Sumerianz Journal of Scientific Research
Online ISSN: 2617-6955
Print ISSN: 2617-765X
Quarterly Published (4 Issues Per Year)
Journal Website: https://www.sumerianz.com/?ic=journal-home&journal=29Archive
Volume 2 Issue 4 (2019)
Are Axioms and Inference Rules Sufficient to Find any True Statement in Science? Gödel, a Great Logician with Psychological Problems Gave the Answer
Authors : Sotirios Sakkopoulos
Abstract:Until 1931 eminent intellectuals, like Russell, Ackermann and Hilbert were trying to find formal systems based of a finite number of axioms and generally accepted rules of inference in which every statement could be proved or disproved, independently from the objects considered. However, to apply this in an endless variety of objects they had to consider them as mere signs drained from any content. This had as a result a statement to be proved or disproved only syntactically, i.e. only formally, without caring if is true or not. Kurt Gödel in 1930 made a distinction between syntactic provability and semantic truth, the latter resulting from the consideration of properties coming from the content of the objects. Finally, in 1931 Gödel, with his two incompleteness theorems, proved that there are true statements in mathematics including elementary arithmetic of natural numbers [0,1,2…] which are impossible to be proved or disproved, demolishing the optimistic opinion prevailing until then. The consequences of these theorems puzzle logicians, mathematicians and physicists ever since. Although Gödel was a leading logician, ironically he was tormented by lifelong illogical fears which finally caused his death.
Pages: 55-62
Evaluation of Viscoelastic Properties of Asphalt Mixtures by Finite Element Modeling Using Abaqus Software
Authors : Seyed Masoud Hadian
Abstract:Pavement with asphalt mixes and good quality and continuous life has been considered. The issues that lead to increased durability, quality and life of asphalt pavements have always been considered, so that pavements known as permanent pavements and high-rise pavements are introduced. Asphalt mixtures, in most cases, the lifetime of the pavement is exposed, they exhibit viscoelastic behavior. One of the methods widely used to predict viscoelastic responses of asphalt mixtures is the finite element method. ABAQUS software is one of the tools that can simulate mixed asphalt behavior based on a finite element method, taking into account all the determinant parameters. The use of the Prony series is one of the common techniques for describing the viscoelastic behavior of asphalt mixtures in ABAQUS software. For this purpose, it is necessary to determine the parameters required for this field, including proven constants, moment elastic modulus, and asphalt mixture poison ratio. On the other hand, the determination of these parameters through testing in addition to spending time and costs requires laboratory equipment. Therefore, in this thesis, a three-dimensional finite element model with ABAQUS software was constructed to analyze the persistent pavement using theoretical relations without conducting the experiment. In order to achieve this goal, in this model, 4 layers of asphaltic were defined as elastic whiskey, and the base layer and sub grid were modeled elastically, and the whiskey analysis for analysis was also used. Based on the results of this thesis, the longitudinal tensile strain model has a very good agreement with the value measured in the U.S.30 project. Also, the areas of traction and pressure are also interconnected. This correlation is also seen in the maximum vertical stresses. The effect of thickness on the finite element model is also considered, and it has been determined that thickness has a significant effect on the durability of pavement performance. By changing the thickness of the layers a little, it can be seen that the effect is on the output values. Also, viscoelastic behavior of common asphalt mixtures and time dependence of its responses at different temperatures can be modeled in ABAQUS software.
Pages: 49-54