Non-linear dynamic analysis of shells with frictional contact ...

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Non-linear dynamic analysis of shells with frictional contact ...

  1. 1. Mathematics for innovative technology development M. Kleiber President of the Polish Academy of Sciences Member of the European Research Council Warsaw , 21.02.2008
  2. 2. <ul><li>Math as backbone of applied science and technology </li></ul><ul><li>Applied math in ERC programme </li></ul><ul><li>Examples of advanced modelling and simulations in developing new technologies (J. Rojek + International Center for Numerical Methods in Engineering – CIMNE, Barcelona ) </li></ul>Mathematics as a key to new technologies
  3. 3. <ul><li>Applied mathematics is a part of mathematics used to model and solve real world problems </li></ul><ul><li>Applied mathematics is used everywhere </li></ul><ul><ul><li>historically: applied analysis (differential equations, approximation theory, applied probability, …) all largely tied to Newtonian physics </li></ul></ul><ul><ul><li>today: truly ubiquitous, used in a very broad context </li></ul></ul>Mathematics as a key to new technologies
  4. 4. Real Problem Mathematical Model Computer Simulation modelling validation of model verification of results algorithm design and implementation Mathematics as a key to new technologies
  5. 5. <ul><li>Applied math for innovative technologies: </li></ul><ul><li>used at every level – </li></ul><ul><ul><li>p roduct analysis and design </li></ul></ul><ul><ul><li>p rocess planning </li></ul></ul><ul><ul><li>q uality assessment </li></ul></ul><ul><ul><li>l ife cycle analysis including environmental issues </li></ul></ul><ul><ul><li>d istribution and promotional techniques </li></ul></ul><ul><ul><li>… </li></ul></ul>Mathematics as a key to new technologies
  6. 6. Members of the ERC Scientific Council <ul><li>Dr. Claudio BORDIGNON (IT) – medicine (hematology, gene therapy) </li></ul><ul><li>Prof . Manuel CASTELLS (ES) – information society, urban sociology </li></ul><ul><li>Prof. Paul J. CRUTZEN (NL) – atmospheric chemistry, climatology </li></ul><ul><li>Prof. Mathias DEWATRIPONT (BE) – economics, science policy </li></ul><ul><li>Dr. Daniel ESTEVE (FR) – physics (quantum electronics, nanoscience) </li></ul><ul><li>Prof. Pavel EXNER (CZ) – mathematical physics </li></ul><ul><li>Prof. Hans-Joachim FREUND (DE) – physical chemistry, surface physics </li></ul><ul><li>Prof . Wendy HALL (UK) – electronics, computer science </li></ul><ul><li>Prof. Carl-Henrik HELDIN (SE) – medicine (cancer research, biochemistry) </li></ul><ul><li>Prof. Michal KLEIBER (PL) – computational science and engineering, solid and fluid mechanics , applied mathematics </li></ul><ul><li>Prof. Maria Teresa V.T. LAGO (PT) – astrophysics </li></ul><ul><li>Prof. Fotis C. KAFATOS (GR) – molecular biology, biotechnology </li></ul><ul><li>Prof. Norbert KROO (HU) – solid-state physics, optics </li></ul><ul><li>Dr. Oscar MARIN PARRA (ES) – biology, biomedicine </li></ul><ul><li>Lord MAY (UK) – zoology, ecology </li></ul><ul><li>P rof. Helga NOWOTNY (AT) – sociology, science policy </li></ul><ul><li>Prof. Christiane N ÜSSLEIN-VOLHARD (DE) – biochemistry, genetics </li></ul><ul><li>Prof. Leena PELTONEN-PALOTIE (FI) – medicine (molecular biology) </li></ul><ul><li>Prof. Alain PEYRAUBE (FR) – linguistics, asian studies </li></ul><ul><li>Dr. Jens R. ROSTRUP-NIELSEN (DK) – chemical and process engineering, materials research </li></ul><ul><li>Prof. Salvatore SETTIS (IT) – history of art, archeology </li></ul><ul><li>Prof. Rolf M. ZINKERNAGEL (CH) – medicine (immunology) </li></ul>Mathematics as a key to new technologies
  7. 7. <ul><li>SH1 INDIVIDUALS, INSTITUTIONS AND MARKETS: economics, finance and management. </li></ul><ul><li>SH2 INSTITUTIONS, VAL U ES AND BELIEFS AND BEHAVIOUR: sociology, social anthropology, political science, law, communication, social studies of science and technology. </li></ul><ul><li>SH3 ENVIRONMENT AND SOCIETY: environmental studies, demography, social geography, urban and regional studies. </li></ul><ul><li>SH4 THE HUMAN MIND AND ITS COMPLEXITY: cognition, psychology, linguistics, philosophy and education. </li></ul><ul><li>SH5 CULTURES AND CULTURAL PRODUCTION: literature, visual and performing arts, music, cultural and comparative studies. </li></ul><ul><li>SH6 THE STUDY OF THE HUMAN PAST: archaeology, history and memory. </li></ul>ERC p anel structure: Social Sciences and Humanities Mathematics as a key to new technologies
  8. 8. <ul><li>LS1 MOLECULAR AND STRUCTURAL BIOLOGY AND BIOCHEMISTRY: molecular biology, biochemistry, biophysics, structural biology, biochemistry of signal transduction. </li></ul><ul><li>LS2 GENETICS, GENOMICS, BIOINFORMATICS AND SYSTEMS BIOLOGY: genetics, population genetics, molecular genetics, genomics, transcriptomics, proteomics, metabolomics, bioinformatics, computational biology, biostatistics, biological modelling and simulation, systems biology, genetic epidemiology. </li></ul><ul><li>LS3 CELLULAR AND DEVELOPMENTAL BIOLOGY: cell biology, cell physiology, signal transduction, organogenesis, evolution and development, developmental genetics, pattern formation in plants and animals. </li></ul><ul><li>LS4 PHYSIOLOGY, PATHOPHYSIOLOGY, ENDOCRINOLOGY: organ physiology, pathophysiology, endocrinology, metabolism, ageing, regeneration, tumorygenesis, cardiovascular disease, metabolic syndrome . </li></ul><ul><li>LS 5 NEUROSCIENCES AND NEURAL DISORDERS: neurobiology, neuroanatomy, neurophysiology, neurochemistry, neuropharmacology, neuroimaging, systems neuroscience, neurological disorders, psychiatry. </li></ul>ERC p anel structure: Life Sciences Mathematics as a key to new technologies
  9. 9. <ul><li>LS6 IMMUNITY AND INFECTION: immunobiology, aetiology of immune disorders, microbiology, virology, parasitology, global and other infectious diseases, population dynamics of infectious diseases, veterinary medicine. </li></ul><ul><li>LS7 DIAGNOSTIC TOOLS, THERAPIES AND PUBLIC HEALTH: aetiology, diagnosis and treatment of disease, public health, epidemiology, pharmacology, clinical medicine, regenerative medicine, medical ethics. </li></ul><ul><li>LS8 EVOLUTIONARY POPULATION AND ENVIRONMENTAL BIOLOGY: evolution, ecology, animal behaviour, population biology, biodiversity, biogeography, marine biology, ecotoxycology, prokaryotic biology. </li></ul><ul><li>LS 9 APPLIED LIFE SCIENCE S AND BIOTECHNOLOGY: agricultural, animal, fishery, forestry and food sciences, biotechnology, chemical biology, genetic engineering, synthetic biology, industrial biosciences, environmental biotechnology and remediation. </li></ul>ERC p anel structure: Life Sciences Mathematics as a key to new technologies
  10. 10. <ul><li>PE1 MATHEMATICAL FOUNDATIONS : all areas of mathematics, pure and applied, plus mathematical foundations of computer science, mathematical physics and statistics. </li></ul><ul><li>PE2 FUNDAMENTAL CONSTITUENTS OF MATTER : particle, nuclear, plasma, atomic, molecular, gas and optical physics. </li></ul><ul><li>PE3 CONDENSED MATTER PHYSICS : structure, electronic properties, fluids, nanosciences. </li></ul><ul><li>PE4 PHYSICAL AND ANALYTICAL CHEMICAL SCIENCES : analytical chemistry, chemical theory, physical chemistry/chemical physics. </li></ul><ul><li>PE5 MATERIAL S AND SYNTHESIS : materials synthesis, structure – properties relations, functional and advanced materials, molecular architecture, organic chemistry. </li></ul><ul><li>PE6 COMPUTE R SCIENCE AND INFORMATICS : i nformatics and information systems, computer science, scientific computing, intelligent systems. </li></ul>ERC p anel structure: Physical Sciences and Engineering Mathematics as a key to new technologies
  11. 11. <ul><li>PE7 SYSTEMS AND COMMUNICATION ENGINEERING : e lectronic, communication, optical and systems engineering. </li></ul><ul><li>PE8 PRODUCTS AND PROCESSES ENGINEERING : product design, process design and control, construction methods, civil engineering, energy systems, material engineering. </li></ul><ul><li>PE9 UNIVERSE SCIENCES : a stro-physics/chemistry/biology; solar system; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation. </li></ul><ul><li>PE10 EARTH SYSTEM SCIENCE : p hysical geography, geology, geophysics, meteorology, oceanography, climatology, ecology, global environmental change, biogeochemical cycles, natural resources management. </li></ul>ERC p anel structure: Physical Sciences and Engineering Mathematics as a key to new technologies
  12. 12. <ul><li>P E 1 MATHEMATICAL FOUNDATIONS : all areas of mathematics, pure and applied, plus mathematical foundations of computer science, mathematical physics and statistics. </li></ul><ul><ul><ul><li>Logic and foundations </li></ul></ul></ul><ul><ul><ul><li>Algebra </li></ul></ul></ul><ul><ul><ul><li>Number theory </li></ul></ul></ul><ul><ul><ul><li>Algebraic and complex geometry </li></ul></ul></ul><ul><ul><ul><li>Geometry </li></ul></ul></ul><ul><ul><ul><li>Topology </li></ul></ul></ul><ul><ul><ul><li>Lie groups, Lie algebras </li></ul></ul></ul><ul><ul><ul><li>Analysis </li></ul></ul></ul><ul><ul><ul><li>Operator algebras and functional analysis </li></ul></ul></ul><ul><ul><ul><li>ODE and dynamical systems </li></ul></ul></ul><ul><ul><ul><li>Partial differential equations </li></ul></ul></ul><ul><ul><ul><li>Mathematical physics </li></ul></ul></ul><ul><ul><ul><li>Probability and statistics </li></ul></ul></ul><ul><ul><ul><li>Combinatorics </li></ul></ul></ul><ul><ul><ul><li>Mathematical aspects of computer science </li></ul></ul></ul><ul><ul><ul><li>Numerical analysis and scientific computing </li></ul></ul></ul><ul><ul><ul><li>Control theory and optimization </li></ul></ul></ul><ul><ul><ul><li>Application of mathematics in sciences </li></ul></ul></ul>Mathematics as a key to new technologies
  13. 13. <ul><li>PE4 PHYSICAL AND ANALYTICAL CHEMICAL SCIENCES: analytical chemistry, chemical theory, physical chemistry/chemical physics </li></ul><ul><ul><ul><li>Physical chemistry </li></ul></ul></ul><ul><ul><ul><li>Nanochemistry </li></ul></ul></ul><ul><ul><ul><li>Spectroscopic and spectrometric techniques </li></ul></ul></ul><ul><ul><ul><li>Molecular architecture and Structure </li></ul></ul></ul><ul><ul><ul><li>Surface science </li></ul></ul></ul><ul><ul><ul><li>Analytical chemistry </li></ul></ul></ul><ul><ul><ul><li>Chemical physics </li></ul></ul></ul><ul><ul><ul><li>Chemical instrumentation </li></ul></ul></ul><ul><ul><ul><li>Electrochemistry, electrodialysis, microfluidics </li></ul></ul></ul><ul><ul><ul><li>Combinatorial chemistry </li></ul></ul></ul><ul><ul><ul><li>Method development in chemistry </li></ul></ul></ul><ul><ul><ul><li>Catalysis </li></ul></ul></ul><ul><ul><ul><li>Physical chemistry of biological systems </li></ul></ul></ul><ul><ul><ul><li>Chemical reactions: mechanisms, dynamics, kinetics and catalytic reactions </li></ul></ul></ul><ul><ul><ul><li>Theoretical and computational chemistry </li></ul></ul></ul><ul><ul><ul><li>Radiation chemistry </li></ul></ul></ul><ul><ul><ul><li>Nuclear chemistry </li></ul></ul></ul><ul><ul><ul><li>Photochemistry </li></ul></ul></ul>Mathematics as a key to new technologies
  14. 14. <ul><li>PE6 COMPUTER SCIENCE AND INFORMATICS: informatics and information systems, computer science, scientific computing, intelligent systems </li></ul><ul><ul><ul><li>Computer architecture </li></ul></ul></ul><ul><ul><ul><li>Database management </li></ul></ul></ul><ul><ul><ul><li>Formal methods </li></ul></ul></ul><ul><ul><ul><li>Graphics and image processing </li></ul></ul></ul><ul><ul><ul><li>Human computer interaction and interface </li></ul></ul></ul><ul><ul><ul><li>Informatics and information systems </li></ul></ul></ul><ul><ul><ul><li>Theoretical computer science including quantum information </li></ul></ul></ul><ul><ul><ul><li>Intelligent systems </li></ul></ul></ul><ul><ul><ul><li>Scientific computing </li></ul></ul></ul><ul><ul><ul><li>Modelling tools </li></ul></ul></ul><ul><ul><ul><li>Multimedia </li></ul></ul></ul><ul><ul><ul><li>Parallel and Distributed Computing </li></ul></ul></ul><ul><ul><ul><li>Speech recognition </li></ul></ul></ul><ul><ul><ul><li>Systems and software </li></ul></ul></ul>Mathematics as a key to new technologies
  15. 15. <ul><li>PE7 SYSTEMS AND COMMUNICATION ENGINEERING: electronic, communication, optical and systems engineering </li></ul><ul><ul><ul><li>Control engineering </li></ul></ul></ul><ul><ul><ul><li>Electrical and electronic engineering: semiconductors, components, systems </li></ul></ul></ul><ul><ul><ul><li>Simulation engineering and modelling </li></ul></ul></ul><ul><ul><ul><li>Systems engineering, sensorics, actorics, automation </li></ul></ul></ul><ul><ul><ul><li>Micro- and nanoelectronics, optoelectronics </li></ul></ul></ul><ul><ul><ul><li>Communication technology, high-frequency technology </li></ul></ul></ul><ul><ul><ul><li>Signal processing </li></ul></ul></ul><ul><ul><ul><li>Networks </li></ul></ul></ul><ul><ul><ul><li>Man-machine-interfaces </li></ul></ul></ul><ul><ul><ul><li>Robotics </li></ul></ul></ul>Mathematics as a key to new technologies
  16. 16. <ul><li>PE8 PRODUCTS AND PROCESS ENGINEERING: product design, process design and control, construction methods, civil engineering, energy systems, material engineering </li></ul><ul><ul><ul><li>Aerospace engineering </li></ul></ul></ul><ul><ul><ul><li>Chemical engineering, technical chemistry </li></ul></ul></ul><ul><ul><ul><li>Civil engineering, maritime/hydraulic engineering, geotechnics, waste treatment </li></ul></ul></ul><ul><ul><ul><li>Computational engineering </li></ul></ul></ul><ul><ul><ul><li>Fluid mechanics, hydraulic-, turbo-, and piston engines </li></ul></ul></ul><ul><ul><ul><li>Energy systems (production, distribution, application) </li></ul></ul></ul><ul><ul><ul><li>Micro(system) engineering, </li></ul></ul></ul><ul><ul><ul><li>Mechanical and manufacturing engineering (shaping, mounting, joining, separation) </li></ul></ul></ul><ul><ul><ul><li>Materials engineering (biomaterials, metals, ceramics, polymers, composites, …) </li></ul></ul></ul><ul><ul><ul><li>Production technology, process engineering </li></ul></ul></ul><ul><ul><ul><li>Product design, ergonomics, man-machine interfaces </li></ul></ul></ul><ul><ul><ul><li>Lightweight construction, textile technology </li></ul></ul></ul><ul><ul><ul><li>Industrial bioengineering </li></ul></ul></ul><ul><ul><ul><li>Industrial biofuel production </li></ul></ul></ul>Mathematics as a key to new technologies
  17. 17. <ul><li>PE9 UNIVERSE SCIENCES: astro-physics/chemistry/biology; solar system; stellar, galactic and extragalactic astronomy, planetary systems, cosmology; space science, instrumentation </li></ul><ul><ul><ul><li>Solar and interplanetary physics </li></ul></ul></ul><ul><ul><ul><li>Planetary systems sciences </li></ul></ul></ul><ul><ul><ul><li>Interstellar medium </li></ul></ul></ul><ul><ul><ul><li>Formation of stars and planets </li></ul></ul></ul><ul><ul><ul><li>Astrobiology </li></ul></ul></ul><ul><ul><ul><li>Stars and stellar systems </li></ul></ul></ul><ul><ul><ul><li>The Galaxy </li></ul></ul></ul><ul><ul><ul><li>Formation and evolution of galaxies </li></ul></ul></ul><ul><ul><ul><li>Clusters of galaxies and large scale structures </li></ul></ul></ul><ul><ul><ul><li>High energy and particles astronomy – X-rays, cosmic rays, gamma rays, neutrinos </li></ul></ul></ul><ul><ul><ul><li>Relativistic astrophysics </li></ul></ul></ul><ul><ul><ul><li>Dark matter, dark energy </li></ul></ul></ul><ul><ul><ul><li>Gravitational astronomy </li></ul></ul></ul><ul><ul><ul><li>Cosmology </li></ul></ul></ul><ul><ul><ul><li>Space Sciences </li></ul></ul></ul><ul><ul><ul><li>Very large data bases: archiving, handling and analysis </li></ul></ul></ul><ul><ul><ul><li>Instrumentation - telescopes, detectors and techniques </li></ul></ul></ul><ul><ul><ul><li>Solar planetology </li></ul></ul></ul>Mathematics as a key to new technologies
  18. 18. <ul><li>Further Information </li></ul><ul><li>Website of the ERC Scientific Council at http:// erc .europa.eu </li></ul>Mathematics as a key to new technologies
  19. 19. Disc rete e lement m ethod – main assumptions <ul><li>Material represented by a collection of particles of different shapes, in the presented formulation spheres (3D) or discs (2D) are used (similar to P. Cundall´s formulation) </li></ul><ul><li>Rigid discrete elements, deformable contact (deformation is localized in discontinuities) </li></ul><ul><li>Adequate contact laws yield desired macroscopic material behaviour </li></ul><ul><li>Contact interaction takes into account friction and cohesion, including the possibility of breakage of cohesive bonds </li></ul>Mathematics as a key to new technologies
  20. 20. M icro - macro relationships <ul><li>Parameters of micromechanical model: k n , k T , R n , R T </li></ul><ul><li>Macroscopic material properties: </li></ul><ul><li>Determination of the relationship between micro- and macroscopic parameters </li></ul><ul><ul><li>Homogenization, averaging procedures </li></ul></ul><ul><ul><li>Simulation of standard laboratory tests (unconfined compression, Brazilian test) </li></ul></ul>Micromechanical constitutive laws Macroscopic stress-strain relationships micro-macro relationships inverse analysis Mathematics as a key to new technologies    
  21. 21. Simulation of the unconfined compression test Distribution of axial stresses Force − strain curve Mathematics as a key to new technologies
  22. 22. Numerical simulation of the Brazilian test Distribution of stresses Syy Force−displacement curve (perpendicular to the direction of loading) Mathematics as a key to new technologies
  23. 23. Numerical simulation of the rock cutting test Failure mode Force vs. time Average cutting force: experiment: 7500 N 2D simulation: 5500 N (force/20mm, 20 mm – spacing between passes of cutting tools) Analysis details: 35 000 discrete elements, 20 hours CPU (Xeon 3.4 GHz) Mathematics as a key to new technologies
  24. 24. Rock cutting in dredging Mathematics as a key to new technologies
  25. 25. <ul><li>Model details: </li></ul><ul><li>92 000 discrete elements </li></ul><ul><li>swing velocity 0.2 m/s, angular velocity 1.62 rad/s </li></ul>Analysis details: 550 000 steps 30 hrs. CPU (Xeon 3.4 GHz) Mathematics as a key to new technologies DEM simulation of dredging
  26. 26. <ul><li>Model details: </li></ul><ul><li>48 000 discrete elements </li></ul><ul><li>340 finite elements </li></ul>Analysis details: 550 000 steps 16 hrs. CPU (Xeon 3.4 GHz) Mathematics as a key to new technologies DEM/FEM simulation of dredging – example of multiscale modelling
  27. 27. DEM/FEM simulation of dredging – example of multiscale modelling Map of equivalent stresses Mathematics as a key to new technologies
  28. 28. Methods of reliability computation Monte Carlo Adapt ive Monte Carlo Importance Sampling FORM SORM Response Surface Method Simulation methods Approximation methods Mathematics as a key to new technologies
  29. 29. Real part (kitchen sink) with breakage Results of simulation Deformed shape with thickness distribution Forming Limit Diagram Failure in metal sheet forming processes Mathematics as a key to new technologies
  30. 30. Forming Limit Diagram (FLD) Major principal strains Blank holding force: 19.6 kN, friction coefficient: 0.162, punch stroke: 20 mm Experiment - breakage at 19 mm punch stroke Minor principal strains D eep drawing of a s quare cup ( Numisheet’93 ) Mathematics as a key to new technologies
  31. 31. Limit state surface – Forming Limit Curve (FLC) Limit state function – minimum distance from FLC = safety margin ( positive in safe domain , negative in failure domain ) M etal sheet forming processes – reliability analysis Mathematics as a key to new technologies
  32. 32. R esults of reliability analysis
  33. 33. Results of reliability analysis Probability of failure in function of the safety margin for two different hardening coefficients
  34. 34. P roces tłoczenia blach - przykład numeryczny, wyniki Odchylenie standardowe współczynnika wzmocnienia  2 = 0.020 <ul><li>Porównanie z metodami symulacyjnymi potwierdza dobrą dokładność wyników otrzymanych metodą powierzchni odpowiedzi </li></ul><ul><li>Metoda powierzchni odpowiedzi wymaga znacznie mniejszej liczby symulacji (jest znacznie efektywniejsza obliczeniowo) </li></ul><ul><li>Dla małych wartości P f metoda adaptacyjna jest efektywniejsza niż klasyczna metoda Monte Carlo </li></ul>Mathematics as a key to new technologies

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