešič PCg s nižší hladinou přesnosti (konvergenční krité- rium pro reziduum neznámé veličiny posunutí bylo F c =1e-4). Vzhledem k předpokládanému vzniku pře-

that is, a slightly lower value when compared with the pure elastic case. The response of the elastic and the elastic – plastic models was compared in terms of energy quantities. The energy balance for the model can be obtained according to the first law of thermodynamics. Fig. 8 shows the evolution of the applied external work with time for both elastic and elastic – plastic models. It can be seen that failure occurs earlier in the elastic – plastic simulation and after failure the external work is also greater for the elastic – plastic case. In order to further investigate the contribution of plasticity, the authors compared recoverable and internal energy and also plastic dissipation and frictional dissipation for both the elastic and the elastic – plastic models. Fig. 9(a) shows that all the internal strain energy is recoverable for the elastic simulation (as shown by the overlapping of the two curves), whereas only approximately one-third of the energy is recoverable in the plastic simulation. This is an indicator of the significant contribution of plasticity on unloading of the grains under shearing. In the elastic – plastic model presented,

As sensory receptors are normally located in the dermis, the current density distribution in the RS was assumed to determine sensation. The FE model predicted that the peak current density (hot spot) in the RS was located in the top corner of the RS layer, adjacent to the SC and the sweat pore (see figure 2). The non-uniformity of current distribution was quantified using a current hogging coefficient (CHC), which was defined as the ratio between the peak current density and the mean current density in the RS. The effects of four variables (hydrogel resistivity, hydrogel thickness, sweat duct resistivity, and SC thickness) on CHC were predicted by the FE model, as shown in figures 3, 4 and 5. Four different hydrogels were modelled, corresponding to commercially available samples (see tables 2 and 3), and their effects on CHC were plotted (figure 6).

The results from analyses of a shear wall with an opening of window shape show that the effect of constraint by the bearing between sheathing panels and slips in frame [r]

Matsumoto et al. [19] proposed a method for calculating the distribution of temperature and stress within a single metallic layer formed on the powder bed in the selective laser melting method. The solidified layer was assumed to be subjected to plane stress deformation and the 2D finite element methods for heat conduction and elastic deformation were combined. They found that the amount of the deflection of the solid layer increased as the track length increased. In order to prevent the distortion of the solid layer on the powder bed, it is desirable to shorten the scanning track. When the neighbouring track began to solidify, a large tensile stress between the solidified tracks appeared at the side end of the solid part, which may cause the cracking of the layer. They also suggested dividing large scan areas into smaller areas and then using short scanning tracks to scan these areas to reduce the possibility of cracking.

model [38–41], however [42], the human body is ac- tually made up of both hyperelastic and nonlinear viscous materials [42]. It performs as hyperelastic material under low speed conditions and its stress– strain curve changes along with the alteration of loading conditions, with high velocity loadings. In order to reflect these two characteristics, our research combines the nonlinear elastic material theory of Ogden [43] with visco- elastic mechanics theory of Christensen [44]. Ogden’ s the- ory takes α and μ as material parameters and can adequately reflect the non-linear stress–strain curve under Quasi static state; Christensen’s theory takes β and G as material parameters and can reflect the mechanical proper- ties that stress and strain change with the alteration of loading velocity, and the mathematic derivation process is as follows:

Computer Aided Design (CAD) geometry for the bats was provided by the manufacturer. The majority of the bat was meshed with quadrilateral elements. Tetrahedral elements were applied to the far ends of the blade and sections of the handle. A linear orthotropic material model (MAT_ORTHOTROPIC_ELASTIC (LSTC, 2012)) was applied to the blade and a linear elastic material model (MAT_ELASTIC (LSTC, 2012)) was applied to the handle. Starting with the material coefficients applied by Smith and Singh (2008) the density and modulus values were systematically adjusted so the inertial and structural properties of the models corresponded to those of the actual bats (Table 3). The inertial properties of the bat models were within 1% of those of the actual bats. Modal analysis simulations were used to determine the structural stiffness of the bat models. The 1 st modes for both bat

The majority of computer simulation studies of conformational change in proteins consider the macromolecule to be constructed from discrete par- ticles, where a particle may represent one (as in atomistic simulation) or more atoms. Although a ‘particle’ description is appropriate for atomically detailed calculations, at the coarse-grained level the particle size and the number of atoms that they represent become arbitrary, and are typically chosen for computational convenience. At the mesoscale (length scales from hundreds of nanometers to microns), hybrid fluid mechanics/solid mechanics techniques, such as the Immersed Boundary Method (IBM) [10] [11] and the Immersed Finite Element Method (IFEM) [12, 13] have been developed to model how the shapes or positions of objects change in response to hydrody- namic fluctuations and fluid flow [14]. These techniques have been used, for example, to study the stochastic desorption of rigid nanoparticles from mem- brane surfaces under shear flows [15], the Brownian motion of nanoparticles in a Newtonian fluid due to thermally induced hydrodynamic fluctuations [16, 17] and the deformation of vesicle being dragged by a Brownian ratchet model of a biological motor protein [18]. The IBM treats an object immersed in a fluid as a series of particles that interact with both with one another and the background fluid, which is placed on a grid [10]. In IFEM, both the object and the fluid are represented on two separate meshes which are superimposed. Thermal fluctuations are introduced by subjecting the mesh to a fluctuating stress using the appropriate Langevin equations [13].