Abstract
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.
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References
H.W. Guggenheimer, Differential Geometry (Dover Publications, New York, 1977)
P.F. Pai, A.N. Palazotto, Large-deformation analysis of flexible beams. Int. J. Solids Struct. 33(9), 1335–1353 (1996)
H.B. Keller, Numerical Methods for Two-Point Boundary-Value Problems (Waltham, Massachusetts, Blaisdell, 1968)
J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1993)
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© 2019 Huazhong University of Science and Technology Press, Wuhan and Springer Nature Singapore Pte Ltd.
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Guo, J., Lee, KM. (2019). Fundamentals of Mathematics. In: Flexonics for Manufacturing and Robotics. Research on Intelligent Manufacturing. Springer, Singapore. https://doi.org/10.1007/978-981-13-2667-7_2
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DOI: https://doi.org/10.1007/978-981-13-2667-7_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2666-0
Online ISBN: 978-981-13-2667-7
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