A finite element study on femoral locking compression plate design using genetic optimization method.

The locking compression plate (LCP) and screw sets are widely used as internal fixator assemblies to treat long bone fractures. However, the surgeon's critical challenge is choosing the implant set (plate and screws) for each patient. The present study introduces a parametrized simulation-based optimization algorithm for determining an LC system with the best bone-implant stability. For this purpose, a three-dimensional fractured bone supported by an LC system was generated, and the discrete genetic optimization approach was utilized to design the optimum implant. Initially, an algorithm was developed to optimize the optimum layouts for different numbers of screws. For the middle third transverse fracture, six screws were selected as the optimal number of the screws. In a second stage, the model was run to determine the best LC plate dimensions for desired fractured bones. Finally, optimal plates were identified for simple middle third transverse, 60° middle third oblique, and distal third transverse femoral fractures. The results of these simulations and those for other fracture types can be exploited to achieve improved surgical outcomes by selecting proper implants and screws configurations.

Mathematical modeling of dynamic behavior of fluid bilayer membranes under the effect of density asymmetry.

Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases.

Numerical simulation of the fatigue behavior of additive manufactured titanium porous lattice structures.

In this paper, the effects of cell geometry and relative density on the high-cycle fatigue behavior of Titanium scaffolds produced by selective laser melting and electron beam melting techniques were numerically investigated by finite element analysis. The regular titanium lattice samples with three different unit cell geometries, namely, diamond, rhombic dodecahedron and truncated cuboctahedron, and the relative density range of 0.1-0.3 were analyzed under uniaxial cyclic compressive loading. A failure event based algorithm was employed to simulate fatigue failure in the cellular material. Stress-life approach was used to model fatigue failure of both bulk (struts) and cellular material. The predicted fatigue life and the damage pattern of all three structures were found to be in good agreement with the experimental fatigue investigations published in the literature. The results also showed that the relationship between fatigue strength and cycles to failure obeyed the power law. The coefficient of power function was shown to depend on relative density, geometry and fatigue properties of the bulk material while the exponent was only dependent on the fatigue behavior of the bulk material. The results also indicated the failure surface at an angle of 45° to the loading direction.

Effect of solid distribution on elastic properties of open-cell cellular solids using numerical and experimental methods.

Effect of solid distribution between edges and vertices of three-dimensional cellular solid with an open-cell structure was investigated both numerically and experimentally. Finite element analysis (FEA) with continuum elements and appropriate periodic boundary condition was employed to calculate the elastic properties of cellular solids using tetrakaidecahedral (Kelvin) unit cell. Relative densities between 0.01 and 0.1 and various values of solid fractions were considered. In order to validate the numerical model, three scaffolds with the relative density of 0.08, but different amounts of solid in vertices, were fabricated via 3-D printing technique. Good agreement was observed between numerical simulation and experimental results. Results of numerical simulation showed that, at low relative densities (<0.03), Young׳s modulus increased by shifting materials away from edges to vertices at first and then decreased after reaching a critical point. However, for the high values of relative density, Young׳s modulus increased monotonically. Mechanisms of such a behavior were discussed in detail. Results also indicated that Poisson׳s ratio decreased by increasing relative density and solid fraction in vertices. By fitting a curve to the data obtained from the numerical simulation and considering the relative density and solid fraction in vertices, empirical relations were derived for Young׳s modulus and Poisson׳s ratio.

Influence of the tip mass and position on the AFM cantilever dynamics: coupling between bending, torsion and flexural modes.

The effects of the geometrical asymmetric related to tip position as a concentrated mass, on the sensitivity of all three vibration modes, lateral excitation (LE), torsional resonance (TR) and vertical excitation (VE), of an atomic force microscopy (AFM) microcantilever have been analyzed. The effects of the tip mass and its position are studied to report the novel results to estimating the vibration behavior of AFM such as resonance frequency and amplitude of the microcantilever. In this way, to achieve more accurate results, the coupled motion in all three modes is considered. In particular, it is investigated that performing the coupled motion in analysis of AFM microcantilever is almost necessary. It is shown that the tip mass and its position have significant effects on vibrational responses. The results show that considering the tip mass decreases the resonance frequencies particularly on high-order modes. However, dislocating of tip position has an inverse effect that causes an increase in the resonance frequencies. In addition, it has been shown that the amplitude of the AFM microcantilever is affected by the influences of tip and its position. These effects are caused by the interaction between flexural and torsional motion due to the moment of inertia of the tip mass.