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

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