Reflections on the correlation between mathematical and experimental analysis

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• 作者：Karl-Hans Laermann (1)
  
  1. Bergische Universit盲t Wuppertal FB D ; LuFG Static and Dynamic of Structures ; Pauluskirchstra脽e 7 ; 42285 ; Wuppertal ; Germany
  
• 关键词：Dependency theory/mathematics/experiment ; Uncertainty quantification ; Sources/causes of errors ; Hybrid approach ; Reliability ; Education
• 刊名：Meccanica
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：50
• 期：4
• 页码：887-891
• 全文大小：159 KB
• 参考文献：1. Leipholz H (1983) On the role of analysis in mechanics. Trans CSME 7:3鈥?
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  3. Laermann K.-H (1997) Bedeutung und Perspektiven der experimentellen Beanspruchungs- und Strukturanalyse. Technische Mechanik, Sonderheft, Hrsg.: Magdeburger Verein f眉r Technische Mechanik e.V. ISSN 0232-3869, pp 5鈥?4
  4. Natke, HG Uncertainties in mechanical system modelling: definitions, models, measurers, applications. In: Ben-Haim, Y, Natke, HG eds. (1997) Uncertainty, models and measures (mathematical research). Akademie-Verlag, Berlin, pp. 44-67
  5. Laermann, KH Hybrid techniques in experimental solid mechanics. In: Laermann, KH eds. (2000) Optical methods in experimental solid mechanics. Springer, Wien, pp. 1-72 CrossRef
  6. Wilks, SS Some aspects of quantification in science. In: Woolf, H eds. (1961) Quantification. The Bobbs-Merrill Company, Indianapolis, pp. 5-12
  7. CEA Numerical Simulation, Collection No. 16. French Alternative Energies and Atomic Energy Commission. Cif-sur-Yvette, 2010
  8. Heuveline, V, Schick, M (2013) Wie sicher oder unsicher ist ihre numerische Simulation?. GAMM-Rundbrief 2: pp. 16-20
  9. Burstedde C (2013) Was ist eigentlich wissenschaftliche Rechnen? Die Modellierung der Wirklichkeit,. Forschung & Lehre, 20.Jg.,Hft.3, DHV, Bonn, pp 216/217
  10. Laermann, KH The future role of experimental mechanics in international aspects. In: Li, Ke-Rong, Ming-Wan, Lu eds. (1992) Acta Mechanica Solida Sinica. Pergamon Press, Oxford, pp. 443-451
  11. Laermann KH (1997) Education and training in experimental mechanics: a challenge. In: Nakamura N (ed.-in-chief), Proc. Internat. Conf. on Materials and Mechanics, Tokyo, 1997, pp 249鈥?32
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

A critical look will be taken on the correlation between mathematical and experimental analysis of solid mechanics problems. The achievements in mathematics and computer technologies have led to remarkable progress in mathematical/numerical solutions based on theoretical modelling. Simultaneously the developments in physics have caused advanced methods and methodologies in experimental analysis based on iconic modelling. However it must be noted that each of these processes is full of causes of uncertainty and sources of errors respectively, biasing the accuracy and reliability of the finally expected results. It will be looked at these causes and sources considering mathematical and experimental analysis separately. To overcome the problem of uncertainties and to guarantee a higher degree of reliability a hybrid approach will be recommended, i.e. combining both the analysing processes. In consequence such procedure presupposes more interdisciplinary cooperation between mathematicians and engineers, between theoreticians and practitioners and must be reflected in the curricula of engineering education.