Papers by Author: E.A. Merchán-Cruz

Abstract: The use in the past of mathematical techniques and methodologies to design macro-world structures in the past are now considered for designing micro-world structures. In this work, a computational algorithm for estimating natural frequencies and mode shapes of cantilever microbeams is presented. The methodology is based on the Rayleigh-Ritz method, which considers the potential and kinetic energies of the mechanical system. A proposed polynomial equation is first considered to establish the behavior of the microstructure. Together with the energy equations, an eigenvalue problem is constructed. The corresponding eigenvalues give an approximate estimation of the frequency values; the corresponding eigenvectors once substituted in the proposed polynomial describe the mode shapes of the microbeam for each frequency value. The results obtained with this methodology were compared with the finite element method. An interesting difference between the methodologies and the algorithm was found and the corresponding results are shown.

Abstract: This work presents an approach based on Genetic Algorithms (GA) for the dimensional synthesis of planar mechanisms as path generators. The study case deals with the development of a four-bar mechanism with application to lower limb prosthesis, specifically the knee joint. The optimization algorithm contains the objective function defined by the synthesis problem and the representation of a set of mathematical relationships that describe the kinematic restrictions of the planar mechanism. The objective function is a given numerical value for every solution that corresponds to the best possible mechanism. In other words, this objective function is the determinant to minimize the error between the desired and the generated points and can be affected by the lengths of the links, the transmission angles, the Grashof conditions, type of mechanisms, etc. The population, crossover or mutation in the GA determines the exactitude in the results. The first goal of this work is to find the optimal dimensions of the links to minimize the error between the actual coupler curve and the desired path.

Abstract: This work assesses the Crack Compliance Method (CCM), which has been extensively used for the experimental evaluation of residual stresses, by the Finite Element Method (FEM) to validate its experimental applicability through numerical evaluation. The CCM is a very powerful method that is based on Fracture Mechanics theory, but its experimental application and set up has not been totally scientifically validated. In this paper, a numerical evaluation is presented on the basic applications of the CCM. The assessment of the CCM is performed on bending beams with and without prior straining history. To determine the best position and orientation of the strain gages, as well as the optimum number of readings, a number of numerical simulations where also performed for the correct performance of the experimental evaluation of the CCM. The prior straining history condition, in the analyzed components, is induced by an axial pulling before the beam is bent. Three levels of preloading are considered: low, medium and high (which are related to the yield strain of the simulated material); Isotropic and Kinematic hardening rules are also considered. After the residual stress field is induced by bending, a slot cutting is simulated and the strain relaxation produced is captured, which is used later in the CCM program for the quantification of the original residual stress field. The results obtained in this work, provide a quantitative demonstration of the effect of hardening strain on the distribution of the residual stress in beams. In the same manner, the theoretical formulation of the CCM has been evaluated validating the application of this method for the determination of residual stress fields in mechanical components.

Abstract: The goal of this paper is to present the results obtained from damage evaluation in automotive axles, which are under torsion fatigue. For this purpose, a Nonlinear Damage Model is used. The mentioned shafts have to satisfy geometry requirements and their material has to be heat treated in order to improve their performance. One has to keep in mind that fatigue strength depends on material properties and geometry. In order to make a precise evaluation of the accumulated damage, the manufactured shafts were tested. In the first instance, the mechanical properties of the material were evaluated with static torsion tests. In the next step, the S-N curves were obtained with torsion fatigue tests. In all these cases, temperature was controlled. Experimental data at different load levels was gathered with strain gages in conjunction with a data acquisition system. The life cycle history of each tested shaft was stored and with this experimental evidence, damage curves were obtained and the cumulative damage of the axle was established. With these damage curves, it is possible to define the relation between damage rate and life for different stress levels.

Abstract: This paper presents the modelling of the effects due to load conditions on the cervical section defined between C3 and C5 after a cervical plate implant is used to transfer the compression loads from C3 to C5 as C4 is considered to be damaged as a result of a medical condition. For this study, three different scenarios which describe the common motion condition of the head-neck system are modelled. The first one refers to the effect of the head weight over the considered section. In the second case the average patient weight is supported by C3 and C5 vertebrae. The last case simulates extreme loading conditions as vertebrae lesions occur when these are compressed beyond its failure limit; the ultimate stress to compression load failure value is applied to C3. The stability and mechanical behaviour of cervical plates under compression loading conditions is evaluated using the Finite Element Method (FEM). Cervical plates are useful to restore stability of the spine by improving the inter-vertebral fusion, particularly when the cervical body has been damaged. The results show that the stresses on the plate and fixation screws, for the three cases, are within the elastic range. Conversely, it has to be considered that cortical and trabecular bone densities vary from one patient to another due to a number of factors, which can influence the fixation conditions of the screws. In the case of this analysis, healthy bone conditions were considered and the obtained results show that the risk of the integrity of the screwimplant- vertebrae system is not compromised.