A minimum weight formulation with stress constraints in topology optimization of structures

El diseño óptimo de estructuras ha estado tradicionalmente orientado a la resolución de problemas de optimización de formas y dimensiones. Sin embargo, más recientemente ha surgido otra rama de investigación que propone modelos que proporcionan soluciones estructurales óptimas y que no requieren la definición previa de la tipología estructural: la optimización topológica de estructuras. Estas formulaciones proporcionan tanto la tipología estructural como la forma y dimensiones óptimas. Las formulaciones más habituales de estos planteamientos pretenden obtener una solución que maximice la rigidez de la estructura dadas unas limitaciones en la cantidad de material a utilizar. Estas formulaciones han sido ampliamente analizadas y utilizadas en la práctica pero presentan inconvenientes muy importantes tanto desde un punto de vista numérico como práctico. En este artículo se propone una formulación diferente a la de máxima rigidez para el problema de optimización topológica de estructuras que minimiza el peso e incorpora restricciones en tensión. Las ventajas de este tipo de planteamientos son muy importantes dado que se minimiza el coste de la solución, que es la situación más habitual en ingeniería, y además se garantiza la validez estructural de la misma. Además esta formulación permite evitar algunos de los problemas e inestabilidades numéricas que presentan las formulaciones de máxima rigidez. Finalmente, se resuelven algunos ejemplos prácticos para comprobar la validez de los resultados y las ventajas que ofrece la formulación propuesta.Optimum design of structures has been traditionally focused on the analysis of shape and dimensions optimization problems. However, more recently a new discipline has emerged: the topology optimization of the structures. This discipline states innovative models that allow to obtain optimal solutions without a previous definition of the type of structure being considered. These formulations obtain the optimal topology and the optimal shape and size of the resulting elements. The most usual formulations of the topology optimization problem try to obtain the structure of maximum stiffness. These approaches maximize the stiffness for a given amount of material to be used. These formulations have been widely analyzed and applied in engineering but they present considerable drawbacks from a numerical and from a practical point of view. In this paper the author propose a different formulation, as an alternative to maximum stiffness approaches, that minimizes the weight and includes stress constraints. The advantages of this kind of formulations are crucial since the cost of the structure is minimized, which is the most frequent objective in engineering, and they guarantee the structural feasibility since stresses are constrained. In addition, this approach allows to avoid some of the drawbacks and numerical instabilities related to maximum stiffness approaches. Finally, some practical examples have been solved in order to verify the validity of the results obtained and the advantages of the proposed formulation.Peer Reviewe

Relativistic K shell decay rates and fluorescence yields for Zn, Cd and Hg

In this work we use the multiconfiguration Dirac-Fock method to calculate the transition probabilities for all possible decay channels, radiative and radiationless, of a K shell vacancy in Zn, Cd and Hg atoms. The obtained transition probabilities are then used to calculate the corresponding fluorescence yields which are compared to existing theoretical, semi-empirical and experimental results

Association Between Advanced Maternal Age and Maternal and Neonatal Morbidity: A Cross-Sectional Study on a Spanish Population

Background and objective: Over recent decades, a progressive increase in the maternal age at childbirth has been observed in developed countries, posing a health risk for both women and infants. The aim of this study was to analyze the association between advanced maternal age (AMA) and maternal and neonatal morbidity. Material and methods: A cross-sectional study of 3,315 births was conducted in the north of Spain in 2014. We compared childbirth between women aged 35 years or older, with a reference group of women aged between 24 and 27 years. AMA was categorized based on ordinal ranking into 35-38 years, 39-42 years, and >42 years to estimate a dose-response pattern (the older the age, the greater the risk). As an association measure, crude and adjusted Odds Ratios (OR) were estimated by non-conditional logistic regression and 95% Confidence Intervals (95%CI) were calculated. Results: Repeated abortions were more common among women of AMA in comparison to pregnant women aged 24-27 years (reference group): adjusted OR = 2.68; 95%CI (1.52-4.73). A higher prevalence of gestational diabetes was also observed among women of AMA, reaching statistical significance when restricted to first time mothers: adjusted OR = 8.55; 95%CI (1.12-65.43). In addition, the possibility of an instrumental delivery was multiplied by 1.6 and the possibility of a cesarean by 1.5 among women of AMA, with these results reaching statistical significance, and observing a dose-response pattern. Lastly, there were associations between preeclampsia, preterm birth (<37 weeks) and low birthweight, however without reaching statistical significance. Conclusion: Our results support the association between AMA and suffering repeated abortions. Likewise, being of AMA was associated with a greater risk of suffering from gestational diabetes, especially among primiparous women, as well as being associated with both instrumental deliveries and cesareans among both primiparous and multiparous women

Mixed optimization of power transmission structures: An application of the simulated annealing algorithm

A general methodology to optimize the weight of power transmission structures is presented in this article. This methodology is based on the simulated annealing algorithm defined by Kirkpatrick in the early &lsquo;80s. This algorithm consists of a stochastic approach that allows to explore and analyze solutions that do not improve the objective function in order to develop a better exploration of the design region and to obtain the global optimum. The proposed algorithm allows to consider the discrete behavior of the sectional variables for each element and the continuous behavior of the general geometry variables. Thus, an optimization methodology that can deal with a mixed optimization problem and includes both continuum and discrete design variables is developed. In addition, it does not require to study all the possible design combinations defined by discrete design variables. The algorithm proposed usually requires to develop a large number of simulations (structural analysis in this case) in practical applications. Thus, the authors have developed first order Taylor expansions and the first order sensitivity analysis involved in order to reduce the CPU time required. Exterior penalty functions have been also included to deal with the design constraints. Thus, the general methodology proposed allows to optimize real power transmission structures in acceptable CPU time

A minimum weight formulation with stress constraints in topology optimization of structures

Optimum design of structures has been traditionally focused on the analysis of shape and dimensions optimization problems. However, more recently a new discipline has emerged: the topology optimization of the structures. This discipline states innovative models that allow to obtain optimal solutions without a previous definition of the type of structure being considered. These formulations obtain the optimal topology and the optimal shape and size of the resulting elements. The most usual formulations of the topology optimization problem try to obtain the structure of maximum stiffness. These approaches maximize the stiffness for a given amount of material to be used. These formulations have been widely analyzed and applied in engineering but they present considerable drawbacks from a numerical and from a practical point of view. In this paper the author propose a different formulation, as an alternative to maximum stiffness approaches, that minimizes the weight and includes stress constraints. The advantages of this kind of formulations are crucial since the cost of the structure is minimized, which is the most frequent objective in engineering, and they guarantee the structural feasibility since stresses are constrained. In addition, this approach allows to avoid some of the drawbacks and numerical instabilities related to maximum stiffness approaches. Finally, some practical examples have been solved in order to verify the validity of the results obtained and the advantages of the proposed formulation