Seminar
MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS

 

PROGRAM

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Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za FEBRUAR 2020.

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UTORAK, 04.02.2020. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Dejan Momčilović, Institute for testing of materials IMS, Belgrade, Serbia
NEW FRACTURE MECHANICS METHODS FOR RESEARCH OF MACHINE ELEMENTS AND SYSTEMS UNDER FATIGUE LOADING
The fracture mechanics, as a branch of classical mechanics deals with crack propagation in materials, under static or fatigue loading, and present highly multidisciplinary field which is studied and used by engineers from many disciplines. Classical fracture mechanics is, strictly speaking, only applicable to cracks in materials and structures. Presence of cracks is not ex nihilo (out of nothing) due to fact that in every material and construction preferential spots for crack initiation exist, which are described as stress concentration features. Such stress concentration features cause failure by cracking processes such as fatigue and brittle fracture, but until recently we had no equivalent of the stress intensity parameter to use for quantify these features, to characterize materials and to predict failure. That is the reason why during mid-seventies of last century, the logical merge of classical approach and fracture mechanics approach occurs with long term consequences, mainly in fatigue resistant design philosophy. During last decade, the recent research results lead to new theoretical approaches and the major breakthrough, based on so called Theory of Critical Distances (TCD). TCD is theory of material behavior, a theory capable of predicting a range of different types of failure caused by cracking, arising in the stress fields created by notches, cracks and other stress-concentration features. The significant part of lecture will be devoted to presentation of mathematical background and present knowledge in this topic, with the emphasize on examples of material and machine elements under fatigue loading. The highlight in this lecture will be on the presentation of concepts of nonlinear fracture mechanics and the simplified mathematics to emphasize physical concepts of crack initiation. The practical applications of the field in materials testing and evaluation and in life prediction models for structural components will be in primary focus of the lecture as well as considering the most efficient strategies suitable for designing real components against uniaxial and multiaxial fatigue.

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UTORAK, 18.02.2020. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Snežana Vulović, Institute for Information Technologies, University of Kragujevac, Serbia
NUMERICAL METHODS FOR SOLUTION OF CONTACT PROBLEM BASED ON THE PENALTY METHOD
The general concept for application of different types of finite elements in the contact problems based on the penalty method will be presented. As the configuration of two bodies coming into the contact is not a priori known, contact represents a nonlinear problem even when the continuum behaves as a linear elastic material. Contact between two deformable bodies is considered as a general case. All relations were accomplished for the case of large deformation of the bodies in the contact. Presented approach, based on the Coulomb's frictional law, elasto-plastic tangential slip decomposition and consistent linearization, results with quadratic rates of convergence using the Newton-Raphson iteration. Due to the substantial similarity between friction and the classical elasto-plasticity, the constitutive model for friction was developed following the same formalism as in classical elasto-plasticity. Standard shape routines are used for the detection of contact between previously separated meshes and for the application of displacement constraints where contact was identified. The numerical examples of the application of contact in solving real problems will be presented.

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Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.

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