Fundamentals of Mathematics

  • Jiajie GuoEmail author
  • Kok-Meng Lee
Part of the Research on Intelligent Manufacturing book series (REINMA)


This chapter presents the mathematic fundamentals for the modeling formulation and numerical algorithm in subsequent chapters. Starting from the basics of differential geometry, the concept of curvature is introduced and the kinematics of beam and plate elements is formulated, after which the multiple shooting method is presented to solve the boundary value problems formulated in the next chapter.


  1. 1.
    H.W. Guggenheimer, Differential Geometry (Dover Publications, New York, 1977)zbMATHGoogle Scholar
  2. 2.
    P.F. Pai, A.N. Palazotto, Large-deformation analysis of flexible beams. Int. J. Solids Struct. 33(9), 1335–1353 (1996)CrossRefGoogle Scholar
  3. 3.
    H.B. Keller, Numerical Methods for Two-Point Boundary-Value Problems (Waltham, Massachusetts, Blaisdell, 1968)Google Scholar
  4. 4.
    J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1993)CrossRefGoogle Scholar

Copyright information

© Huazhong University of Science and Technology Press, Wuhan and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.The George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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